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/*
* /MathJax/jax/output/HTML-CSS/autoload/mglyph.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.7.5";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"],d=MathJax.Localization;a.mglyph.Augment({toHTML:function(k,g){var j=k,l=this.getValues("src","width","height","valign","alt"),f;k=this.HTMLcreateSpan(k);if(l.src===""){var i=this.Get("index");if(i){g=this.HTMLgetVariant();var e=g.defaultFont;if(e){e.noStyleChar=true;e.testString=String.fromCharCode(i)+"ABCabc";if(b.Font.testFont(e)){this.HTMLhandleVariant(k,g,String.fromCharCode(i))}else{if(l.alt===""){l.alt=d._(["MathML","BadMglyphFont"],"Bad font: %1",e.family)}f=a.Error(l.alt,{mathsize:"75%"});this.Append(f);f.toHTML(k);this.data.pop();k.bbox=f.HTMLspanElement().bbox}}}}else{if(!this.img){this.img=a.mglyph.GLYPH[l.src]}if(!this.img){this.img=a.mglyph.GLYPH[l.src]={img:new Image(),status:"pending"};var h=this.img.img;h.onload=MathJax.Callback(["HTMLimgLoaded",this]);h.onerror=MathJax.Callback(["HTMLimgError",this]);h.src=l.src;MathJax.Hub.RestartAfter(h.onload)}if(this.img.status!=="OK"){f=a.Error(d._(["MathML","BadMglyph"],"Bad mglyph: %1",l.src),{mathsize:"75%"});this.Append(f);f.toHTML(k);this.data.pop();k.bbox=f.HTMLspanElement().bbox}else{var m=this.HTMLgetMu(k);h=b.addElement(k,"img",{isMathJax:true,src:l.src,alt:l.alt,title:l.alt});if(l.width){h.style.width=b.Em(b.length2em(l.width,m,this.img.img.width/b.em))}if(l.height){h.style.height=b.Em(b.length2em(l.height,m,this.img.img.height/b.em))}k.bbox.w=k.bbox.rw=h.offsetWidth/b.em;k.bbox.h=h.offsetHeight/b.em;if(l.valign){k.bbox.d=-b.length2em(l.valign,m,this.img.img.height/b.em);h.style.verticalAlign=b.Em(-k.bbox.d);k.bbox.h-=k.bbox.d}}}if(!j.bbox){j.bbox={w:k.bbox.w,h:k.bbox.h,d:k.bbox.d,rw:k.bbox.rw,lw:k.bbox.lw}}else{if(k.bbox){j.bbox.w+=k.bbox.w;if(j.bbox.w>j.bbox.rw){j.bbox.rw=j.bbox.w}if(k.bbox.h>j.bbox.h){j.bbox.h=k.bbox.h}if(k.bbox.d>j.bbox.d){j.bbox.d=k.bbox.d}}}this.HTMLhandleSpace(k);this.HTMLhandleColor(k);return k},HTMLimgLoaded:function(f,e){if(typeof(f)==="string"){e=f}this.img.status=(e||"OK")},HTMLimgError:function(){this.img.img.onload("error")}},{GLYPH:{}});MathJax.Hub.Startup.signal.Post("HTML-CSS mglyph Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/mglyph.js")});
| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/HTML-CSS/autoload/ms.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.7.5";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a.ms.Augment({toHTML:function(e){e=this.HTMLhandleSize(this.HTMLcreateSpan(e));var d=this.getValues("lquote","rquote","mathvariant");if(!this.hasValue("lquote")||d.lquote==='"'){d.lquote="\u201C"}if(!this.hasValue("rquote")||d.rquote==='"'){d.rquote="\u201D"}if(d.lquote==="\u201C"&&d.mathvariant==="monospace"){d.lquote='"'}if(d.rquote==="\u201D"&&d.mathvariant==="monospace"){d.rquote='"'}var f=d.lquote+this.data.join("")+d.rquote;this.HTMLhandleVariant(e,this.HTMLgetVariant(),f);this.HTMLhandleSpace(e);this.HTMLhandleColor(e);this.HTMLhandleDir(e);return e}});MathJax.Hub.Startup.signal.Post("HTML-CSS ms Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/ms.js")});
| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/HTML-CSS/autoload/annotation-xml.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var c="2.7.5";var a=MathJax.ElementJax.mml,b=MathJax.OutputJax["HTML-CSS"];a["annotation-xml"].Augment({toHTML:function(f){f=this.HTMLhandleSize(this.HTMLcreateSpan(f));var g=this.Get("encoding");for(var e=0,d=this.data.length;e<d;e++){this.data[e].toHTML(f,g)}this.HTMLhandleSpace(f);this.HTMLhandleColor(f);return f},HTMLgetScale:function(){return this.SUPER(arguments).HTMLgetScale.call(this)/b.scale}});a.xml.Augment({toHTML:function(f,g){for(var e=0,d=this.data.length;e<d;e++){f.appendChild(this.data[e].cloneNode(true))}var j=f.bbox;f.bbox=null;j.rw=j.w=b.getW(f);var h=b.getHD(f);j.h=h.h;j.d=h.d;f.bbox=j}});MathJax.Hub.Startup.signal.Post("HTML-CSS annotation-xml Ready");MathJax.Ajax.loadComplete(b.autoloadDir+"/annotation-xml.js")});
| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/CommonHTML/config.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.5",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js");
| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/CommonHTML/fonts/TeX/Script-Regular.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
(function(b){var a="MathJax_Script";b.FONTDATA.FONTS[a]={className:b.FONTDATA.familyName(a),centerline:211,ascent:735,descent:314,skew:{65:0.389,66:0.194,67:0.278,68:0.111,69:0.139,70:0.222,71:0.25,72:0.333,73:0.333,74:0.417,75:0.361,76:0.306,77:0.444,78:0.389,79:0.167,80:0.222,81:0.278,82:0.194,83:0.333,84:0.222,85:0.25,86:0.222,87:0.25,88:0.278,89:0.194,90:0.306},32:[0,0,250,0,0],65:[717,8,803,35,1016],66:[708,28,908,31,928],67:[728,26,666,26,819],68:[708,31,774,68,855],69:[707,8,562,46,718],70:[735,36,895,39,990],71:[717,37,610,12,738],72:[717,36,969,29,1241],73:[717,17,809,59,946],74:[717,314,1052,92,1133],75:[717,37,914,29,1204],76:[717,17,874,14,1035],77:[721,50,1080,30,1216],78:[726,36,902,29,1208],79:[707,8,738,96,805],80:[716,37,1013,90,1031],81:[717,17,883,54,885],82:[717,17,850,-2,887],83:[708,36,868,29,1016],84:[735,37,747,92,996],85:[717,17,800,55,960],86:[717,17,622,56,850],87:[717,17,805,46,1026],88:[717,17,944,103,1131],89:[716,17,710,57,959],90:[717,16,821,83,1032],160:[0,0,250,0,0]};b.fontLoaded("TeX/"+a.substr(8))})(MathJax.OutputJax.CommonHTML);
| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/CommonHTML/fonts/TeX/SansSerif-Regular.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
(function(b){var a="MathJax_SansSerif";b.FONTDATA.FONTS[a]={className:b.FONTDATA.familyName(a),centerline:250,ascent:750,descent:250,32:[0,0,250,0,0],33:[694,0,319,110,208],34:[694,-471,500,32,325],35:[694,194,833,56,777],36:[750,56,500,44,444],37:[750,56,833,56,776],38:[716,22,758,42,702],39:[694,-471,278,89,188],40:[750,250,389,74,333],41:[750,250,389,55,314],42:[750,-306,500,63,436],43:[583,82,778,56,722],44:[98,125,278,89,188],45:[259,-186,333,11,277],46:[98,0,278,90,188],47:[750,250,500,56,445],48:[678,22,500,39,460],49:[678,0,500,83,430],50:[677,0,500,42,449],51:[678,22,500,42,457],52:[656,0,500,28,471],53:[656,21,500,33,449],54:[677,22,500,42,457],55:[656,11,500,42,457],56:[678,22,500,43,456],57:[677,22,500,42,457],58:[444,0,278,90,188],59:[444,125,278,89,188],61:[370,-130,778,56,722],63:[704,0,472,55,416],64:[704,11,667,56,612],65:[694,0,667,28,638],66:[694,0,667,90,610],67:[705,11,639,59,587],68:[694,0,722,88,666],69:[691,0,597,86,554],70:[691,0,569,86,526],71:[704,11,667,59,599],72:[694,0,708,86,621],73:[694,0,278,87,191],74:[694,22,472,42,388],75:[694,0,694,88,651],76:[694,0,542,87,499],77:[694,0,875,92,782],78:[694,0,708,88,619],79:[715,22,736,55,680],80:[694,0,639,88,583],81:[715,125,736,55,680],82:[694,0,646,88,617],83:[716,22,556,44,500],84:[688,0,681,36,644],85:[694,22,688,87,600],86:[694,0,667,14,652],87:[694,0,944,14,929],88:[694,0,667,14,652],89:[694,0,667,3,663],90:[694,0,611,55,560],91:[750,250,289,94,266],93:[750,250,289,22,194],94:[694,-527,500,78,421],95:[-38,114,500,0,499],97:[460,10,481,38,407],98:[694,11,517,75,482],99:[460,10,444,34,415],100:[694,10,517,33,441],101:[461,10,444,28,415],102:[705,0,306,27,347],103:[455,206,500,28,485],104:[694,0,517,73,443],105:[680,0,239,67,171],106:[680,205,267,-59,192],107:[694,0,489,76,471],108:[694,0,239,74,164],109:[455,0,794,73,720],110:[455,0,517,73,443],111:[460,10,500,28,471],112:[455,194,517,75,483],113:[455,194,517,33,441],114:[455,0,342,74,327],115:[460,10,383,28,360],116:[571,10,361,18,333],117:[444,10,517,73,443],118:[444,0,461,14,446],119:[444,0,683,14,668],120:[444,0,461,0,460],121:[444,204,461,14,446],122:[444,0,435,28,402],126:[327,-193,500,83,416],160:[0,0,250,0,0],305:[444,0,239,74,164],567:[444,205,267,-59,192],768:[694,-527,0,-417,-199],769:[694,-527,0,-302,-84],770:[694,-527,0,-422,-79],771:[677,-543,0,-417,-84],772:[631,-552,0,-431,-70],774:[694,-508,0,-427,-74],775:[680,-576,0,-302,-198],776:[680,-582,0,-397,-104],778:[694,-527,0,-319,-99],779:[694,-527,0,-399,-84],780:[654,-487,0,-422,-79],915:[691,0,542,87,499],916:[694,0,833,42,790],920:[716,21,778,56,722],923:[694,0,611,28,582],926:[688,0,667,42,624],928:[691,0,708,86,621],931:[694,0,722,55,666],933:[716,0,778,55,722],934:[694,0,722,55,666],936:[694,0,778,55,722],937:[716,0,722,44,677],8211:[312,-236,500,0,499],8212:[312,-236,1000,0,999],8216:[694,-471,278,90,189],8217:[694,-471,278,89,188],8220:[694,-471,500,174,467],8221:[694,-471,500,32,325]};b.fontLoaded("TeX/"+a.substr(8))})(MathJax.OutputJax.CommonHTML);
| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/CommonHTML/fonts/TeX/Typewriter-Regular.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
(function(b){var a="MathJax_Typewriter";b.FONTDATA.FONTS[a]={className:b.FONTDATA.familyName(a),centerline:233,ascent:694,descent:229,32:[0,0,250,0,0],33:[622,0,525,206,320],34:[623,-333,525,122,402],35:[611,0,525,36,489],36:[694,82,525,58,466],37:[694,83,525,35,489],38:[622,11,525,28,490],39:[611,-287,525,175,349],40:[694,82,525,166,437],41:[694,82,525,87,358],42:[520,-90,525,68,456],43:[531,-81,525,38,487],44:[140,139,525,173,353],45:[341,-271,525,57,468],46:[140,-1,525,193,332],47:[694,83,525,58,466],48:[621,10,525,42,482],49:[622,-1,525,99,450],50:[622,-1,525,52,472],51:[622,11,525,44,479],52:[624,-1,525,29,495],53:[611,10,525,52,472],54:[622,11,525,45,479],55:[627,10,525,44,480],56:[621,10,525,45,479],57:[622,11,525,46,479],58:[431,-1,525,193,332],59:[431,139,525,175,337],60:[557,-55,525,57,468],61:[417,-195,525,38,487],62:[557,-55,525,57,468],63:[617,0,525,62,462],64:[617,6,525,44,481],65:[623,-1,525,28,496],66:[611,-1,525,17,482],67:[622,11,525,40,484],68:[611,-1,525,16,485],69:[611,-1,525,19,502],70:[611,-1,525,22,490],71:[622,11,525,38,496],72:[611,-1,525,16,508],73:[611,-1,525,72,452],74:[611,11,525,57,479],75:[611,-1,525,18,495],76:[611,0,525,25,488],77:[611,-1,525,12,512],78:[611,0,525,20,504],79:[621,10,525,56,468],80:[611,-1,525,19,480],81:[621,138,525,56,468],82:[611,11,525,16,522],83:[622,11,525,52,472],84:[611,-1,525,26,498],85:[611,11,525,-3,528],86:[611,7,525,19,505],87:[611,7,525,12,512],88:[611,-1,525,28,495],89:[611,-1,525,20,505],90:[611,-1,525,48,481],91:[694,82,525,214,483],92:[694,83,525,58,466],93:[694,82,525,41,310],94:[611,-460,525,96,428],95:[-25,95,525,57,468],96:[681,-357,525,176,350],97:[439,6,525,48,524],98:[611,6,525,4,492],99:[440,6,525,66,466],100:[611,6,525,31,520],101:[440,6,525,48,464],102:[617,-1,525,35,437],103:[442,229,525,28,509],104:[611,-1,525,4,520],105:[612,-1,525,72,462],106:[612,228,525,48,376],107:[611,-1,525,13,507],108:[611,-1,525,51,474],109:[436,-1,525,-12,536],110:[436,-1,525,4,520],111:[440,6,525,52,472],112:[437,221,525,4,492],113:[437,221,525,34,545],114:[437,-1,525,24,487],115:[440,6,525,72,458],116:[554,6,525,25,448],117:[431,5,525,4,520],118:[431,4,525,24,500],119:[431,4,525,16,508],120:[431,-1,525,29,495],121:[431,228,525,26,500],122:[431,-1,525,34,475],123:[694,83,525,50,475],124:[694,82,525,228,297],125:[694,83,525,49,475],126:[611,-466,525,87,437],127:[612,-519,525,104,421],160:[0,0,250,0,0],305:[431,-1,525,72,462],567:[431,228,525,48,376],768:[611,-485,0,-409,-195],769:[611,-485,0,-331,-117],770:[611,-460,0,-429,-97],771:[611,-466,0,-438,-88],772:[577,-500,0,-452,-74],774:[611,-504,0,-446,-79],776:[612,-519,0,-421,-104],778:[619,-499,0,-344,-182],780:[577,-449,0,-427,-99],915:[611,0,525,25,488],916:[623,0,525,35,489],920:[621,10,525,56,468],923:[623,-1,525,30,495],926:[611,-1,525,33,491],928:[611,-1,525,16,508],931:[611,-1,525,40,484],933:[622,-1,525,38,486],934:[611,-1,525,41,483],936:[611,-1,525,37,487],937:[622,-1,525,32,492],2018:[611,-287,525,175,349],2019:[681,-357,525,176,350],8242:[623,-334,525,211,313]};b.fontLoaded("TeX/"+a.substr(8))})(MathJax.OutputJax.CommonHTML);
| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/CommonHTML/fonts/TeX/Fraktur-Bold.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
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/*
* /MathJax/jax/output/CommonHTML/fonts/TeX/Fraktur-Regular.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
(function(b){var a="MathJax_Fraktur";b.FONTDATA.FONTS[a]={className:b.FONTDATA.familyName(a),centerline:258,ascent:740,descent:224,32:[0,0,250,0,0],33:[689,12,296,91,204],34:[695,-432,215,8,196],38:[698,11,738,49,733],39:[695,-436,212,69,134],40:[737,186,389,114,293],41:[735,187,389,89,276],42:[692,-449,278,33,234],43:[598,82,756,47,709],44:[107,191,278,99,213],45:[275,-236,756,46,706],46:[102,15,278,87,200],47:[721,182,502,34,466],48:[492,13,502,42,456],49:[468,2,502,47,460],50:[474,-1,502,60,484],51:[473,182,502,39,429],52:[476,191,502,10,481],53:[458,184,502,47,440],54:[700,13,502,45,471],55:[468,181,502,37,498],56:[705,10,502,40,461],57:[469,182,502,28,466],58:[457,12,216,50,168],59:[458,189,216,47,179],61:[368,-132,756,54,725],63:[693,11,362,46,357],65:[696,26,718,22,708],66:[691,27,884,48,820],67:[685,24,613,59,607],68:[685,27,832,27,745],69:[685,24,663,86,634],70:[686,153,611,11,612],71:[690,26,785,66,710],72:[666,133,720,1,644],73:[686,26,554,30,532],74:[686,139,552,-10,522],75:[680,27,668,17,682],76:[686,26,666,33,644],77:[692,27,1050,27,1048],78:[686,25,832,27,825],79:[729,27,827,12,744],80:[692,218,828,28,804],81:[729,69,827,11,782],82:[686,26,828,27,824],83:[692,27,829,66,756],84:[701,27,669,34,676],85:[697,27,646,-25,665],86:[686,26,831,26,825],87:[686,27,1046,32,1054],88:[688,27,719,28,709],89:[686,218,833,27,740],90:[729,139,602,11,532],91:[740,130,278,117,278],93:[738,131,278,-4,160],94:[734,-452,500,0,495],97:[470,35,500,66,497],98:[685,31,513,87,442],99:[466,29,389,72,359],100:[609,33,499,13,428],101:[467,30,401,70,364],102:[681,221,326,30,323],103:[470,209,504,17,455],104:[688,205,521,77,434],105:[673,20,279,14,267],106:[672,208,281,-9,196],107:[689,25,389,24,362],108:[685,20,280,98,276],109:[475,26,767,8,753],110:[475,22,527,20,514],111:[480,28,489,67,412],112:[541,212,500,12,430],113:[479,219,489,60,419],114:[474,21,389,17,387],115:[478,29,443,-18,406],116:[640,20,333,27,348],117:[474,23,517,9,513],118:[530,28,512,55,434],119:[532,28,774,45,688],120:[472,188,389,10,363],121:[528,218,499,45,431],122:[471,214,391,-7,314],160:[0,0,250,0,0],8216:[708,-410,215,45,158],8217:[692,-395,215,49,163],58112:[683,32,497,75,430],58113:[616,30,498,35,432],58114:[680,215,333,29,339],58115:[679,224,329,28,318],58116:[471,214,503,52,449],58117:[686,20,333,26,315],58118:[577,21,334,29,347],58119:[475,22,501,10,514]};b.fontLoaded("TeX/"+a.substr(8))})(MathJax.OutputJax.CommonHTML);
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/*
* /MathJax/jax/output/CommonHTML/fonts/TeX/SansSerif-Bold.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
(function(b){var a="MathJax_SansSerif-Bold";b.FONTDATA.FONTS[a]={className:b.FONTDATA.familyName(a),centerline:250,ascent:750,descent:250,weight:"bold",32:[0,0,250,0,0],33:[694,0,367,110,256],34:[694,-442,558,37,420],35:[694,193,917,61,855],36:[750,56,550,49,488],37:[750,56,1029,61,966],38:[716,22,831,47,769],39:[694,-442,306,80,226],40:[750,249,428,79,366],41:[750,250,428,61,348],42:[750,-293,550,67,482],43:[617,116,856,61,794],44:[146,106,306,80,226],45:[273,-186,367,12,305],46:[146,0,306,80,226],47:[750,249,550,61,488],48:[715,22,550,43,506],49:[716,-1,550,76,473],50:[716,0,550,46,495],51:[716,22,550,46,503],52:[694,0,550,31,518],53:[694,22,550,37,494],54:[716,22,550,46,503],55:[695,11,550,46,503],56:[715,22,550,46,503],57:[716,22,550,46,503],58:[458,0,306,80,226],59:[458,106,306,80,226],61:[407,-94,856,61,794],63:[705,0,519,61,457],64:[704,11,733,61,671],65:[694,0,733,42,690],66:[694,-1,733,92,671],67:[704,11,703,61,647],68:[694,-1,794,92,732],69:[691,0,642,92,595],70:[691,0,611,92,564],71:[705,11,733,61,659],72:[694,0,794,92,702],73:[694,0,331,85,246],74:[694,22,519,46,427],75:[694,0,764,92,701],76:[694,0,581,92,534],77:[694,0,978,92,886],78:[694,0,794,92,702],79:[716,22,794,62,731],80:[694,0,703,92,641],81:[716,106,794,62,732],82:[694,0,703,92,654],83:[716,22,611,49,549],84:[688,0,733,40,692],85:[694,22,764,92,672],86:[694,-1,733,27,705],87:[694,0,1039,24,1014],88:[694,0,733,37,694],89:[694,0,733,24,708],90:[694,0,672,61,616],91:[750,250,343,79,318],93:[750,250,343,24,263],94:[694,-537,550,108,441],95:[-23,110,550,0,549],97:[475,11,525,31,472],98:[694,10,561,54,523],99:[475,11,489,37,457],100:[694,11,561,37,507],101:[474,10,511,30,480],102:[705,0,336,29,381],103:[469,206,550,17,534],104:[694,0,561,53,508],105:[695,0,256,46,208],106:[695,205,286,-71,232],107:[694,0,531,63,496],108:[694,0,256,54,201],109:[469,0,867,53,815],110:[468,0,561,53,508],111:[474,11,550,32,518],112:[469,194,561,54,523],113:[469,194,561,37,507],114:[469,0,372,54,356],115:[474,10,422,30,396],116:[589,10,404,20,373],117:[458,11,561,52,508],118:[458,0,500,26,473],119:[458,0,744,24,719],120:[458,0,500,24,475],121:[458,205,500,29,473],122:[458,0,476,31,442],126:[344,-198,550,92,457],160:[0,0,250,0,0],305:[458,0,256,54,201],567:[458,205,286,-71,232],768:[694,-537,0,-458,-218],769:[694,-537,0,-334,-93],770:[694,-537,0,-442,-109],771:[694,-548,0,-458,-93],772:[660,-560,0,-474,-77],774:[694,-552,0,-470,-80],775:[695,-596,0,-356,-194],776:[695,-595,0,-459,-91],778:[694,-538,0,-365,-119],779:[694,-537,0,-440,-94],780:[657,-500,0,-442,-109],915:[691,0,581,92,534],916:[694,0,917,60,856],920:[716,22,856,62,793],923:[694,0,672,41,630],926:[688,0,733,46,686],928:[691,0,794,92,702],931:[694,0,794,61,732],933:[715,0,856,62,793],934:[694,0,794,62,732],936:[694,0,856,61,794],937:[716,0,794,49,744],8211:[327,-240,550,0,549],8212:[327,-240,1100,0,1099],8216:[694,-443,306,81,226],8217:[694,-442,306,80,226],8220:[694,-443,558,138,520],8221:[694,-442,558,37,420]};b.fontLoaded("TeX/"+a.substr(8))})(MathJax.OutputJax.CommonHTML);
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/*
* /MathJax/jax/output/CommonHTML/fonts/TeX/SansSerif-Italic.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
(function(b){var a="MathJax_SansSerif-Italic";b.FONTDATA.FONTS[a]={className:b.FONTDATA.familyName(a),centerline:250,ascent:750,descent:250,style:"italic",32:[0,0,250,0,0],33:[694,0,319,110,355],34:[694,-471,500,133,472],35:[694,194,833,87,851],36:[750,56,500,56,565],37:[750,56,833,165,815],38:[716,22,758,71,747],39:[694,-471,278,190,335],40:[750,250,389,104,491],41:[750,250,389,2,390],42:[750,-306,500,156,568],43:[583,83,778,108,775],44:[98,125,278,63,209],45:[259,-186,333,51,332],46:[98,0,278,90,209],47:[750,250,500,6,600],48:[678,22,500,88,549],49:[678,0,500,88,451],50:[678,0,500,50,551],51:[678,22,500,56,544],52:[656,0,500,62,521],53:[656,22,500,50,555],54:[678,22,500,94,548],55:[656,11,500,143,596],56:[678,22,500,77,554],57:[677,22,500,77,545],58:[444,0,278,90,282],59:[444,125,278,63,282],61:[370,-130,778,88,796],63:[704,0,472,173,536],64:[705,10,667,120,707],65:[694,0,667,28,638],66:[694,0,667,90,696],67:[705,10,639,124,719],68:[694,0,722,88,747],69:[691,0,597,86,688],70:[691,0,569,86,673],71:[705,11,667,125,730],72:[694,0,708,86,768],73:[694,0,278,87,338],74:[694,22,472,46,535],75:[694,0,694,88,785],76:[694,0,542,87,516],77:[694,0,875,92,929],78:[694,0,708,88,766],79:[716,22,736,118,763],80:[694,0,639,88,690],81:[716,125,736,118,763],82:[694,0,646,88,698],83:[716,22,556,54,609],84:[688,0,681,165,790],85:[694,22,688,131,747],86:[694,0,667,161,799],87:[694,0,944,161,1076],88:[694,0,667,14,758],89:[694,0,667,151,810],90:[694,0,611,55,702],91:[750,250,289,41,425],93:[750,250,289,-31,353],94:[694,-527,500,190,533],95:[-38,114,500,50,565],97:[461,10,481,61,473],98:[694,11,517,75,539],99:[460,11,444,75,499],100:[694,10,517,73,588],101:[460,11,444,71,472],102:[705,0,306,94,494],103:[455,206,500,12,568],104:[694,0,517,73,513],105:[680,0,239,74,315],106:[680,204,267,-96,336],107:[694,0,489,76,543],108:[694,0,239,74,311],109:[455,0,794,73,790],110:[454,0,517,73,513],111:[461,11,500,69,523],112:[455,194,517,34,538],113:[455,194,517,72,538],114:[455,0,342,74,424],115:[461,11,383,35,436],116:[571,11,361,97,410],117:[444,10,517,90,537],118:[444,0,461,108,540],119:[444,0,683,108,762],120:[444,0,461,1,537],121:[444,205,461,1,540],122:[444,0,435,28,494],126:[327,-193,500,199,560],160:[0,0,250,0,0],305:[444,0,239,74,258],567:[444,204,267,-96,286],768:[694,-527,0,-270,-87],769:[694,-527,0,-190,63],770:[694,-527,0,-310,33],771:[677,-543,0,-301,60],772:[631,-552,0,-314,64],774:[694,-508,0,-284,73],775:[680,-576,0,-180,-54],776:[680,-582,0,-273,40],778:[693,-527,0,-227,-2],779:[694,-527,0,-287,63],780:[654,-487,0,-283,60],915:[691,0,542,87,646],916:[694,0,833,42,790],920:[715,22,778,119,804],923:[694,0,611,28,582],926:[688,0,667,42,765],928:[691,0,708,86,768],931:[694,0,722,55,813],933:[716,0,778,173,843],934:[694,0,722,124,743],936:[694,0,778,171,854],937:[716,0,722,44,769],8211:[312,-236,500,50,565],8212:[312,-236,1000,50,1065],8216:[694,-471,278,190,336],8217:[694,-471,278,190,335],8220:[694,-471,500,274,614],8221:[694,-471,500,133,472]};b.fontLoaded("TeX/"+a.substr(8))})(MathJax.OutputJax.CommonHTML);
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/*
* /MathJax/jax/output/CommonHTML/fonts/TeX/Caligraphic-Bold.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
(function(b){var a="MathJax_Caligraphic-Bold";b.FONTDATA.FONTS[a]={className:b.FONTDATA.familyName(a),centerline:315,ascent:840,descent:211,weight:"bold",skew:{65:0.224,66:0.16,67:0.16,68:0.0958,69:0.128,70:0.128,71:0.128,72:0.128,73:0.0319,74:0.192,75:0.0639,76:0.16,77:0.16,78:0.0958,79:0.128,80:0.0958,81:0.128,82:0.0958,83:0.16,84:0.0319,85:0.0958,86:0.0319,87:0.0958,88:0.16,89:0.0958,90:0.16},32:[0,0,250,0,0],48:[460,17,575,46,528],49:[461,0,575,80,494],50:[460,0,575,51,517],51:[461,211,575,48,525],52:[469,194,575,32,542],53:[461,211,575,57,517],54:[660,17,575,48,526],55:[476,211,575,64,558],56:[661,17,575,48,526],57:[461,210,575,48,526],65:[751,49,921,39,989],66:[705,17,748,40,740],67:[703,20,613,20,599],68:[686,0,892,20,885],69:[703,16,607,37,627],70:[686,30,814,17,930],71:[703,113,682,50,671],72:[686,48,987,20,946],73:[686,0,642,-27,746],74:[686,114,779,53,937],75:[703,17,871,40,834],76:[703,17,788,41,751],77:[703,49,1378,38,1353],78:[840,49,937,-24,1105],79:[703,17,906,63,882],80:[686,67,810,20,846],81:[703,146,939,120,905],82:[686,17,990,20,981],83:[703,16,696,25,721],84:[720,69,644,38,947],85:[686,24,715,-10,771],86:[686,77,737,25,774],87:[686,77,1169,25,1206],88:[686,-1,817,56,906],89:[686,164,759,36,797],90:[686,0,818,46,853],160:[0,0,250,0,0]};b.fontLoaded("TeX/"+a.substr(8))})(MathJax.OutputJax.CommonHTML);
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/*
* /MathJax/jax/output/CommonHTML/autoload/mglyph.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
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"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
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/*
* /MathJax/jax/output/CommonHTML/autoload/ms.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
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"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/CommonHTML/autoload/annotation-xml.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
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| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/PlainSource/jax.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
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"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
/*
* /MathJax/jax/output/PlainSource/config.js
*
* Copyright (c) 2009-2018 The MathJax Consortium
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
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| {
"repo_name": "corollari/ankiTab",
"stars": "168",
"repo_language": "JavaScript",
"file_name": "config.js",
"mime_type": "text/plain"
} |
module Ex1 where
open import Ex1Prelude
{----------------------------------------------------------------------------}
{- Name: -}
{----------------------------------------------------------------------------}
{----------------------------------------------------------------------------}
{- DEADLINE: Week 3 Monday 13 October 23:59 (preferably by BitBucket) -}
{----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
TOP TIP: if you have annoyingly many open goals, comment out big chunks of the
file with a multi-line comment a bit like this one.
-----------------------------------------------------------------------------}
{----------------------------------------------------------------------------}
{- 1.1: Tree Sort -}
{----------------------------------------------------------------------------}
-- 1.1.1 implement concatenation for lists
_++_ : {X : Set} -> List X -> List X -> List X
xs ++ ys = {!!}
infixr 3 _++_
-- a datatype of node-labelled binary trees is given as follows
data Tree (X : Set) : Set where
leaf : Tree X
_<[_]>_ : Tree X -> X -> Tree X -> Tree X
{-
data Tree x = Leaf | Node (Tree X) X (Tree X)
Leaf :: Tree x
Node :: Tree x -> x -> Tree x -> Tree x
-}
demoTree : Tree Nat
demoTree = ({!!} <[ 3 ]> {!!}) <[ 5 ]> {!!}
-- 1.1.2 implement the insertion of a number into a tree, ensuring that
-- the numbers in the tree are in increasing order from left to right;
-- make sure to retain duplicates
insertTree : Nat -> Tree Nat -> Tree Nat
insertTree x t = {!!}
-- 1.1.3 implement the function which takes the elements of a list and
-- builds an ordered tree from them, using insertTree
makeTree : List Nat -> Tree Nat
makeTree xs = {!!}
-- 1.1.4 implement the function which flattens a tree to a list,
-- using concatenation
flatten : {X : Set} -> Tree X -> List X
flatten t = {!!}
-- 1.1.5 using the above components, implement a sorting algorithm which
-- works by building a tree and then flattening it
treeSort : List Nat -> List Nat
treeSort = {!!}
-- 1.1.6 give a collection of unit tests which cover every program line
-- from 1.1.1 to 1.1.5
-- 1.1.7 implement a fast version of flatten, taking an accumulating parameter,
-- never using ++. and ensuring that the law
--
-- fastFlatten t xs == flatten t ++ xs
--
-- is true; for an extra style point, ensure that the accumulating parameter
-- is never given a name in your program
fastFlatten : {X : Set} -> Tree X -> List X -> List X
fastFlatten t = {!!}
-- 1.1.8 use fastFlatten to build a fast version of tree sort
fastTreeSort : List Nat -> List Nat
fastTreeSort xs = {!!}
-- 1.1.9 again, give unit tests which cover every line of code
{----------------------------------------------------------------------------}
{- 1.2: Shooting Propositional Logic Fish In A Barrel -}
{----------------------------------------------------------------------------}
-- 1.2.1 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
orCommute : {A B : Set} -> A /+/ B -> B /+/ A
orCommute x = {!!}
orAbsorbL : {A : Set} -> Zero /+/ A -> A
orAbsorbL x = {!!}
orAbsorbR : {A : Set} -> A /+/ Zero -> A
orAbsorbR x = {!!}
orAssocR : {A B C : Set} -> (A /+/ B) /+/ C -> A /+/ (B /+/ C)
orAssocR x = {!!}
orAssocL : {A B C : Set} -> A /+/ (B /+/ C) -> (A /+/ B) /+/ C
orAssocL x = {!!}
-- 1.2.2 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
andCommute : {A B : Set} -> A /*/ B -> B /*/ A
andCommute x = {!!}
andAbsorbL : {A : Set} -> A -> One /*/ A
andAbsorbL x = {!!}
andAbsorbR : {A : Set} -> A -> A /*/ One
andAbsorbR x = {!!}
andAssocR : {A B C : Set} -> (A /*/ B) /*/ C -> A /*/ (B /*/ C)
andAssocR x = {!!}
andAssocL : {A B C : Set} -> A /*/ (B /*/ C) -> (A /*/ B) /*/ C
andAssocL x = {!!}
-- how many times is [C-c C-c] really needed?
-- 1.2.3 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
distribute : {A B C : Set} -> A /*/ (B /+/ C) -> (A /*/ B) /+/ (A /*/ C)
distribute x = {!!}
factor : {A B C : Set} -> (A /*/ B) /+/ (A /*/ C) -> A /*/ (B /+/ C)
factor x = {!!}
-- 1.2.4 try to implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]; at least one of them will prove to be
-- impossible, in which case you should comment it out and explain
-- why it's impossible
Not : Set -> Set
Not X = X -> Zero
deMorgan1 : {A B : Set} -> (Not A /+/ Not B) -> Not (A /*/ B)
deMorgan1 x y = {!!}
deMorgan2 : {A B : Set} -> Not (A /*/ B) -> (Not A /+/ Not B)
deMorgan2 x = {!!}
deMorgan3 : {A B : Set} -> (Not A /*/ Not B) -> Not (A /+/ B)
deMorgan3 x y = {!!}
deMorgan4 : {A B : Set} -> Not (A /+/ B) -> (Not A /*/ Not B)
deMorgan4 x = {!!}
-- 1.2.5 try to implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]; at least one of them will prove to be
-- impossible, in which case you should comment it out and explain
-- why it's impossible
dnegI : {X : Set} -> X -> Not (Not X)
dnegI = {!!}
dnegE : {X : Set} -> Not (Not X) -> X
dnegE = {!!}
neg321 : {X : Set} -> Not (Not (Not X)) -> Not X
neg321 = {!!}
hamlet : {B : Set} -> B /+/ Not B
hamlet = {!!}
nnHamlet : {B : Set} -> Not (Not (B /+/ Not B))
nnHamlet = {!!}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Hutton where
open import Ex1Prelude
open import Ex2Prelude
{-
data Nat : Set where
zero : Nat
suc : Nat -> Nat
{-# BUILTIN NATURAL Nat #-}
data List (X : Set) : Set where
[] : List X
_:>_ : X -> List X -> List X
infixr 5 _:>_
_+_ : Nat -> Nat -> Nat
zero + y = y
suc x + y = suc (x + y)
-}
data HExp : Set where
val : Nat -> HExp
_+++_ : HExp -> HExp -> HExp
{-
id : {X : Set} -> X -> X
id x = x
-}
eval : HExp -> Nat
eval (val n) = id n
eval (d +++ e) = eval d + eval e
leaves : HExp -> List Nat
leaves (val n) = n :> []
leaves (d +++ e) = {!leaves d ++ leaves e!}
data HCode : List One -> List One -> Set where
PUSH : {i : List One} -> Nat -> HCode i (<> :> i)
ADD : {i : List One} -> HCode (<> :> <> :> i) (<> :> i)
_-SEQ-_ : {i j k : List One} -> HCode i j -> HCode j k -> HCode i k
infixr 3 _-SEQ-_
{-
data Vec (X : Set) : Nat -> Set where
[] : Vec X zero
_,_ : forall {n} -> X -> Vec X n -> Vec X (suc n)
-}
Stk : List One -> Set
Stk xs = All (\ _ -> Nat) xs
exec : {i j : List One} -> HCode i j -> Stk i -> Stk j
exec (PUSH x) s = x , s
exec ADD (x , (y , s)) = (y + x) , s
exec (h -SEQ- k) s = exec k (exec h s)
exec' : (i j : List One) -> HCode i j -> Stk i -> Stk j
exec' i .(<> :> i) (PUSH x) s = x , s
exec' .(<> :> <> :> i) .(<> :> i) (ADD {i}) (y , (x , s)) = (x + y) , s
exec' i j (c -SEQ- c') s = {!exec' _ j c' (exec' i _ c s)!}
{-
compile : HExp -> {i : Nat} -> HCode i (suc i)
compile (val n) = PUSH n
compile (d +++ e) = compile d -SEQ- compile e -SEQ- ADD
-}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex2Prelude where
open import Ex1Prelude
All : {X : Set} -- element type
-> (X -> Set) -- property of elements
-> List X -> Set -- property of whole lists
All P [] = One
All P (x :> xs) = P x /*/ All P xs
{- If X = One, then List X is like a copy of Nat, and All is a bit like Vec -}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex4 where
{- I'm sorry I haven't quite finished setting this exercise yet, but by
the joy of version control, the rest of it can be merged in later
(quite soon). At least you can get cracking: I promise not to break
anything, just to add a bit more on the end.
The deadline for this is midnight on the Monday of Week 12 (15 Dec).
It'd be good to get the marks in before Christmas, but if the end of
term is looking deadlinetastic, please open negotiations.
-}
open import Ex1Prelude
open import IxCon
{-# BUILTIN BOOL Two #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #-}
{-# BUILTIN CONS _:>_ #-}
postulate -- this means that we just suppose the following things exist...
Char : Set
String : Set
{-# BUILTIN CHAR Char #-}
{-# BUILTIN STRING String #-}
primitive -- these are baked in; they even work!
primCharEquality : Char -> Char -> Two
primStringAppend : String -> String -> String
primStringToList : String -> List Char
primStringFromList : List Char -> String
---------------------------------------------------------------------------
-- WRITING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- If you possess the ability to open a file for writing, you might
have the following interface. -}
-- States
data WriteState : Set where
opened closed : WriteState -- do you currently have a file open or not?
-- Commands
data WriteC : WriteState -> Set where
openWrite : (fileName : String) -> WriteC closed
writeChar : Char -> WriteC opened
closeWrite : WriteC opened
-- Responses
WriteR : (j : WriteState)(c : WriteC j) -> Set
WriteR .closed (openWrite fileName) = WriteState -- we get told whether it worked
WriteR .opened (writeChar x) = One -- always works
WriteR .opened closeWrite = One -- always works
{- 4.1 Implement the following operation which determines the next
state. You should ensure that you can write characters only to
a successfully opened file, and that you can write as many as
you want. It should also be possible to insist that a process
closes its file. -}
writeNext : (j : WriteState)(c : WriteC j) -> WriteR j c -> WriteState
writeNext j c r = {!!}
-- the file writing interface, assembled as an indexed container
WRITE : WriteState => WriteState
WRITE = WriteC <! WriteR / writeNext
---------------------------------------------------------------------------
-- READING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- To read from a file, it should be open, and you shouldn't be at the
end of it. -}
-- States
data ReadState : Set where
opened : (eof : Two) -> ReadState -- eof is tt if we're at end of file
closed : ReadState
{- 4.2 Finish the READ implementation, in accordance with the description. -}
-- Commands
data ReadC : ReadState -> Set where
openRead : {- your stuff -} ReadC {!!} -- needs a filename; might not open successfully;
-- might open an empty file
readChar : {- your stuff -} ReadC {!!} -- makes sense only if we're not at end of file
-- and might take us to end of file
closeRead : {- your stuff -} ReadC {!!} -- makes sense only if the file is open
-- Responses
ReadR : (j : ReadState)(c : ReadC j) -> Set
ReadR j c = {!!}
-- next State; you need to make sure the response gives enough info
readNext : (j : ReadState)(c : ReadC j) -> ReadR j c -> ReadState
readNext j c r = {!!}
READ : ReadState => ReadState
READ = ReadC <! ReadR / readNext
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SHARED STATE
---------------------------------------------------------------------------
{- 4.3 Let's suppose we have two command-response interfaces which offer
different functionality for the same system. Correspondingly, we'll
have two indexed containers for the same index set. Show that you
can combine them into one indexed container which lets you choose a
command from either menu and evolves the state as specified by
whichever interface offered the chosen command.
-}
_=+=_ : {I : Set} -> I => I -> I => I -> I => I
CRn0 =+= CRn1 = {!!}
---------------------------------------------------------------------------
-- WHEN IGNORANCE IS BLISS, BIS
---------------------------------------------------------------------------
{- 4.4 If we have a command-response interface with index I representing
states of the system, show that we can index basically the same
commands and responses over a state, I /*/ J, where the J is just
useless information which never changes. (This operation isn't
super-useful on its own, but it's handy in combination with other
things. -}
GrowR : {I J : Set} -> I => I -> (I /*/ J) => (I /*/ J)
GrowR CRn = {!!}
-- do the same for "growing the index on the left"
GrowL : {I J : Set} -> I => I -> (J /*/ I) => (J /*/ I)
GrowL CRn = {!!}
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SEPARATE STATE
---------------------------------------------------------------------------
{- 4.5 Making use of 4.4 and 4.5, show how to combine two interfaces which
operate independently on separate state: commands from one should
not affect the state of the other.
-}
_<+>_ : {I0 I1 : Set} -> I0 => I0 -> I1 => I1 -> (I0 /*/ I1) => (I0 /*/ I1)
CRn0 <+> CRn1 = {!!}
---------------------------------------------------------------------------
-- ERROR REPORTING, AN INTERFACE
---------------------------------------------------------------------------
{- I'm building the next bit for you.
When things go wrong, we need to trigger an error condition and abort
mission. However, if we have other stuff going on (open files, etc),
it may not always be ok to drop everything and run away. There will
be some states in which it is safe to escape (and deliver a suitable
error message, perhaps) and other states in which escape should be
impossible.
If it is safe to issue an error message, we should be able to do so
without fear of any response from the environment that would oblige
us to carry on.
-}
data ErrorC {I : Set}(SafeMessage : I -> Set)(i : I) : Set where
error : SafeMessage i -> ErrorC SafeMessage i
-- the SafeMessage parameter tells us what is an acceptable
-- error message in any given state; in states where this gives
-- Zero, it will be impossible to trigger an error!
ErrorR : {I : Set}{SafeMessage : I -> Set}(i : I)(c : ErrorC SafeMessage i) -> Set
ErrorR _ _ = Zero -- there's no comeback
errorNext : {I : Set}{SafeMessage : I -> Set}
(i : I)(c : ErrorC SafeMessage i) -> ErrorR i c -> I
errorNext i c () -- so we don't have to say how the state will evolve
ERROR : {I : Set}(SafeMessage : I -> Set) -> I => I
ERROR SafeMessage = ErrorC SafeMessage <! ErrorR / errorNext
---------------------------------------------------------------------------
-- COPY A FILE
---------------------------------------------------------------------------
{- 4.6 Implement a process which, given access to suitable interfaces, will
give the process for copying a named source file to a named target
file. This goes in two phases.
-}
{- 4.6.1 Firstly, you should identify the command-reponse interface within
which you need to work. You will need to be able to read and write files,
but also to signal errors (in case a file fails to open for some reason).
You must ensure that it is impossible for any process using your interface
to escape with an error leaving a file open. You must also make it
possible to guarantee that your copying process will, error or not, leave
all files closed.
-}
CPState : Set
CPState = {!!}
CPInterface : CPState => CPState
CPInterface = {!!}
{- 4.6.2 Secondly, you should implement your copying process, working to your
interface. I will let you switch off the termination checker: you cannot
predict in advance how long the copying process will go on, as you have
not seen the source file yet. (Later, we'll learn how to be honest about
things which might go on for ever, but for now, let's cheat.)
-}
{-# NO_TERMINATION_CHECK #-}
cp : (sourceFile targetFile : String) -> Game CPInterface {!!} {!!}
cp sourceFile targetFile = {!!}
{- HINTS
You will certainly need to build some extra bits and pieces.
You have the components for reading, writing and error handling, and
suitable kit with which to combine them. Reading and writing don't
interfere with each other, but it's important to make sure that you
can't bomb out with an error, so some shared state seems important.
There are really two phases to the process:
(1) getting the files open -- this may go wrong
(2) copying from one to the other -- this will work if we reach it
You might want to split these phases apart.
-}
---------------------------------------------------------------------------
-- SCRIPTING INTERACTION
---------------------------------------------------------------------------
{- 4.7.1 Show how to take a command-response interface and deliver its
"scripted" version, where a script command consists of any permitted
(possibly empty) sequence of the given commands. -}
SCRIPT : {I : Set} -> I => I -> I => I
SCRIPT {I} CRn = Game CRn (\ I -> One) <! Rs / ns where
Rs : (i : I) -> Game CRn (\ I -> One) i -> Set
Rs i cs = {!!}
ns : (i : I)(cs : Game CRn (\ I -> One) i) -> Rs i cs -> I
ns i cs rs = {!!}
{- 4.7.2 Show how to take a strategy for scripted interaction and turn
it into a strategey for unscripted interaction, by running the scripts
one command at a time. You may find it useful to build a helper function
to process one script. -}
unScript : {I : Set}(CRn : I => I){X : I -> Set}{i : I} ->
Game (SCRIPT CRn) X i -> Game CRn X i
unScript CRn g = {!!}
-- HINT doing recursion in the "fold" pattern may help
---------------------------------------------------------------------------
-- INDEXED CONTAINER DRIVERS(*)
-- (*) The researchers who invented this stuff are fans of The Fall
-- (by which I mean the group led my Mark E Smith who wrote the song
-- The Container Drivers, not some johnny-come-lately Northern Irish
-- serial killer drama).
---------------------------------------------------------------------------
record Driver {I J : Set}(Sync : I -> J -> Set)
(Hi : I => I)(Lo : J => J) : Set where
-- Hi is a high-level command-response interface
-- Lo is a low-level command-response interface
-- Sync specifies which high and low level states are compatible
-- and what you expect to know at the time
field
-- assuming states are in sync; it should be possible to map
-- high-level commands to low-level commands...
hiClo : (i : I)(j : J) -> Sync i j ->
Command Hi i -> Command Lo j
-- ...and afterwards to translate the low-level response to that
-- command back up to the high-level
loRhi : (i : I)(j : J)(s : Sync i j)(c : Command Hi i) ->
Response Lo j (hiClo i j s c) -> Response Hi i c
-- moreover, the resulting states should be in sync
nSync : (i : I)(j : J)(s : Sync i j)(c : Command Hi i)
(r : Response Lo j (hiClo i j s c)) ->
Sync (next Hi i c (loRhi i j s c r)) (next Lo j (hiClo i j s c) r)
open Driver public
---------------------------------------------------------------------------
-- A DANGEROUS HASKELL IO COMMAND-RESPONSE SYSTEM
---------------------------------------------------------------------------
data Maybe (X : Set) : Set where
yes : X -> Maybe X
no : Maybe X
data IOMode : Set where
readMode writeMode appendMode readWriteMode : IOMode
postulate Handle : Set
data HaskellIOCommand (_ : One) : Set where
hOpen : String -> IOMode -> HaskellIOCommand <>
hClose hIsEOF hGetChar : Handle -> HaskellIOCommand <>
hPutChar : Handle -> Char -> HaskellIOCommand <>
hError : String -> HaskellIOCommand <>
HaskellIOResponse : (i : One) -> HaskellIOCommand i -> Set
HaskellIOResponse i (hOpen f m) = Maybe Handle
HaskellIOResponse i (hClose h) = One
HaskellIOResponse i (hIsEOF h) = Two
HaskellIOResponse i (hGetChar h) = Char
HaskellIOResponse i (hPutChar h c) = One
HaskellIOResponse i (hError e) = Zero
HASKELLIO : One => One
HASKELLIO = HaskellIOCommand <! HaskellIOResponse / _
---------------------------------------------------------------------------
-- SCRIPTING INTERACTION
---------------------------------------------------------------------------
{- 4.8 Your mission is to translate your lovely, safe characterisation
of reading and writing into its dodgy Haskell counterpart. Of course,
your code shouldn't do anything dodgy. You will need to think what
information must be available when you are in each state.
-}
safe2unsafe : Driver (\ i j -> {!!}) CPInterface (SCRIPT HASKELLIO)
safe2unsafe = {!!}
---------------------------------------------------------------
-- TO BE CONTINUED... BUT NOT WITH ANY MORE CODING OBLIGATIONS
---------------------------------------------------------------
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Hello where
-- Oh, you made it! Well done! This line is a comment.
-- In the beginning, Agda knows nothing, but we can teach it about numbers.
data Nat : Set where
zero : Nat
suc : Nat -> Nat
-- Now we can say how to add numbers.
_+_ : Nat -> Nat -> Nat
zero + n = n
suc m + n = suc (m + n)
-- Now we can try adding some numbers.
four : Nat
four = (suc (suc zero)) + (suc (suc zero))
-- To make it go, select "Evaluate term to normal form" from the
-- Agda menu, then type "four", without the quotes, and press return.
-- Hopefully, you should get a response
-- suc (suc (suc (suc zero)))
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
\chapter{Hutton's Razor}
This chapter is inspired by Professor Graham Hutton, author of
\emph{Programming in Haskell}. We investigate various topics
in the semantics (static and dynamic) of programming languages
by considering minimal extensions to a very simple programming
language---the expressions built from addition and natural numbers.
The idea is that adding up numbers is indicative of `ordinary
computation' in general, and we need add only the extra features
required to expose whatever departure from the ordinary we care
about. Why use complicated examples when simple ones will do?
Graham champions simplicity, and thus gives very clear explanations
of important things. His friends call the adding-up-numbers language
\emph{Hutton's Razor} in his honour.
%format Razor = "\M{Razor}"
\begin{code}
module Razor where
open import BasicPrelude
\end{code}
Without further ado, let us have a datatype of `Hutton expressions'.
%format HExp = "\D{HExp}"
%format val = "\C{val}"
%format +++ = "\C{+\!\!\!\!+\!\!\!\!+}"
%format _+++_ = _ +++ _
\begin{code}
data HExp : Set where
val : Nat -> HExp
_+++_ : HExp -> HExp -> HExp
\end{code}
Evaluating expressions is quite easy. Let us do it. The essence of it
is to replace the type |HExp| of syntactic things with a type of
semantic values, in this case, |Nat| itself. To do that, we need to
replace the constructors, which make syntactic things, with semantic
counterparts. In effect, |val| becomes |id| and |+++| becomes |+|.
%format Val = "\F{Val}"
%format eval = "\F{eval}"
%format e1 = "\V{e_1}"
%format e2 = "\V{e_2}"
\begin{code}
Val : Set
Val = Nat
eval : HExp -> Val
eval (val n) = n -- which is equal to |id n|
eval (e1 +++ e2) = eval e1 + eval e2
\end{code}
So
\begin{spec}
eval ((val 1 +++ val 2) +++ val 3) = ((id 1 + id 2) + id 3) = 6
\end{spec}
We could think up other ways to interpret the syntax of Hutton's
Razor. We might, for example, just collect the list of numerical
constants which occur in an expression.
%format constants = "\F{constants}"
\begin{code}
constants : HExp -> List Nat
constants (val n) = n :> []
constants (e1 +++ e2) = constants e1 ++ constants e2
\end{code}
An interpretation of a bunch of operators for a given `value type' |T| is called
an \textbf{algebra} for those operators: |T| is called the \textbf{carrier} of the
algebra. That is |id| and |+| give an algebra for |HExp| with carrier |Val|;
|(\ n -> n :> [])| and |++| give an algebra for |HExp| with carrier |List Nat|.
Of course, |val| and |+++| give an algebra for |HExp| with carrier |HExp|, and we
call it the \textbf{free} algebra because it is not obliged to obey any mathematical
laws. E.g., we expect |+| to be associative, and more to the point, we expect |2 + 2 = 4|,
but |val 2 +++ val 2| is \emph{not} the same \emph{expression} as |val 4|. So you can
think of `free' as meaning `nothing more than syntax'.
For the rest of this chapter, we shall explore variations on the theme of Hutton's
Razor, illustrative of all sorts of computational ideas, in search of common patterns.
\section{Compiling for a Stack Machine}
Our first variation is to consider |compiling| rather than |interpreting| Hutton's Razor.
The compilation target will be a simple machine which manages the evaluation process via
a \emph{stack}. The machine has just two instructions:
\begin{description}
\item[\texttt{PUSH} |n|] puts the number |n| on top of the stack;
\item[\texttt{ADD}] pops |n| and then |m| from the stack, then pushes |m + n|.
\end{description}
Our mission is to write a compiler which turns an expression into a sequence of
these instructions which leaves the expression's value on the top of the stack,
with the original stack below. For example, compiling |(val 2 +++ val 3) +++ val 1|
should give us
\begin{verbatim}
code stack after instruction
...
PUSH 2 2 , ...
PUSH 3 3 , 2 , ...
ADD 5 , ...
PUSH 1 1 , 5 , ...
ADD 6 , ...
\end{verbatim}
Correspondingly, let me give a type for code sequences. (I grew up in the 1970s, so
assembly language operators are in ALL CAPS.)
%format HCode = "\D{HCode}"
%format PUSH = "\C{PUSH}"
%format ADD = "\C{ADD}"
%format -SEQ- = "\C{-SEQ-}"
%format _-SEQ-_ = _ -SEQ- _
\begin{code}
data HCode : Set where
PUSH : Nat -> HCode
ADD : HCode
_-SEQ-_ : HCode -> HCode -> HCode
infixr 3 _-SEQ-_
\end{code}
That is, we have our two instructions, along with a \emph{sequential composition}
operator, allowing us to plug programs together. I could have used \emph{lists} of
instructions, but this gives a slightly simpler and more extensible treatment: watch
this space.
Based on our informal description of what the stack machine code should do, we can
have a go at implementing the compiler.
%format compile = "\F{compile}"
%format c1 = "\V{c_1}"
%format c2 = "\V{c_2}"
\begin{code}
compile : HExp -> HCode
compile (val n) = PUSH n
compile (e1 +++ e2) = compile e1 -SEQ- compile e2 -SEQ- ADD
\end{code}
That is, we have implemented yet another algebra for |HExp|, this time with carrier
|HCode|, with |PUSH| for |val| and |\ c1 c2 -> c1 -SEQ- c2 -SEQ- ADD| for |+++|.
%format exec = "\F{exec}"
However, if we want to see it working, we need to say how to \emph{execute} programs
in |HCode|. We need to write some
\[
|exec : HCode -> List Nat -> List Nat|
\]
interpreting code as a function from the initial stack (represented as a list) to the
final stack. We need to give an algebra for |HCode| with carrier |List Nat -> List Nat|.
But when we try, we hit a snag.
%if False
\begin{code}
postulate HOLE : Nat -> {X : Set} -> X
\end{code}
%endif
%format (HOLE n) = "\greenBG{\ensuremath{\{\;\}" n "}}"
\begin{code}
exec : HCode -> List Nat -> List Nat
exec (PUSH x) s = x :> s
exec ADD [] = (HOLE 0)
exec ADD (n :> []) = (HOLE 1)
exec ADD (n :> (m :> s)) = (m + n) :> s
exec (c1 -SEQ- c2) s = exec c2 (exec c1 s)
\end{code}
We are obliged to say what happens when there are not enough values in the stack for the
correct execution of |ADD|. How will we handle stack \emph{underflow}? We could just give
back any old rubbish, but then we would have to worry that the old rubbish we give back
might actually happen, when we intend that underflow should \emph{never} happen. Moreover,
if we have been competent, at least the |HCode| which comes from |compile| will never
cause underflow.
It is clear that we need to manage the height of the stack somehow, and Agda lets us do it
with \emph{types}. We can express requirements and guarantees about the length of lists by
working with the type of \emph{vectors}, or `lists indexed by their length'.
%format Vec = "\D{Vec}"
\begin{code}
data Vec (X : Set) : Nat -> Set where
[] : Vec X zero
_:>_ : {n : Nat} -> X -> Vec X n -> Vec X (suc n)
\end{code}
The type constructor |Vec| now has the type
\[
|Vec : Set -> Nat -> Set|
\]
so that, for example, |Vec Two 8| is the type of bit-vectors of length \emph{exactly} 8.
You can see that, as with list, we have a type |(X : Set)| of elements declared left of
the |:| in the head of the |data| declaration, so it scopes over the whole of the rest
of the declaration. By writing |Nat -> Set| instead of |Set| to the right of |:|, we are
saying that we want a whole \emph{family} of vector types, one for each length, and that
we want to be free to choose the lengths that show up in the constructor types. Specifically,
we fix it so that |[]| makes only vectors with length |zero| and that |x :> xs| has length
one more than |xs|. The curly braces in |{n : Nat} ->| mean that the |n| which gives the
length of the vector's tail will be kept hidden by default.
By the same facility, we can refine |HCode| with our knowledge of how instructions affect
stack height. This time, we index by two numbers, respectively representing the initial
and final heights of the stack when the code is executed.
%format HCodeI = HCode
\begin{code}
data HCodeI : Nat -> Nat -> Set where
PUSH : {i : Nat} -> Nat -> HCodeI i (suc i) -- one goes on
ADD : {i : Nat} -> HCodeI (suc (suc i)) (suc i) -- two off, one on
_-SEQ-_ : {i j k : Nat} -> HCodeI i j -> HCodeI j k -> HCodeI i k
-- dominoes!
\end{code}
We can use |ADD| only in situations where it is known that there is enough stuff on the
stack. We have made underflow \emph{impossible}!
%format execI = exec
Now, we can give |execI| a type that makes the promise implicit in our claim that the
indices of |HCodeI| represent the initial and final stack heights: we should input a
stack of the initial height and output a stack of the final height. The code keeps the
promise.
\begin{code}
execI : {i j : Nat} -> HCodeI i j -> Vec Nat i -> Vec Nat j
execI (PUSH x) s = x :> s
execI ADD (x :> (y :> s)) = (y + x) :> s
execI (c1 -SEQ- c2) s = execI c2 (execI c1 s)
\end{code}
If you build this program, you will see that the underflow cases do not even appear.
To see what is going on, let me use the `manual override' syntax to show you some of
the hidden numbers.
%format execIx = exec
%format . = ".\!\!"
\begin{code}
execIx : {i j : Nat} -> HCodeI i j -> Vec Nat i -> Vec Nat j
execIx .{i} .{suc i} (PUSH {i} n) s
= n :> s
execIx .{suc (suc i)} .{suc i} (ADD {i}) (n :> (m :> s))
= (m + n) :> s
execIx .{i} .{k} (_-SEQ-_ {i}{j}{k} c1 c2) s
= execIx {j} {k} c2 (execIx {i} {j} c1 s)
\end{code}
The curly braces show the height information which is usually hidden in the calls to
|execIx| and in the |HCode I| constructors. Some of the patterns are marked with a
|.| which you can read as `no choice but'. When splitting gives us the case that the
code was |PUSH {i} n|, the initial stack height must be |i| and the final stack height
must be |suc i|, because nothing else fits the types we have given: fortunately,
|n :> s| is a vector one longer than |s|. Similarly, in the |ADD| case, the initial
height must be at least two, so when we match on the stack, the underflow cases do not
fit the known information and are rejected by Agda as impossible.
When we split a scrutinee, for each constructor case Agda learns that
the indices of the scrutinee's type must equal those of the
constructor's return type, and she tries to solve the equations:
sometimes she learns that the case cannot happen; sometimes she learns
useful information about the indices. Crucially, as soon as we have
types which are related to each other by indexing, inspecting data
(e.g., the |HCodeI| code) no longer happens in isolation. Instead, we
can learn useful information about other data (e.g., the stack).
To finish the job, we need to fix up |compile|. Here, we must be sure
that the code we generate can run starting from any height of stack.
Further, we can promise that the stack will only grow by one: that promise
used to be \emph{waffle}, but now it is in the type and checked! Happily,
our old |compile| function really did keep the promise, so it typechecks
without further ado.
%format compileI = compile
\begin{code}
compileI : HExp -> {i : Nat} -> HCodeI i (suc i)
compileI (val n) = PUSH n
compileI (e1 +++ e2) = compileI e1 -SEQ- compileI e2 -SEQ- ADD
\end{code}
We have used types to eliminate underflow and to keep the promise that
compiled expressions grow the stack by one value. However, we might like to
know that the compiler really works. It is not enough just to push some value:
we need to know that we get the value we expect---the value given by |eval|.
Our |==| type allows us to express that very property, and we may then write
a \emph{program} which computes the evidence for that property.
%format correct = "\F{correct}"
\begin{code}
correct : (e : HExp){i : Nat}(s : Vec Nat i) ->
execI (compileI e) s == eval e :> s
correct (val n) s = refl
correct (e1 +++ e2) s
rewrite correct e1 s
| correct e2 (eval e1 :> s)
= refl
\end{code}
It is a little difficult to do the process justice on paper. When the expression
is |val n|, we discover that our return type is
\[
|execI (compileI (val n)) s == eval (val n) :> s|
\]
but, just by the computation rules we wrote in our programs,
\[
|execI (compileI (val n)) s = execI (PUSH n) s = n :> s|
\]
and
\[
|eval (val n) :> s = n :> s|
\]
so both sides of the equation are already equal, and the |refl| constructor typechecks!
We have a harder time of it with addition. After computation, the goal is
\[
|execI ADD (execI (compileI e2) (execI (compileI e1) s)) == (eval e1 + eval e2) :> s|
\]
and we can get no further. However, we could make a recursive call on a subexpression,
\[
|correct e1 s : execI (compileI e1) s == eval e1 :> s|
\]
If you have learned \emph{proof by induction}, you may have encountered the notion of
`inductive hypothesis'. For us that is exactly `the type of a permitted recursive call'.
The special |rewrite| syntax works specifically with the |==| type, allowing us to rewrite
the goal by any equation we can prove. After the first step, we get
\begin{spec}
correct : (e : HExp){i : Nat}(s : Vec Nat i) ->
execI (compileI e) s == eval e :> s
correct (val n) s = refl
correct (e1 +++ e2) s
rewrite correct e1 s
= (HOLE 0)
\end{spec}
where we have made some definite progress.
\[
|(HOLE 0) : execI ADD (execI (compileI e2) (eval e1 :> s)) == (eval e1 + eval e2) :> s|
\]
Agda allows us a further rewrite by glueing on another proof with the $\mid$ symbol. This time,
we can use the inductive hypothesis for the other subexpression, giving the stack that the
goal presents us,
\[
|correct e2 (eval e1 :> s) : execI (compileI e2) (eval e1 :> s) == eval e2 :> eval e1 :> s|
\]
so that the goal becomes
\[
|execI ADD (eval e2 :> eval e1 :> s) == (eval e1 + eval e2) :> s|
\]
Now,xs the left-hand side computes to the right-hand side, so |refl| brings us home.
You can compute
\[
|execI (compileI (val 2 +++ val 2))|
\]
and be glad of the answer |4|, but be aware that you now work in a world where you can show
that your program is \emph{always} correct, for all possible inputs.
\section{Hutton's Razor with Variables}
%format HExpV = "\F{HExp}"
%format var = "\C{var}"
So far, we have considered \emph{closed} expressions built from
operators and constants. When we implement functions, we often work
with \emph{open} expressions which also contain \emph{variables},
e.g., the formal parameters of the functions. We can extend our little
syntax to allow for this possibility.
\begin{code}
data HExpV (V : Set) : Set where
var : V -> HExpV V
val : Nat -> HExpV V
_+++_ : HExpV V -> HExpV V -> HExpV V
\end{code}
Our type has acquired a parameter |V|, being the set of variables which
may occur in expressions, and an extra constructor, |var| which makes
every variable an expression. I encourage you to think of |V| not as the
set of syntactically valid identifiers, but rather as the set of variables
\emph{in scope}. Correspondingly, we should be able to evaluate expressions
if we give a value for each of the variables which may occur in them. An
assignment of values to variables is called an \textbf{environment}, and
here we may represent such a thing simply as a function of type |V -> Val|.
%format evalV = "\F{eval}"
%format gam = "\V{\gamma}"
\begin{code}
evalV : {V : Set} -> HExpV V -> (V -> Val) -> Val
evalV (var x) gam = gam x
evalV (val n) gam = n
evalV (e1 +++ e2) gam = evalV e1 gam + evalV e2 gam
\end{code}
For example, we might have two variables, represented by the elements of |Two|.
%format myHExp = "\F{myHExp}"
\begin{code}
myHExp : HExpV Two
myHExp = ((val 1 +++ var tt) +++ (var tt +++ var ff))
\end{code}
\[
|(evalV myHExp \ { tt -> 7 ; ff -> 11 }) == 26|
\]
\textbf{Notation.~} In Agda, the scope of a |\| extends as far as possible to the
right, so there is a common tendency not to parenthesize |\|-abstractions when
they are the last argument to a function. Meanwhile, the braces-and-semicolons
notation allows you to do a little bit of local case-splitting inside a
|\|-abstraction, used here to give a different value to each variable.
We can recover plain Hutton's Razor by making variables impossible: all expressions
in |HExpV Zero| are \emph{closed}. Indeed one motivation for bothering with |Zero|
is to give a uniform treatment to open and closed expressions, but recover closed
expressions specifically whenever we need them. If we have no variables, we can
evaluate without an environment as before, or rather, it is easy to come up with an
environment which assigns values to all none of the variables.
%format eval0 = "\F{eval0}"
\begin{code}
eval0 : HExpV Zero -> Nat
eval0 e = evalV e magic
\end{code}
\section{Simultaneous Substitution for Open Expressions}
Environments map variables to values, but that is not all we can do with variables
in expressions. In particular, we may systematically replace variables by expressions,
performing \emph{substitution}.
%format subst = "\F{subst}"
%format sg = "\V{\sigma}"
\begin{code}
subst : {U V : Set} -> HExpV U -> (U -> HExpV V) -> HExpV V
subst (var x) sg = sg x
subst (val n) sg = val n
subst (e1 +++ e2) sg = subst e1 sg +++ subst e2 sg
\end{code}
The function |sg : U -> HExpV V| maps each variable in |U| to some expression whose
variables are drawn from |V|. We can roll out this substitution to all the variables
in a |HExpV U| to get a |HExpV V|: because we act on all the variables, not just one
of them, we call this operation \emph{simultaneous} substitution.
Substitution is a lot like evaluation, but where |evalV| extends our
original evaluation algebra with an environment, |subst| extends the
original free algebra with the substitution. We can prove a useful fact relating
the two.
%format evalSubstFact = "\F{evalSubstFact}"
\begin{code}
evalSubstFact : {U V : Set}(e : HExpV U)(sg : U -> HExpV V)(gam : V -> Val) ->
(evalV (subst e sg) gam) == (evalV e \ u -> evalV (sg u) gam)
evalSubstFact (var x) sg gam = refl
evalSubstFact (val n) sg gam = refl
evalSubstFact (e1 +++ e2) sg gam
rewrite evalSubstFact e1 sg gam | evalSubstFact e2 sg gam
= refl
\end{code}
If you substitute then evaluate, you get the same answer as if you build an
environment from the substitution. The proof is an easy induction on expressions,
rewriting the goal for |e1 +++ e2| by both inductive hypotheses. Why is this
fact useful? It tells us that the typical way we evaluate function calls is
sensible: when we give the \emph{actual} parameters to a function, they are
expressions, and what we do in theory is substitute those \emph{expressions} for the
formal parameters and evaluate, but what we really do is evaluate the actual
parameters to construct an environment which assigns \emph{values} to the formal
parameters.
A special case of this useful fact is that, if we had to, we could make do with
evaluation for \emph{closed} terms only by turning the environment into a
substitution, replacing each variable by a numerical constant.
%format eval0Fact = "\F{eval0Fact}"
\begin{code}
eval0Fact : {V : Set}(e : HExpV V)(gam : V -> Val) ->
eval0 (subst e (val o gam)) == evalV e gam
eval0Fact e gam = evalSubstFact e (val o gam) magic
\end{code}
\subsection{Identity and Composition for Substitution}
Recall the type of |subst|.
\[
|subst : {U V : Set} -> HExpV U -> (U -> HExpV V) -> HExpV V|
\]
Now, taking |U = V|, the constructor |var : V -> HExpV V| could be used as the
substitution, which would give us
\[
|subst (var x) var = var x|
\]
It looks like there is a `do nothing' option! Let's prove it, trying the standard
`proof plan' of induction on expressions, rewriting by the inductive hypotheses.
%format idSubstFact = "\F{idSubstFact}"
\begin{code}
idSubstFact : {V : Set}(e : HExpV V) -> subst e var == e
idSubstFact (var x) = refl
idSubstFact (val n) = refl
idSubstFact (e1 +++ e2)
rewrite idSubstFact e1 | idSubstFact e2
= refl
\end{code}
We call |var| the \textbf{identity substitution} because it maps expressions to
themselves, just like the identity function.
%format sg1 = "\V{\sigma_1}"
%format sg2 = "\V{\sigma_2}"
Meanwhile, suppose we have substitutions
\[
|sg1 : U -> HExpV V| \qquad |sg2 : V -> HExpV W|
\]
We can deploy them, one then the other, on some |e : HExpV U| to get
\[
|subst (subst e sg1) sg2 : HExpV W|
\]
%format -after- = "\F{-after-}"
%format _-after-_ = _ -after- _
but is there a \emph{single} substitution which would do the same job in one pass?
Of course there is. We can \emph{compose} substitutions: it is conventional to make
composition work right-to-left, so I call the operator |-after-| as a reminder.
\begin{code}
_-after-_ : {U V W : Set} -> (V -> HExpV W) -> (U -> HExpV V) -> U -> HExpV W
(sg2 -after- sg1) u = subst (sg1 u) sg2
\end{code}
We had better check that it works as claimed. Again, the standard proof pattern works.
%format compSubstFact = "\F{compSubstFact}"
\begin{code}
compSubstFact : {U V W : Set}(sg2 : V -> HExpV W)(sg1 : U -> HExpV V)(e : HExpV U) ->
subst e (sg2 -after- sg1) == subst (subst e sg1) sg2
compSubstFact sg2 sg1 (var x) = refl
compSubstFact sg2 sg1 (val x) = refl
compSubstFact sg2 sg1 (e1 +++ e2)
rewrite compSubstFact sg2 sg1 e1 | compSubstFact sg2 sg1 e2
= refl
\end{code}
%format tsbus = "\F{tsbus}"
So, |var| and |-after-| are related to |subst| in much the way that |id| and |o| relate
to ordinary function application. We can tease that out a little more clearly if we consider
the `agree on all inputs' relation for functions.\nudge{Many of us would
prefer if this relation were just given by |==|, but that is sadly not so in today's
Agda.}
%format =^= = "\F{\doteq}"
%format _=^=_ = _ =^= _
\begin{code}
_=^=_ : {S T : Set}(f g : S -> T) -> Set
f =^= g = (s : _) -> f s == g s
infixl 2 _=^=_
\end{code}
\textbf{Notation.~} When we write an |_| in a pattern, we are saying that
some input information is unimportant, but Agda also lets us write |_| in
an \emph{expression}, in places where the thing we give is unimportant
enough that we are willing not to read it. But the flipside is that the
information has to be obviously inferrable. We're saying ``that bit's
boring; you figure it out''. In the above example, the missing information is the type of |s|, but |s| is used as an argument to |f| and to |g|, so its
type can only be |S|. By writing |_|, I saved myself the bother of bringing
|S| into scope.
Ordinary function composition, |o|, absorbs |id| and is associative.
%format funAbsorbLeft = "\F{funAbsorbLeft}"
%format funAbsorbRight = "\F{funAbsorbRight}"
%format funAssociative = "\F{funAssociative}"
\begin{code}
funAbsorbLeft : {S T : Set}(g : S -> T) ->
id o g =^= g
funAbsorbLeft g s = refl
funAbsorbRight : {S T : Set}(f : S -> T) ->
f o id =^= f
funAbsorbRight f s = refl
funAssociative : {R S T U : Set }(f : T -> U)(g : S -> T)(h : R -> S) ->
(f o g) o h =^= f o (g o h)
funAssociative f g h r = refl
\end{code}
With a little more work, the corresponding thing is true for substitutions.
%format Subst = "\F{Subst}"
%format substAbsorbLeft = "\F{substAbsorbLeft}"
%format substAbsorbRight = "\F{substAbsorbRight}"
%format substAssociative = "\F{substAssociative}"
\begin{code}
Subst : Set -> Set -> Set
Subst S T = S -> HExpV T
substAbsorbLeft : {S T : Set}(g : Subst S T) ->
var -after- g =^= g
substAbsorbLeft g s = idSubstFact (g s)
substAbsorbRight : {S T : Set}(f : Subst S T) ->
f -after- var =^= f
substAbsorbRight f s = refl
substAssociative : {R S T U : Set }(f : Subst T U)(g : Subst S T)(h : Subst R S) ->
(f -after- g) -after- h =^= f -after- (g -after- h)
substAssociative f g h r = compSubstFact f g (h r)
\end{code}
Moreover, if we flip |subst| around,\nudge{Programmers use |subst|;
mathematicians use |tsbus|. I'm both.} we can see it as a map from substitutions to ordinary functions.
\begin{code}
tsbus : {U V : Set} -> Subst U V -> (HExpV U -> HExpV V)
tsbus sg e = subst e sg
\end{code}
What our earlier proofs really tell us is that |tsbus| fits the identity and composition structure
of substitutions into that of functions.
\[\begin{array}{lcl}
|idSubstFact| & |:| & |{S : Set} ->| \\
& & |tsbus {S}{S} var =^= id| \smallskip \\
|compSubstFact| & |:| & |{R S T : Set}(f : Subst S T)(g : Subst R S) ->| \\
& & |tsbus (f -after- g) =^= tsbus f o tsbus g|
\end{array}\]
\section{A Categorical Interlude}
\textbf{Need to expand on this.}
A \textbf{category} is a collection of \textbf{objects} (which could
be all sorts of things); between any two objects, there is a
collection of \textbf{arrows}\nudge{or `morphisms' is you want to
sound posh}. There is an \textbf{identity} arrow from each object to
itself, and if one arrow finishes where another starts, you can form
their \textbf{composition}. Composition is associative and absorbs
identity on either side.
We have seen that |Set| forms a category, with arrows |S -> T|. We have
also seen that |Set| forms a category, with arrows |Subst U V|.
Here's another category. This time, the objects are values in |Nat|. The
arrows are given like so:
%format >= = "\F{\ge}"
%format _>=_ = _ >= _
%format geRefl = >= "\F{Refl}"
%format geTrans = >= "\F{Trans}"
%format geUnique = >= "\F{Unique}"
\begin{code}
_>=_ : Nat -> Nat -> Set
m >= zero = One
zero >= suc n = Zero
suc m >= suc n = m >= n
\end{code}
To say that |Nat| with |>=| forms a category is just to say that it is
a \emph{preorder}: reflexive and transitive.
\begin{code}
geRefl : (n : Nat) -> n >= n -- `identity'
geRefl zero = <>
geRefl (suc x) = geRefl x
geTrans : (l m n : Nat) -> m >= n -> l >= m -> l >= n -- `composition'
geTrans l m zero mn lm = <>
geTrans l zero (suc n) () lm
geTrans zero (suc m) (suc n) mn ()
geTrans (suc l) (suc m) (suc n) mn lm = geTrans l m n mn lm
\end{code}
Of course, we must check that composition is associative and absorbs
identity. In this instance, that's an immediate consequence of the
fact that there can be at most one proof of any |m >= n|.
\begin{code}
geUnique : (m n : Nat)(p q : m >= n) -> p == q
geUnique m zero p q = refl
geUnique zero (suc n) () q
geUnique (suc m) (suc n) p q = geUnique m n p q
\end{code}
A \textbf{functor} $F$ mapping between categories $\mathbb{C}$ and $\mathbb{D}$, say,
\begin{itemize}
\item translates $\mathbb{C}$ objects to $\mathbb{D}$ objects by some operation $F_0$
\item translates $\mathbb{C}$'s $S$-to-$T$ arrows into $\mathbb{D}$ arrows from $F_0\:S$ to $F_0\:T$
by some operation $F_1$, such that
\item $F_1$ maps the $\mathbb{C}$-identity on $S$ to the $\mathbb{D}$-identity on $F_0\:S$
\item $F_1$ maps every $\mathbb{C}$-composition |f o g| to the
$\mathbb{D}$-composition $(F_1\:|f|)$|o|$(F_1\:|g|)$
\end{itemize}
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\documentclass{book}
\usepackage{a4}
\usepackage{palatino}
\usepackage{natbib}
\usepackage{amsfonts}
\usepackage{stmaryrd}
\usepackage{upgreek}
\usepackage{url}
\DeclareMathAlphabet{\mathkw}{OT1}{cmss}{bx}{n}
\usepackage{color}
\newcommand{\redFG}[1]{\textcolor[rgb]{0.6,0,0}{#1}}
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\newcommand{\ColourStuff}{
\newcommand{\red}{\redFG}
\newcommand{\green}{\greenFG}
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\newcommand{\orange}{\orangeFG}
\newcommand{\purple}{\purpleFG}
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\newcommand{\brown}{\brownFG}
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\newcommand{\white}{\whiteFG}
}
\newcommand{\MonochromeStuff}{
\newcommand{\red}{\blackFG}
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\newcommand{\orange}{\blackFG}
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\newcommand{\black}{\blackFG}
\newcommand{\white}{\blackFG}
}
\ColourStuff
\newcommand{\M}[1]{\mathsf{#1}}
\newcommand{\D}[1]{\blue{\mathsf{#1}}}
\newcommand{\C}[1]{\red{\mathsf{#1}}}
\newcommand{\F}[1]{\green{\mathsf{#1}}}
\newcommand{\V}[1]{\purple{\mathit{#1}}}
\newcommand{\T}[1]{\raisebox{0.02in}{\tiny\green{\textsc{#1}}}}
\newcommand{\us}[1]{\_\!#1\!\_}
%include lhs2TeX.fmt
%include lhs2TeX.sty
%include polycode.fmt
%subst keyword a = "\mathkw{" a "}"
%subst conid a = "\V{" a "}"
%subst varid a = "\V{" a "}"
%format -> = "\blue{\rightarrow}"
\newcommand{\nudge}[1]{\marginpar{\footnotesize #1}}
\newtheorem{exe}{Exercise}[chapter]
%format rewrite = "\mathkw{rewrite}"
%format constructor = "\mathkw{constructor}"
%format ? = "\orange{?}"
\parskip 0.1in
\parindent 0in
\begin{document}
\title{CS410\\
Advanced Functional Programming}
\author{Conor McBride \\
Mathematically Structured Programming Group \\
Department of Computer and Information Sciences \\
University of Strathclyde}
\maketitle
%include Introduction.lagda
%include BasicPrelude.lagda
%include Logic.lagda
%include Razor.lagda
\appendix
%include EmacsCheatSheet.lagda
\bibliographystyle{plainnat}
\bibliography{CS410.bib}
\end{document}
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"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
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module Ex1Prelude where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
{-# BUILTIN NATURAL Nat #-}
_+_ : Nat -> Nat -> Nat
zero + n = n
suc m + n = suc (m + n)
infixr 5 _+_
data Zero : Set where
magic : {X : Set} ->
Zero -> X
magic ()
record One : Set where
constructor <>
data Two : Set where
tt ff : Two
if_then_else_ : {X : Set} -> Two -> X -> X -> X
if tt then t else f = t
if ff then t else f = f
_/\_ : Two -> Two -> Two
b1 /\ b2 = if b1 then b2 else ff
_<=_ : Nat -> Nat -> Two
zero <= y = tt
suc x <= zero = ff
suc x <= suc y = x <= y
data List (X : Set) : Set where
[] : List X
_:>_ : X -> List X -> List X
infixr 5 _:>_
data _==_ {l}{X : Set l}(x : X) : X -> Set l where
refl : x == x
infix 4 _==_
{-# BUILTIN EQUALITY _==_ #-}
{-# BUILTIN REFL refl #-}
infixr 1 _/+/_
data _/+/_ (S T : Set) : Set where
inl : S -> S /+/ T
inr : T -> S /+/ T
_<?>_ : {S T X : Set} ->
(S -> X) -> (T -> X) ->
S /+/ T -> X
(f <?> g) (inl s) = f s
(f <?> g) (inr t) = g t
infixr 2 _/*/_
record _/*/_ (S T : Set) : Set where -- (S , T)
constructor _,_
field
outl : S
outr : T
open _/*/_ public
infixr 4 _,_
curry : {S T X : Set} ->
(S /*/ T -> X) ->
S -> T -> X
curry f s t = f (s , t)
uncurry : {S T X : Set} ->
(S -> T -> X) ->
S /*/ T -> X
uncurry f (s , t) = f s t
id : {X : Set} -> X -> X
id x = x
_o_ : {A B C : Set} -> (B -> C) -> (A -> B) -> (A -> C)
(f o g) a = f (g a)
infixr 2 _o_
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"stars": "64",
"repo_language": "Agda",
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module Ex2Tut where
{-----------------------------------------------------------------------------
Name:
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
CS410 Exercise 2, due 5pm on Monday of Week 6 (3 November 2014)
NOTE: I am well aware that week 6 is quite busy with deadlines,
what with CS408-related obligations and so on. I'd much prefer
you did things to the best of your ability rather than on time,
so I would be sympathetic to requests for some flexibility.
Still, your best bet is to make an early start rather than a
late finish.
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
This exercise is based around extending Hutton's razor with Boolean
values and conditional expressions. By introducing a second value
type, we acquire the risk of type mismatch. The idea here is to
explore different approaches to managing that risk.
-----------------------------------------------------------------------------}
open import Ex1Prelude
open import Ex2Prelude
{- The extended Hutton's Razor syntax -}
data HExpIf : Set where
num : Nat -> HExpIf
boo : Two -> HExpIf
_+++_ : HExpIf -> HExpIf -> HExpIf
hif_then_else_ : HExpIf -> HExpIf -> HExpIf -> HExpIf
{- Note that an expression
hif eb then ex1 else ex2
makes sense only when
* eb produces a Boolean value
* ex1 and ex2 produce the same sort of value (numeric or Boolean)
-}
HValIf : Set
HValIf = Two /+/ Nat
{- We now have the risk of run time type errors. Let's introduce a type
for things which can go wrong. -}
data Error (E X : Set) : Set where
ok : X -> Error E X
error : E -> Error E X
{- 2.1 Add a constructor to the following datatype for each different
kind of run time error that can happen. (Come back to this exercise
when you're writing the evaluator in 2.3.) Make these error reports
as informative as you can.
-}
data EvalError : Set where
-- your constructors here
{- 2.2 Write a little piece of "glue code" to make it easier to manage
errors. The idea is to combine error-prone process in *sequence*, where
the second process can depend on the value produced by the first if it
succeeds. The resulting process is, of course, also error-prone, failing
as soon as either component fails.
-}
_>>=_ : {E S T : Set}
-> Error E S -- process which tries to get an S
-> (S -> Error E T) -- given an S, process which tries for a T
-> Error E T -- combined in sequence
es >>= s2et = {!!}
{- 2.3 Implement an evaluator for HExpIf. Be sure to add only numbers and
to branch only on Booleans. Report type mismatches as errors. You should
use _>>=_ to help with the propagation of error messages.
-}
eval : HExpIf -> Error EvalError HValIf
eval e = {!!}
{- Note that the type of eval is not specific about whether the value
expected is numeric or Boolean. It may help to introduce auxiliary
definitions of error-prone processes which are "ok" only for the
type that you really want.
-}
{- Next up, stack machine code, and its execution. -}
data HBCode : Set where
PUSHN : Nat -> HBCode
PUSHB : Two -> HBCode
ADD : HBCode
_SEQ_ : HBCode -> HBCode -> HBCode
_IFPOP_ : HBCode -> HBCode -> HBCode
{- The intended behaviour of (t IFPOP f) is as follows
* pop the (we hope) Boolean value from top of stack
* if it's tt, execute t, else execute f
* whichever branch is executed, it gets the popped stack to start
-}
{- 2.4 Populate the type of possible execution errors and implement the
execution behaviour of HBCode, operating on a stack represented as
a list of HValIf values.
-}
data ExecError : Set where
-- your constructors here
exec : HBCode -> List HValIf -> Error ExecError (List HValIf)
exec c s = {!!}
{- Next, we take a look at code generation and type safety. -}
data HTy : Set where -- we have two types in HExpIf
NUM BOOL : HTy
_=HTy=_ : HTy -> HTy -> Two -- we can test if two types are equal
NUM =HTy= NUM = tt
NUM =HTy= BOOL = ff
BOOL =HTy= NUM = ff
BOOL =HTy= BOOL = tt
{- 2.5 Write a type-synthesizing compiler, computing both the HTy type and
the HBCode executable for a given expression. Your compiler should
give an informative error report if the expression it receives is
ill typed. Your compiler should also ensure (at least informally) that
the code produced will never trigger any execution errors.
-}
data CompileError : Set where
-- your constructors here
compile : HExpIf -> Error CompileError (HTy /*/ HBCode)
compile (num x) = {!!}
compile (boo x) = {!!}
compile (e1 +++ e2) = compile e1 >>= \
{ (BOOL , c1) -> error {!!}
; (NUM , c1) -> {!!}
}
compile (hif e then e₁ else e₂) = {!!}
{- You have a little bit more room for creative problem-solving in what's
left of the exercise. The plan is to build the type system into expressions
and code, the same way we did with plain Hutton's Razor in class.
-}
{- If we *know* which HTy type we want, we can compute which Agda type we
expect our value to take. -}
HVal : HTy -> Set
HVal NUM = Nat
HVal BOOL = Two
{- 2.6 Finish the type of typed expressions. You should ensure that only
well HTy-typed expressions can be constructed. -}
data THExpIf : HTy -> Set where
val : {t : HTy} -> HVal t -> THExpIf t
-- you fill in addition and if-then-else
{- 2.7 Implement a type-safe evaluator. -}
teval : {t : HTy} -> THExpIf t -> HVal t
teval (val x) = x
myNUMExp : THExpIf NUM
myNUMExp = val 42
myBOOLExp : THExpIf BOOL
myBOOLExp = val ff
{- 2.8 Implement a type checker. -}
data TypeError : Set where
-- your constructors here
tcheck : (t : HTy) -> HExpIf -> Error TypeError (THExpIf t)
tcheck t e = {!!}
{- 2.9 Adapt the technique from Hutton.agda to give a type-safe underflow-free
version of HBCode. You will need to think what is a good type to represent
the "shape" of a stack: before, we just used Nat to represent the *height* of
the stack, but now we must worry about types. See next question for a hint. -}
data THBCode : {- your indices here -} Set where
-- your constructor here
{- 2.10 Implement the execution semantics for your code. You will need to think
about how to represent a stack. The Ex2Prelude.agda file contains a very
handy piece of kit for this purpose. You write the type, too. -}
-- your code here
{- 2.11 Write the compiler from well typed expressions to safe code. -}
tcompile : {t : HTy} -> THExpIf t -> {!!}
tcompile e = {!!}
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"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
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module ListSuccess where
open import Ex1Prelude
_++_ : {X : Set} -> List X -> List X -> List X
[] ++ ys = ys
x :> xs ++ ys = x :> (xs ++ ys)
infixr 3 _++_
win : {X : Set} -> X -> List X
win x = x :> []
_>>=_ : {X Y : Set} -> List X -> (X -> List Y) -> List Y
[] >>= x2ys = []
(x :> xs) >>= x2ys = (x2ys x) ++ xs >>= x2ys
try2 : {R S T : Set} -> (R -> S -> T) -> List R -> List S -> List T
try2 f rs ss = rs >>= (\ r -> ss >>= \ s -> win (f r s))
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\chapter{A Basic Prelude}
Let us build some basic types and equipment for general use. We might need to
rethink some of this stuff later, but it's better to keep things simple until
life forces complexity upon us. In the course of establishing this setup, we'll
surely encounter language features in need of explanation.
Concretely, we shall implement
%format BasicPrelude = "\M{BasicPrelude}"
\begin{code}
module BasicPrelude where
\end{code}
the source code for this chapter of the notes is indeed that very module.
We'll be able to import this module into others that we define later.
The first exercise will put it to good use.
\section{Natural Numbers}
We have already had a quick preview of the datatype of natural numbers.
Let us have it in our prelude.
%format Set = "\D{Set}"
%format Nat = "\D{Nat}"
%format zero = "\C{zero}"
%format suc = "\C{suc}"
\begin{code}
data Nat : Set where
zero : Nat
suc : Nat -> Nat
{-# BUILTIN NATURAL Nat #-}
\end{code}
The funny comment-like BUILTIN things are not comments, but
\emph{pragmas}---not quite official parts of the language. Agda's
implementers expected that we might need to define numbers, so these
pragmas just tell Agda what we've chosen to call the bits and
pieces. The payoff is that we are now allowed write numbers in
\emph{decimal}, leaving Agda to do all that |suc|cing.
If we define addition,
%format + = "\F{+}"
%format _+_ = "\us{" + "}"
\begin{code}
_+_ : Nat -> Nat -> Nat
zero + n = n
suc m + n = suc (m + n)
infixr 5 _+_
\end{code}
then we can try evaluating expressions (using [C-c C-n]) such as
\begin{spec}
1 + 2 + 3 + 4
\end{spec}
Note that the |infixr 5| declaration assigns a precedence level of 5 to |+|
(with higher binding more tightly) and ensures that multiple additions group
to the right. The above means
\begin{spec}
1 + (2 + (3 + 4))
\end{spec}
\section{Impossible, Trivial, and Different}
In this section, we build three finite types, capturing important basic
concepts.
%format Zero = "\D{Zero}"
%format magic = "\F{magic}"
\subsection{|Zero|}
The |Zero| type has nothing after its |where| but silence. There is no way
to make a \emph{value} of type |Zero|. In Haskell, you could just write an
infinite recursion or take the head of an empty list, but Agda won't
countenance such dodges.
\begin{code}
data Zero : Set where
\end{code}
The |Zero| type represents the idea of \emph{impossibility}, which is a very useful
idea, because if it's impossible to get into a situation, you don't need to worry
about how to get out of it. The following definition bottles that intuition.
\begin{code}
magic : {X : Set} ->
Zero -> X
magic ()
\end{code}
There's plenty to explain here. The |{X : Set} ->| means
`for all |Set|s, |X|'. So, the whole type says `for all |Set|s |X|, there is a
function from |Zero| to |X|'. To define a function, we must explain which
value of the output type to return for each value of the input type. But that
ought to be very easy, because there are no values of the input type! It's
a bit like saying `if you believe \emph{that}, you'll believe anything'.
The braces have a secondary meaning: they tell Agda that we don't want
to write |X| explicitly when we use |magic|. Rather, we want Agda to
infer which |X| is relevant from the context in which |magic| is being
used, just the same way that Haskell silently infers the types at
which polymorphic functions are used. So, the first visible argument
of |magic| has type |Zero|. If we're refining a
goal by |magic ?|, then it's clear that |X| should be the goal type, and
then we are left finding something of type |Zero| to fill in for the |?|.
But how do way say what |magic| does? We don't. Instead, we say that
it doesn't. The definition of |magic| is not given by an equation,
but rather by \emph{refutation}. In Agda, if we can point out that an
input to a function is impossible, we do not have to write an |=| sign
and an output. The way we point it out is to write the
\emph{absurd pattern} |()| in the place of the impossible thing. We're
effectively saying `BUSTED!'.
Note, by the way, that Agda's notation thus makes |()| mean the
opposite of what it means in Haskell, where it's the empty tuple,
easily constructed but not very informative. That's also a useful
thing to have around.
%format One = "\D{One}"
%format <> = "\C{\left<\right>}"
\subsection{|One|}
\textbf{tl;dr} There is a type called |One|. It has one element, written |<>|.
I could define a |data|type with one constructor. Instead, let me show
you another feature of Agda---|record|s. Where a |data|type is given
by a \emph{choice} of constructors, a |record| type is given by a
\emph{collection} of fields. To build a record value, one must supply
a value for each field. I define |One| to be the record type with
\emph{no fields}, so it is very easy to give a value for each field: there's
only one way to do it.
\begin{code}
record One : Set where
\end{code}
Values of |record| types are officially written
|record {field1 = value1;...;fieldn = valuen}|, so the only value in |One| is
\begin{spec}
record {}
\end{spec}
which is a bit of a mouthful for something so trivial. Fortunately, Agda lets
us give a neater notation. We may optionally equip a record type with a
\emph{constructor}---the function which makes a record, taking the values of the
fields as arguments. As part of the record declaration, I write
\begin{code}
constructor <>
\end{code}
which means, because there are no arguments, that
\begin{spec}
<> : One
\end{spec}
We are allowed to use either the official |record| notation or the constructor
shorthand when we write patterns. Note that pattern matching an element of |One|
does not tell us anything we didn't already know. Think:
\begin{tabular}{cccc}
|Zero| & impossible to make & useful to possess & not representable with bits \\
|One| & trivial to make & useless to possess & representable with no bits \\
\end{tabular}
On reflection, it is perhaps perverse to introduce record types with such a
degenerate example. We'll have some proper records with fields in, shortly.
But first, let us complete our trinity of finite types by getting our hands
on a bit, at last.
%format Two = "\D{Two}"
%format tt = "\C{t\!t}"
%format ff = "\C{f\!f}"
\section{|Two|}
The type |Two| represents a choice between exactly two things. As it is a
choice, let's define it as a |data|type. As the two constructors have the
same type, I can save space and declare them on the same line.
\begin{code}
data Two : Set where
tt ff : Two
\end{code}
In Haskell, this type is called Bool and has values True and False. I call
the type |Two| to remind you how big it is, and I use ancient abbreviations
for the constructors.
Agda's cunning mixfix syntax lets you rebuild familiar notations.
%format if = "\F{if}"
%format then = "\F{then}"
%format else = "\F{else}"
%format if_then_else_ = if _ then _ else _
\begin{code}
if_then_else_ : {X : Set} -> Two -> X -> X -> X
if tt then t else f = t
if ff then t else f = f
\end{code}
Again, we expect Agda to figure out the type of the conditional expression
from the context, so we use braces to indicate that it should be hidden.
(Here are some dangling questions. Is it good that the types of the
two branches are just the same as the type of the overall expression?
Do we not know more, once we have checked the condition? How could we
know that we know more?)
We can use conditionals to define conjunction of two Booleans:
\begin{code}
_/\_ : Two -> Two -> Two
b1 /\ b2 = if b1 then b2 else ff
\end{code}
%
Now that we have a way to represent Boolean values and conditional expressions,
we might like to have some conditions. E.g., let us be able to compare numbers.
%format <= = "\F{\le}"
%format _<=_ = "\us{" <= "}"
\begin{code}
_<=_ : Nat -> Nat -> Two
zero <= y = tt
suc x <= zero = ff
suc x <= suc y = x <= y
\end{code}
%format List = "\D{List}"
%format :> = "\C{:\!>}"
%format _:>_ = "\us{" :> "}"
\section{|List|s}
We can declare a |data|type which does the job of Haskell's workhorse
|[a]|. The definition of |List| is parametrized by some |X|, the set
in to which the list's elements belong. I write the parameters for the
datatype to the left of the |:| in the declaration.
\nudge{A typesetting gremlin prevents me from colouring |[]| red.}
\begin{code}
data List (X : Set) : Set where
[] : List X
_:>_ : X -> List X -> List X
infixr 5 _:>_
\end{code}
I give a `nil' constructor, |[]|, and a right associative infix `cons' constructor,
|:>|, which is arrowhead-shaped to remind you that you access list elements
from left to right. We can write lists like
\begin{spec}
1 :> 2 :> 3 :> 4 :> 5 :> []
\end{spec}
but Agda does not supply any fancy syntax like Haskell's |[1,2,3,4,5]|.
How many values are there in the set |List Zero|?
Does the set |List One| remind you of any other set that you know?
\begin{code}
infixr 5 _++_
_++_ : {A : Set} -> List A -> List A -> List A
[] ++ ys = ys
(x :> xs) ++ ys = x :> (xs ++ ys)
\end{code}
\section{Interlude: Insertion}
%format insertionSort = "\F{insertionSort}"
%format insertList = "\F{insertList}"
We've got quite a bit of kit now. Let's take a break from grinding out
library components and write a program or two. In particular, as we have
numbers and lists and comparison, we could write insertion sort. Let's
see if we can remember how it goes. Split into cases, and the empty case
is clear.
\begin{spec}
insertionSort : List Nat -> List Nat
insertionSort [] = []
insertionSort (x :> xs) = ?
\end{spec}
What happens next? If we can insert |x| into the right place after sorting
|xs|, we'll be home. Agda is a declare-before-use language, but a declaration
does not have to be right next to the corresponding definition. We can make
progress like this.
\begin{code}
insertionSort : List Nat -> List Nat
insertList : Nat -> List Nat -> List Nat
insertionSort [] = []
insertionSort (x :> xs) = insertList x (insertionSort xs)
\end{code}
\begin{spec}
insertList y xs = ?
\end{spec}
Now, how do we insert? Again, we need to split the list into its cases.
the |[]| case is easy. (It's also easy to get wrong.)
\begin{spec}
insertList y [] = y :> []
insertList y (x :> xs) = ?
\end{spec}
To proceed in the `cons` case, we need to know whether or not |y| should
come before |x|. We could go with
\[
|if y <= x then ? else ?|
\]
but let me take the chance to show you another feature. Instead of moving
to the right and giving an expression, Agda lets us bring the extra information
we need to the \emph{left}, where we can pattern match on it.
\begin{spec}
insertList y [] = y :> []
insertList y (x :> xs) with y <= x
insertList y (x :> xs) | b = ?
\end{spec}
The |with| construct adds an extra column to the left-hand side, tabulating
cases for the result of the given expression. Now, if we split on |b|, we get
\begin{spec}
insertList y [] = y :> []
insertList y (x :> xs) with y <= x
insertList y (x :> xs) | tt = ?
insertList y (x :> xs) | ff = ?
\end{spec}
and for each line of this extended table, it is clear what the output must be.
\begin{code}
insertList y [] = y :> []
insertList y (x :> xs) with y <= x
insertList y (x :> xs) | tt = y :> x :> xs
insertList y (x :> xs) | ff = x :> insertList y xs
\end{code}
If the patterns to the left of the bar stay just the same as on the |with|-line,
we're allowed to abbreviate them, as folllows.
\begin{spec}
insertList y [] = y :> []
insertList y (x :> xs) with y <= x
... | tt = y :> x :> xs
... | ff = x :> insertList y xs
\end{spec}
Which of these strikes you as a better document is a matter of taste.
\subsection{Programs as Decision Trees}
It's good to think of a function definition as the description of a
\emph{decision tree}. We start by considering a bunch of inputs and we need
a strategy
to deliver an output. We can
\begin{itemize}
\item give an output built from the stuff we've got, with the |= output| strategy;
\item split one of our things into constructor cases, in each case considering
the structures inside (and if there are no cases, we document that with an
absurd pattern);
\item get more stuff to consider by asking the value of some |extra| expressed
in terms
of the stuff we already have---that's what the right-hand side, |with extra|,
achieves.
\end{itemize}
You can read a program as a dialogue between the machine, saying `what
am I supposed to do with this stuff?' on the left, and the programmer,
explaining how to proceed on the right by one of the above strategies.
The case-splitting nodes aren't documented by an explicit
right-hand-side in the final program, but you see them in passing
while you work, and you can see that they result in multiple left-hand
sides for distinguished cases. Agda figures out how to compute your
functions by reconstructing the full decision tree from the
constructors in your patterns.
\section{Unit Testing with Dependent Types}
%format == = "\D{==}"
%format _==_ = "\us{" == "}"
%format refl = "\C{refl}"
I'm only in chapter two and I can't resist the temptation. I want to be able
to write unit tests in my code---example expressions which should have the
values given, e.g.
\[
|insertionSort (5 :> 2 :> 4 :> 3 :> 1 :> []) == (1 :> 2 :> 3 :> 4 :> 5 :> [])|
\]
The good news is that Agda can run old programs \emph{during} typechecking of
new programs. We can make the typechecker run our unit tests for us, making use
of the following\nudge{Yes, it is scary.} piece of kit.
\begin{spec}
infix 4 _==_
data _==_ {X : Set}(x : X) : X -> Set where
refl : x == x
\end{spec}
%if False
\begin{code}
data _==_ {l}{X : Set l}(x : X) : X -> Set l where
refl : x == x
infix 4 _==_
{-# BUILTIN EQUALITY _==_ #-}
{-# BUILTIN REFL refl #-}
\end{code}
%endif
This |data|type has two parameters: the |X| in braces is a |Set|, and the
braces, as ever, mean that it should be hidden; the |x| is an element of |X|,
and its \emph{round} brackets mean that it should be \emph{visible}, in this
case as the thing to the left of the |==| sign. However, right of the |:|,
we have |X -> Set|, not just |Set|, because this is an \emph{indexed} collection
of sets. For each |y : X|, we get a set |x == y| whose elements represent
\emph{evidence} that |x| and |y| are equal. The constructor tells us the only
way to generate the evidence. The return type of a constructor may choose any
value for the index, and it delivers values only for that index. Here, by
choosing |x| for the index in the type of |refl|, we ensure that for equality
evidence to exist, the two sides of the equation must have the very same value.
The upshot of all this is that we can write a unit test like this:
%format iTest = "\F{iTest}"
\begin{code}
iTest : insertionSort (5 :> 2 :> 4 :> 3 :> 1 :> []) == (1 :> 2 :> 3 :> 4 :> 5 :> [])
iTest = refl
\end{code}
The typechecker must make sure it is valid to use the |refl| constructor,
so it evaluates both sides of the equation to ensure that they are the same.
Try messing up the program to see what happens!
Even better, try deleting the program and rebuilding it interactively. While
your program is under construction and the test might possibly work out fine in
the end, the |refl| evidence in the unit test will have a yellow background,
indicating that it is \yellowBG{suspicious}\nudge{sus-pish-ous}. But you will not
be allowed to do anything interactively which makes the test actually fail, and if
you override the interactive system and load a silly program, the refl will
have the brown background of \brownBG{steaming unpleasantness}.
We won't be fooling around with fancy types in programming for a while yet,
but unit testing is a good engineering practice, so let us take advantage
of Agda's capacity to support it.
\section{More Prelude: Sums and Products}
%format /+/ = "\D{/\!\!+\!\!/}"
%format _/+/_ = "\us{" /+/ "}"
%format inl = "\C{inl}"
%format inr = "\C{inr}"
We often build datatypes which offer some sort of choice. Sometimes we just
want to give a choice between two types which are already established. The
type which offers `an |S| or a |T|' is called the \emph{sum} of |S| and
|T|.\nudge{Haskell calls this construction |Either|.} We define it as a datatype
with |S| and |T| as parameters, allowing
constructors, for `left injection' and `right injection', respectively.
\begin{code}
infixr 1 _/+/_
data _/+/_ (S T : Set) : Set where
inl : S -> S /+/ T
inr : T -> S /+/ T
\end{code}
To see why it really is a kind of sum, try finding all the \emph{values} in each of
\[
|Zero /+/ Zero|\quad |Zero /+/ One|\quad |One /+/ One|\quad
|One /+/ Two|\quad |Two /+/ Two|
\]
When we offer a choice, we need to able to cope with either possibility.
The following gadget captures the idea of `computing by cases'.
%format <?> = "\F{\left<?\right>}"
%format _<?>_ = "\us{" <?> "}"
\begin{code}
_<?>_ : {S T X : Set} ->
(S -> X) -> (T -> X) ->
S /+/ T -> X
(f <?> g) (inl s) = f s
(f <?> g) (inr t) = g t
\end{code}
It might look a bit weird that it's an \emph{infix} operator with \emph{three}
arguments, but it's used in a higher-order way. To make a function,
|f <?> g| which takes |S /+/ T| to some |X|, you need to have a function for each
case, so |f| in |S -> X| and |g| in |T -> X|.
%format /*/ = "\D{/\!\!\times\!\!/}"
%format _/*/_ = "\us{" /*/ "}"
%format , = "\C{,}"
%format outl = "\F{outl}"
%format outr = "\F{outr}"
Meanwhile, another recurrent theme in type design is that we ask for a \emph{pair}
of things, drawn from existing types.\nudge{Haskell uses the notation |(s,t)| for
both the types and values.} This is, somehow, the classic example of a |record|.
\begin{code}
infixr 2 _/*/_
record _/*/_ (S T : Set) : Set where
constructor _,_
field
outl : S
outr : T
open _/*/_ public
infixr 4 _,_
\end{code}
I have a little explaining to do, here. The |field| keyword introduces the
declarations of the record's fields, which must be indented below it.
We have two fields, so it makes sense to have an infix |constructor|, which is
just a comma---unlike Haskell, parentheses are needed only to resolve ambiguity.
The |open| declaration makes |outl| and |outr| available as the `left projection'
and `right projection' functions, respectively. You can check that
\[
|outl : {S T : Set} -> S /*/ T -> S| \qquad
|outr : {S T : Set} -> S /*/ T -> T|
\]
The |public| means that |outl| and |outr| stay in scope whenever any other module
imports this one.
To see why |S /*/ T| is called the \emph{product} of |S| and |T|, try finding
all the values in the following types.
\[
|Zero /*/ Zero|\quad |Zero /*/ One| \quad |One /*/ One|\quad
|One /*/ Two|\quad |Two /*/ Two|
\]
It is sometimes useful to be able to convert a function which takes a
pair into a function which takes its arguments one at a time. This
conversion is called `currying' after the logician, Haskell Curry,
even though Moses Scho\"nfinkel invented it slightly earlier.
%format curry = "\F{curry}"
\begin{code}
curry : {S T X : Set} ->
(S /*/ T -> X) ->
S -> T -> X
curry f s t = f (s , t)
\end{code}
Its inverse is, arguably, even more useful, as it tells you how to build a
function from pairs by considering each component separately.
%format uncurry = "\F{uncurry}"
\begin{code}
uncurry : {S T X : Set} ->
(S -> T -> X) ->
S /*/ T -> X
uncurry f (s , t) = f s t
\end{code}
\section{Interlude: Exponentiation}
How many functions are there in a type |S -> T|? It depends on when we consider
two functions to be the same. Mathematically, such a function is considered just
to be the choice of a |T| value corresponding to each |S| value. There might be
lots of different ways to \emph{implement} that function, but if two programs
of type |S -> T| agree on outputs whenever we feed them the same inputs, we say
they are two implementations of the same function.
So it's easy to count functions, at least if the sets involved are
finite. If there are |t| different elements of |T| and |s| different
elements of |S|, then we need to choose one of the |t| for each one of
the |s|, so that's $t^s$ different possibilities. Just as |S /+/ T| really
behaves like a sum and |S /*/ T| really behaves like a product, we
find that |S -> T| really behaves like the exponential $|T|^{|S|}$.
The fact that |curry| and |uncurry| are mutually inverse (or \emph{isomorphic})
just tells us something we learned in school
\[
|X|^{(|S /*/ T|)} \cong (|X|^{|T|})^{|S|}
\]
You might also remember that
\[
|X|^{(|S /+/ T|)} \cong |X|^{|S|} |/*/| |X|^{|T|}
\]
and it's not hard to see why that makes sense in terms of counting functions.
(Think about what |<?>| does.)
Many of the algebraic laws you learned for numeric operations at school
make perfect sense for \emph{type} operations and account for structures
fundamental to computation. That's (to some extent) how the Mathematically
Structured Programming Group came by its name. Keep your eyes peeled for more!
\section{More Prelude: Basic Functional Plumbing}
%format id = "\F{id}"
%format o = "\F{\circ}"
%format _o_ = "\us{" o "}"
Functions are a bit like machines with an input pipe and an output pipe. Their
types tell us whether it's safe to plumb them together. Any functional plumber
needs some basic tools.
Firstly, here's a bit of pipe with no machine in the middle---the \emph{identity}
function. What comes out is what went in!
\begin{code}
id : {X : Set} -> X -> X
id x = x
\end{code}
Secondly, we need to be able to plumb the output from one machine to the input
of another. Here's function \emph{composition}.
\begin{code}
_o_ : {A B C : Set} -> (B -> C) -> (A -> B) -> (A -> C)
(f o g) a = f (g a)
infixr 2 _o_
\end{code}
What laws do you think |id| and |o| should obey? If you plumb an extra bit of pipe
onto a machine, does it change what the machine does? If you plumb a sequence of
machines together, the order of the machines can clearly matter, but does the
order in which you did the plumbing jobs affect the behaviour of the end product?
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module FuncKit where
open import Ex1Prelude
_=^=_ : {S T : Set}(f g : S -> T) -> Set
f =^= g = (s : _) -> f s == g s
infixl 2 _=^=_
map : {S T : Set} -> (S -> T) -> (List S -> List T)
map f [] = []
map f (s :> ss) = f s :> map f ss
mapId : {S : Set} -> map (id {S}) =^= id {List S}
mapId [] = refl
mapId (x :> ss) rewrite mapId ss = refl
mapComp : {R S T : Set}(f : S -> T)(g : R -> S) ->
map f o map g =^= map (f o g)
mapComp f g [] = refl
mapComp f g (x :> ss) rewrite mapComp f g ss = refl
_>=_ : Nat -> Nat -> Set
m >= zero = One
zero >= suc n = Zero
suc m >= suc n = m >= n
geRefl : (n : Nat) -> n >= n
geRefl zero = <>
geRefl (suc x) = geRefl x
geTrans : (l m n : Nat) -> m >= n -> l >= m -> l >= n
geTrans l zero zero mn lm = <>
geTrans zero zero (suc x) mn lm = mn
geTrans (suc x) zero (suc zero) mn lm = <>
geTrans (suc x) zero (suc (suc x₁)) mn lm = geTrans x zero (suc x₁) mn <>
geTrans l (suc x) zero mn lm = <>
geTrans zero (suc x) (suc x₁) mn lm = lm
geTrans (suc x) (suc x₁) (suc x₂) mn lm = geTrans x x₁ x₂ mn lm
data Vec (X : Set) : Nat -> Set where
[] : Vec X zero
_,_ : forall {n} -> X -> Vec X n -> Vec X (suc n)
take : {X : Set}(m n : Nat) -> m >= n -> (Vec X m -> Vec X n)
take m zero mn xs = []
take .0 (suc n) () []
take ._ (suc n) mn (x , xs) = x , take _ n mn xs
From : Set -> Set -> Set
From A X = A -> X
fromMap : {A S T : Set} -> (S -> T) -> ((From A) S -> (From A) T)
fromMap f g = f o g
{-
To : Set -> Set -> Set
To B X = X -> B
toMap : {B S T : Set} -> (S -> T) -> ((To B) S -> (To B) T)
toMap {B}{S}{T} f g = {!!}
-}
NotNot : Set -> Set
NotNot X = (X -> Zero) -> Zero
nnMap : {S T : Set} -> (S -> T) -> (NotNot S -> NotNot T)
nnMap f nns = \ nt -> nns (\ s -> nt (f s))
good : Zero -> One
good ()
{-
bad : One -> Zero
bad = toMap good id
-}
Id : Set -> Set
Id X = X
idMap : {S T : Set} -> (S -> T) -> (Id S -> Id T)
idMap {S}{T} = id
Product : (F G : Set -> Set) -> Set -> Set
Product F G X = F X /*/ G X
prodMap : {F G : Set -> Set} ->
({S T : Set} -> (S -> T) -> (F S -> F T)) ->
({S T : Set} -> (S -> T) -> (G S -> G T)) ->
({S T : Set} -> (S -> T) -> ((Product F G) S -> (Product F G) T))
prodMap fmap gmap h (fs , gs) = fmap h fs , gmap h gs
ex1 : Product Id Id Nat
ex1 = 6 , 7
ex2 : Product Id Id Two
ex2 = prodMap idMap idMap (\ n -> n <= 6) ex1
Sum : (F G : Set -> Set) -> Set -> Set
Sum F G X = F X /+/ G X
sumMap : {F G : Set -> Set} ->
({S T : Set} -> (S -> T) -> (F S -> F T)) ->
({S T : Set} -> (S -> T) -> (G S -> G T)) ->
({S T : Set} -> (S -> T) -> ((Sum F G) S -> (Sum F G) T))
sumMap fmap gmap h (inl fs) = inl (fmap h fs)
sumMap fmap gmap h (inr gs) = inr (gmap h gs)
ex3 : Sum (Product Id Id) Id Two
ex3 = inl (tt , ff)
K : Set -> Set -> Set
K A X = A
kMap : {A S T : Set} -> (S -> T) -> (K A S -> K A T)
kMap f a = a
Mystery : Set -> Set
Mystery = Sum (K One) Id
mystery : Mystery Two
mystery = inl <>
data Kit : Set1 where
kK : Set -> Kit
kId : Kit
_k+_ : Kit -> Kit -> Kit
_k*_ : Kit -> Kit -> Kit
kFun : Kit -> (Set -> Set)
kFun (kK A) X = A
kFun kId X = X
kFun (f k+ g) X = kFun f X /+/ kFun g X
kFun (f k* g) X = kFun f X /*/ kFun g X
kitMap : (k : Kit){S T : Set} -> (S -> T) -> (kFun k) S -> (kFun k) T
kitMap (kK A) h a = a
kitMap kId h s = h s
kitMap (f k+ g) h (inl fs) = inl (kitMap f h fs)
kitMap (f k+ g) h (inr gs) = inr (kitMap g h gs)
kitMap (f k* g) h (fs , gs) = kitMap f h fs , kitMap g h gs
data Data (k : Kit) : Set where
[_] : (kFun k) (Data k) -> Data k
fold : (k : Kit){X : Set} -> (kFun k X -> X) -> Data k -> X
fold k {X} f [ kd ] = -- f (kitMap k (fold k f) kd)
f (kitMapFold k kd) where
kitMapFold : (j : Kit) -> kFun j (Data k) -> kFun j X
kitMapFold (kK A) a = a
kitMapFold kId s = fold k f s
kitMapFold (f k+ g) (inl fs) = inl (kitMapFold f fs)
kitMapFold (f k+ g) (inr gs) = inr (kitMapFold g gs)
kitMapFold (f k* g) (fs , gs) = kitMapFold f fs , kitMapFold g gs
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex4Lec where
{- I'm sorry I haven't quite finished setting this exercise yet, but by
the joy of version control, the rest of it can be merged in later
(quite soon). At least you can get cracking: I promise not to break
anything, just to add a bit more on the end.
The deadline for this is midnight on the Monday of Week 12 (15 Dec).
It'd be good to get the marks in before Christmas, but if the end of
term is looking deadlinetastic, please open negotiations.
-}
open import Ex1Prelude
open import IxCon
{-# BUILTIN BOOL Two #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #-}
{-# BUILTIN CONS _:>_ #-}
postulate -- this means that we just suppose the following things exist...
Char : Set
String : Set
{-# BUILTIN CHAR Char #-}
{-# BUILTIN STRING String #-}
primitive -- these are baked in; they even work!
primCharEquality : Char -> Char -> Two
primStringAppend : String -> String -> String
primStringToList : String -> List Char
primStringFromList : List Char -> String
---------------------------------------------------------------------------
-- WRITING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- If you possess the ability to open a file for writing, you might
have the following interface. -}
-- States
data WriteState : Set where
opened closed : WriteState -- do you currently have a file open or not?
-- Commands
data WriteC : WriteState -> Set where
openWrite : (fileName : String) -> WriteC closed
writeChar : Char -> WriteC opened
closeWrite : WriteC opened
-- Responses
WriteR : (j : WriteState)(c : WriteC j) -> Set
WriteR .closed (openWrite fileName) = WriteState -- we get told whether it worked
WriteR .opened (writeChar x) = One -- always works
WriteR .opened closeWrite = One -- always works
{- 4.1 Implement the following operation which determines the next
state. You should ensure that you can write characters only to
a successfully opened file, and that you can write as many as
you want. It should also be possible to insist that a process
closes its file. -}
writeNext : (j : WriteState)(c : WriteC j) -> WriteR j c -> WriteState
writeNext j c r = {!!}
-- the file writing interface, assembled as an indexed container
WRITE : WriteState => WriteState
WRITE = WriteC <! WriteR / writeNext
---------------------------------------------------------------------------
-- READING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- To read from a file, it should be open, and you shouldn't be at the
end of it. -}
-- States
data ReadState : Set where
opened : (eof : Two) -> ReadState -- eof is tt if we're at end of file
closed : ReadState
{- 4.2 Finish the READ implementation, in accordance with the description. -}
-- Commands
data ReadC : ReadState -> Set where
openRead : {- your stuff -} ReadC {!!} -- needs a filename; might not open successfully;
-- might open an empty file
readChar : {- your stuff -} ReadC {!!} -- makes sense only if we're not at end of file
-- and might take us to end of file
closeRead : {- your stuff -} ReadC {!!} -- makes sense only if the file is open
-- Responses
ReadR : (j : ReadState)(c : ReadC j) -> Set
ReadR j c = {!!}
-- next State; you need to make sure the response gives enough info
readNext : (j : ReadState)(c : ReadC j) -> ReadR j c -> ReadState
readNext j c r = {!!}
READ : ReadState => ReadState
READ = ReadC <! ReadR / readNext
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SHARED STATE
---------------------------------------------------------------------------
{- 4.3 Let's suppose we have two command-response interfaces which offer
different functionality for the same system. Correspondingly, we'll
have two indexed containers for the same index set. Show that you
can combine them into one indexed container which lets you choose a
command from either menu and evolves the state as specified by
whichever interface offered the chosen command.
-}
_=+=_ : {I : Set} -> I => I -> I => I -> I => I
CRn0 =+= CRn1 = {!!}
---------------------------------------------------------------------------
-- WHEN IGNORANCE IS BLISS, BIS
---------------------------------------------------------------------------
{- 4.4 If we have a command-response interface with index I representing
states of the system, show that we can index basically the same
commands and responses over a state, I /*/ J, where the J is just
useless information which never changes. (This operation isn't
super-useful on its own, but it's handy in combination with other
things. -}
GrowR : {I J : Set} -> I => I -> (I /*/ J) => (I /*/ J)
GrowR CRn = {!!}
-- do the same for "growing the index on the left"
GrowL : {I J : Set} -> I => I -> (J /*/ I) => (J /*/ I)
GrowL CRn = {!!}
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SEPARATE STATE
---------------------------------------------------------------------------
{- 4.5 Making use of 4.4 and 4.5, show how to combine two interfaces which
operate independently on separate state: commands from one should
not affect the state of the other.
-}
_<+>_ : {I0 I1 : Set} -> I0 => I0 -> I1 => I1 -> (I0 /*/ I1) => (I0 /*/ I1)
CRn0 <+> CRn1 = {!!}
---------------------------------------------------------------------------
-- ERROR REPORTING, AN INTERFACE
---------------------------------------------------------------------------
{- I'm building the next bit for you.
When things go wrong, we need to trigger an error condition and abort
mission. However, if we have other stuff going on (open files, etc),
it may not always be ok to drop everything and run away. There will
be some states in which it is safe to escape (and deliver a suitable
error message, perhaps) and other states in which escape should be
impossible.
If it is safe to issue an error message, we should be able to do so
without fear of any response from the environment that would oblige
us to carry on.
-}
data ErrorC {I : Set}(SafeMessage : I -> Set)(i : I) : Set where
error : SafeMessage i -> ErrorC SafeMessage i
-- the SafeMessage parameter tells us what is an acceptable
-- error message in any given state; in states where this gives
-- Zero, it will be impossible to trigger an error!
ErrorR : {I : Set}{SafeMessage : I -> Set}(i : I)(c : ErrorC SafeMessage i) -> Set
ErrorR _ _ = Zero -- there's no comeback
errorNext : {I : Set}{SafeMessage : I -> Set}
(i : I)(c : ErrorC SafeMessage i) -> ErrorR i c -> I
errorNext i c () -- so we don't have to say how the state will evolve
ERROR : {I : Set}(SafeMessage : I -> Set) -> I => I
ERROR SafeMessage = ErrorC SafeMessage <! ErrorR / errorNext
---------------------------------------------------------------------------
-- COPY A FILE
---------------------------------------------------------------------------
{- 4.6 Implement a process which, given access to suitable interfaces, will
give the process for copying a named source file to a named target
file. This goes in two phases.
-}
{- 4.6.1 Firstly, you should identify the command-reponse interface within
which you need to work. You will need to be able to read and write files,
but also to signal errors (in case a file fails to open for some reason).
You must ensure that it is impossible for any process using your interface
to escape with an error leaving a file open. You must also make it
possible to guarantee that your copying process will, error or not, leave
all files closed.
-}
CPState : Set
CPState = {!!}
CPInterface : CPState => CPState
CPInterface = {!!}
{- 4.6.2 Secondly, you should implement your copying process, working to your
interface. I will let you switch off the termination checker: you cannot
predict in advance how long the copying process will go on, as you have
not seen the source file yet. (Later, we'll learn how to be honest about
things which might go on for ever, but for now, let's cheat.)
-}
{-# NO_TERMINATION_CHECK #-}
cp : (sourceFile targetFile : String) -> Game CPInterface {!!} {!!}
cp sourceFile targetFile = {!!}
{- HINTS
You will certainly need to build some extra bits and pieces.
You have the components for reading, writing and error handling, and
suitable kit with which to combine them. Reading and writing don't
interfere with each other, but it's important to make sure that you
can't bomb out with an error, so some shared state seems important.
There are really two phases to the process:
(1) getting the files open -- this may go wrong
(2) copying from one to the other -- this will work if we reach it
You might want to split these phases apart.
-}
---------------------------------------------------------------
-- TO BE CONTINUED...
---------------------------------------------------------------
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex1Sol where
open import Ex1Prelude
{----------------------------------------------------------------------------}
{- Name: Conor McSpecimen -}
{----------------------------------------------------------------------------}
{----------------------------------------------------------------------------}
{- DEADLINE: Week 3 Monday 13 October 23:59 (preferably by BitBucket) -}
{----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
TOP TIP: if you have annoyingly many open goals, comment out big chunks of the
file with a multi-line comment a bit like this one.
-----------------------------------------------------------------------------}
{- Mark scheme:
The programming for each part is worth one mark.
the explanation of why the impossible cases are impossible is worth
one mark.
The total number of available marks is 15.
-}
{----------------------------------------------------------------------------}
{- 1.1: Tree Sort -}
{----------------------------------------------------------------------------}
-- 1.1.1 implement concatenation for lists
_++_ : {X : Set} -> List X -> List X -> List X
[] ++ ys = ys
x :> xs ++ ys = x :> (xs ++ ys)
infixr 3 _++_
-- a datatype of node-labelled binary trees is given as follows
data Tree (X : Set) : Set where
leaf : Tree X
_<[_]>_ : Tree X -> X -> Tree X -> Tree X
{-
data Tree x = Leaf | Node (Tree X) X (Tree X)
Leaf :: Tree x
Node :: Tree x -> x -> Tree x -> Tree x
-}
demoTree : Tree Nat
demoTree = (leaf <[ 3 ]> leaf) <[ 5 ]> leaf
-- 1.1.2 implement the insertion of a number into a tree, ensuring that
-- the numbers in the tree are in increasing order from left to right;
-- make sure to retain duplicates
insertTree : Nat -> Tree Nat -> Tree Nat
insertTree x leaf = leaf <[ x ]> leaf
insertTree x (l <[ y ]> r) with x <= y -- or use if_then_else_
insertTree x (l <[ y ]> r) | tt = insertTree x l <[ y ]> r
insertTree x (l <[ y ]> r) | ff = l <[ y ]> insertTree x r
-- 1.1.3 implement the function which takes the elements of a list and
-- builds an ordered tree from them, using insertTree
makeTree : List Nat -> Tree Nat
makeTree [] = leaf
makeTree (x :> xs) = insertTree x (makeTree xs)
-- 1.1.4 implement the function which flattens a tree to a list,
-- using concatenation
flatten : {X : Set} -> Tree X -> List X
flatten leaf = []
flatten (l <[ x ]> r) = flatten l ++ x :> flatten r
-- 1.1.5 using the above components, implement a sorting algorithm which
-- works by building a tree and then flattening it
treeSort : List Nat -> List Nat
treeSort = flatten o makeTree
-- 1.1.6 give a collection of unit tests which cover every program line
-- from 1.1.1 to 1.1.5
treeSortTest : treeSort (1 :> 5 :> 2 :> 4 :> 3 :> [])
== (1 :> 2 :> 3 :> 4 :> 5 :> [])
treeSortTest = refl
-- 1.1.7 implement a fast version of flatten, taking an accumulating parameter,
-- never using ++. and ensuring that the law
--
-- fastFlatten t xs == flatten t ++ xs
--
-- is true;
{-
fastFlatten : {X : Set} -> Tree X -> (List X -> List X)
fastFlatten leaf xs
-- = flatten leaf ++ xs -- by specification
-- = [] ++ xs -- definition of flatten
= xs -- definition of ++
fastFlatten (l <[ x ]> r) xs
-- = flatten (l <[ x ]> r) ++ xs -- by specification
-- = (flatten l ++ x :> flatten r) ++ xs -- definition of flatten
-- = flatten l ++ x :> flatten r ++ xs -- ++ is associative
-- = flatten l ++ x :> fastFlatten r xs -- by specification
= fastFlatten l (x :> fastFlatten r xs) -- by specification
-}
-- for an extra style point, ensure that the accumulating parameter
-- is never given a name in your program
fastFlatten : {X : Set} -> Tree X -> (List X -> List X)
fastFlatten leaf = id
fastFlatten (l <[ x ]> r) = (fastFlatten l) o (_:>_ x) o (fastFlatten r)
-- 1.1.8 use fastFlatten to build a fast version of tree sort
fastTreeSort : List Nat -> List Nat
fastTreeSort xs = fastFlatten (makeTree xs) []
-- 1.1.9 again, give unit tests which cover every line of code
fastTreeSortTest : fastTreeSort (1 :> 5 :> 2 :> 4 :> 3 :> [])
== (1 :> 2 :> 3 :> 4 :> 5 :> [])
fastTreeSortTest = refl
{----------------------------------------------------------------------------}
{- 1.2: Shooting Propositional Logic Fish In A Barrel -}
{----------------------------------------------------------------------------}
-- 1.2.1 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
orCommute : {A B : Set} -> A /+/ B -> B /+/ A
orCommute (inl a) = inr a
orCommute (inr b) = inl b
orAbsorbL : {A : Set} -> Zero /+/ A -> A
orAbsorbL (inl ())
orAbsorbL (inr a) = a
orAbsorbR : {A : Set} -> A /+/ Zero -> A
orAbsorbR (inl a) = a
orAbsorbR (inr ())
orAssocR : {A B C : Set} -> (A /+/ B) /+/ C -> A /+/ (B /+/ C)
orAssocR (inl (inl a)) = inl a
orAssocR (inl (inr b)) = inr (inl b)
orAssocR (inr c) = inr (inr c)
orAssocL : {A B C : Set} -> A /+/ (B /+/ C) -> (A /+/ B) /+/ C
orAssocL (inl a) = inl (inl a)
orAssocL (inr (inl b)) = inl (inr b)
orAssocL (inr (inr c)) = inr c
-- 1.2.2 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
andCommute : {A B : Set} -> A /*/ B -> B /*/ A
andCommute (a , b) = b , a
andAbsorbL : {A : Set} -> A -> One /*/ A
andAbsorbL a = <> , a
andAbsorbR : {A : Set} -> A -> A /*/ One
andAbsorbR a = a , <>
andAssocR : {A B C : Set} -> (A /*/ B) /*/ C -> A /*/ (B /*/ C)
andAssocR ((a , b) , c) = a , (b , c)
andAssocL : {A B C : Set} -> A /*/ (B /*/ C) -> (A /*/ B) /*/ C
andAssocL (a , (b , c)) = (a , b) , c
-- how many times is [C-c C-c] really needed?
-- NEVER, but I'd rather use patterns than projections
-- 1.2.3 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
distribute : {A B C : Set} -> A /*/ (B /+/ C) -> (A /*/ B) /+/ (A /*/ C)
distribute (a , inl b) = inl (a , b)
distribute (a , inr c) = inr (a , c)
factor : {A B C : Set} -> (A /*/ B) /+/ (A /*/ C) -> A /*/ (B /+/ C)
factor (inl (a , b)) = (a , inl b)
factor (inr (a , c)) = (a , inr c)
-- 1.2.4 try to implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]; at least one of them will prove to be
-- impossible, in which case you should comment it out and explain
-- why it's impossible
Not : Set -> Set
Not X = X -> Zero
deMorgan1 : {A B : Set} -> (Not A /+/ Not B) -> Not (A /*/ B)
deMorgan1 (inl na) (a , b) = na a
deMorgan1 (inr nb) (a , b) = nb b
{-
All I know is that A and B are not both true. That does not tell
me which of the two is false. To give a value in S /+/ T, I must
come off the fence and choose either the inl constructor and give
an S value or the inr constructor with a T. I can't just say "well,
I'm sure it isn't neither of those".
deMorgan2 : {A B : Set} -> Not (A /*/ B) -> (Not A /+/ Not B)
deMorgan2 x = inl (\ a -> {!!})
Closer to the detail, a value of type Not (A /*/ B) is really a
function of type (A /*/ B) -> Zero, so I can never get any actual
data out of it that would help me come off the fence. If I plump
for one side (inl, above), I get offered an A, but that isn't
enough to make use of the hypoothesis.
-}
deMorgan3 : {A B : Set} -> (Not A /*/ Not B) -> Not (A /+/ B)
deMorgan3 (na , nb) (inl a) = na a
deMorgan3 (na , nb) (inr b) = nb b
deMorgan4 : {A B : Set} -> Not (A /+/ B) -> (Not A /*/ Not B)
deMorgan4 n = (\ a -> n (inl a)) , (\ b -> n (inr b))
-- 1.2.5 try to implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]; at least one of them will prove to be
-- impossible, in which case you should comment it out and explain
-- why it's impossible
dnegI : {X : Set} -> X -> Not (Not X)
dnegI = \ x nx → nx x
{-
dnegE : {X : Set} -> Not (Not X) -> X
dnegE = {!!}
Just because you can't prove that X's don't exist, it doesn't mean
you actually know how to compute an X.
-}
neg321 : {X : Set} -> Not (Not (Not X)) -> Not X
neg321 = λ nnx x → nnx \ nx -> nx x
{-
hamlet : {B : Set} -> B /+/ Not B
hamlet = {!!}
For any proposition (e.g., the halting of a Turing machine), that
we can encode as a Set, hamlet promises to compute whether or not
it has a proof. That's far cleverer than a real computer.
-}
nnHamlet : {B : Set} -> Not (Not (B /+/ Not B))
nnHamlet z = z (inr (\ b -> z (inl b)))
{- Just for fun... -}
DEMORGAN2 : Set1
DEMORGAN2 = {A B : Set} -> Not (A /*/ B) -> (Not A /+/ Not B)
DNEGE : Set1
DNEGE = {X : Set} -> Not (Not X) -> X
HAMLET : Set1 -- also known as "the law of the excluded middle"
HAMLET = {B : Set} -> B /+/ Not B -- or "tertium non datur" (third (way) not given)
-- and one more variation, Peirce's Law, also a classical truth
PEIRCE : Set1
PEIRCE = {P Q : Set} -> ((P -> Q) -> P) -> P
-- DNEGE, PEIRCE and HAMLET are equivalent
imp1 : DNEGE -> HAMLET
imp1 dne = dne nnHamlet
imp2 : HAMLET -> PEIRCE
imp2 h {P} {Q} pqp with h {P}
imp2 h pqp | inl p = p
imp2 h pqp | inr np = pqp (\ p -> magic (np p)) where
imp3 : PEIRCE -> DNEGE
imp3 peirce nnx = peirce (\ nx -> magic (nnx nx))
-- they all imply DEMORGAN2
impDeMorgan : DNEGE -> DEMORGAN2
impDeMorgan dne nab = dne (\ z -> z (inl (\ a -> z (inr (\ b → nab (a , b))))))
-- but (and sorry if I led some of you to believe the opposite)
-- DEMORGAN2 is weaker than the others, because you can only
-- get one bit at at time
{- So, the business of constructing values as evidence for
propositions corresponds to functional programming in a "total"
language, but it doesn't give us quite the same logic as the
Boolean logic we teach you when you start. That logic (aka
"classical logic") makes "true" some things which do not correspond
to computations.
The logic you get here is sometimes called "constructive logic"
because we ask not "is it true?" but "can you make the evidence?".
FUN FACT (due to Kurt Goedel): if something is true, classically,
you can prove that it's not false, constructively.
WEIRD POSSIBILITY: there are such things as "anti-classical" logics
which are even more constructive, in which things like HAMLET are
actually false; these logics build in the idea that the *only*
truths arise by construction.
-}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex3 where
open import Ex1Prelude
open import FuncKit
{- 3.1 Numbers in the Kit -}
{- We can define the type of natural numbers using the tools
from the functor kit like this: -}
kNat : Kit
kNat = kK One k+ kId
NAT : Set
NAT = Data kNat
-- Define the function which sends "ordinary" numbers to
-- the corresponding kit-encoded numbers.
Nat2NAT : Nat -> NAT
Nat2NAT n = {!!}
-- Use fold to define the function which sends them back.
NAT2Nat : NAT -> Nat
NAT2Nat = fold (kK One k+ kId) {!!}
-- Show that you get the "round trip" property (by writing
-- recursive functions that use rewrite.
Nat2NAT2Nat : NAT2Nat o Nat2NAT =^= id
Nat2NAT2Nat n = {!!}
NAT2Nat2NAT : Nat2NAT o NAT2Nat =^= id
NAT2Nat2NAT n = {!!}
{- 3.2 Lists in the Kit -}
-- find the code which gives you lists with a given element
-- type (note that the kId constructor marks the place for
-- recursive *sublists* not for list elements
kLIST : Set -> Kit
kLIST A = {!!}
LIST : Set -> Set
LIST A = Data (kLIST A)
-- define nil and cons for your lists
nil : {A : Set} -> LIST A
nil = {!!}
cons : {A : Set} -> A -> LIST A -> LIST A
cons a as = {!!}
-- use fold to define concatenation
conc : {A : Set} -> LIST A -> LIST A -> LIST A
conc {A} xs ys = fold (kLIST A) {!!} xs
-- prove the following (the yellow bits should disappear when
-- you define kLIST);
-- maddeningly, "rewrite" won't do it, but this piece of kit
-- (which is like a manual version of rewrite) will do it
cong : {S T : Set}(f : S -> T){a b : S} -> a == b -> f a == f b
cong f refl = refl
concNil : {A : Set}(as : LIST A) -> conc as nil == as
concNil as = {!!}
concAssoc : {A : Set}(as bs cs : LIST A) ->
conc (conc as bs) cs == conc as (conc bs cs)
concAssoc as bs cs = {!!}
{- 3.3 Trees in the Kit -}
-- give a kit code for binary trees with unlabelled leaves
-- and nodes labelled with elements of NAT
kTREE : Kit
kTREE = {!!}
TREE : Set
TREE = Data kTREE
-- give the constructors
leaf : TREE
leaf = {!!}
node : TREE -> NAT -> TREE -> TREE
node l n r = {!!}
-- implement flattening (slow flattening is ok) as a fold
flatten : TREE -> LIST NAT
flatten = fold kTREE {!!}
{- 3.4 "rec" from "fold" -}
-- The recursor is a variation on the theme of fold, but you
-- get a wee bit more information at each step. In particular,
-- in each recursive position, you get the original substructure
-- *as well as* the value that is computed from it.
rec : (k : Kit){X : Set} ->
(kFun k (Data k /*/ X) -> X) ->
-- ^^^^^^ ^
-- substructure value
Data k -> X
-- Demonstrate that rec is no more powerful than fold by constructing
-- rec from fold. The trouble is that fold throws away the original
-- substructures. But you can compensate by computing something extra
-- as well as the value you actually want.
rec k {X} f d = outr (fold k {{!!} /*/ X} {!!} d)
-- use rec to implement "insList", being the function which inserts
-- a number in a list, such that if the input list is in increasing
-- order, so is the output list; you may assume that "lessEq" exists
lessEq : NAT -> NAT -> Two
insList : NAT -> LIST NAT -> LIST NAT
insList n = rec (kLIST NAT) {!!}
-- justify the assumption by defining "lessEq"; do not use explicit
-- recursion;
-- note that the thing we build for each number is its less-or-equal
-- test;
-- do use "rec kNat" once more to take numbers apart
lessEq x y = rec kNat {NAT -> Two} {!!} x y
-- implement insertion for binary search trees using "rec"
insTree : NAT -> TREE -> TREE
insTree n = rec kTREE {!!}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Lambda where
open import Ex1Prelude
data Ty : Set where
base : Ty
_>>_ : Ty -> Ty -> Ty
data Cx : Set where
C0 : Cx
_/_ : Cx -> Ty -> Cx
infixl 4 _/_
infixr 3 _<:_
data _<:_ (T : Ty) : Cx -> Set where
zero : {G : Cx} -> T <: G / T
suc : {G : Cx}{S : Ty} -> T <: G -> T <: G / S
data Term (G : Cx) : Ty -> Set where
var : {S : Ty} -> S <: G -> Term G S
lam : {S T : Ty} -> Term (G / S) T -> Term G (S >> T)
_$_ : {S T : Ty} -> Term G (S >> T) -> Term G S -> Term G T
myTerm : Term (C0 / base) base
myTerm = lam (var zero $ (var zero $ var (suc zero))) $ lam (var zero)
Semantics : Ty -> Set
Semantics base = Nat
Semantics (S >> T) = Semantics S -> Semantics T
Env : Cx -> Set
Env G = {T : Ty} -> T <: G -> Semantics T
_//_ : {G : Cx}{S : Ty} -> Env G -> Semantics S -> Env (G / S)
(g // s) zero = s
(g // s) (suc x) = g x
eval : {G : Cx}{T : Ty} -> Term G T -> Env G -> Semantics T
eval (var x) g = g x
eval (lam t) g = \ s -> eval t (g // s)
eval (f $ s) g = eval f g (eval s g)
myTest : Nat
myTest = eval myTerm ((\ ()) // 42)
myTerm' : Term (C0 / (base >> base) / base) base
myTerm' = lam (var zero $ (var zero $ var (suc zero))) $
lam (var (suc (suc zero)) $ (var (suc (suc zero)) $ var zero))
myTest' : Nat
myTest' = eval myTerm' (((\ ()) // suc) // 42)
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module FuncLec where
open import Ex1Prelude
_=^=_ : {S T : Set}(f g : S -> T) -> Set
f =^= g = (s : _) -> f s == g s
infixl 2 _=^=_
map : {S T : Set} -> (S -> T) -> (List S -> List T)
map f [] = []
map f (s :> ss) = f s :> map f ss
mapId : {S : Set} -> map (id {S}) =^= id {List S}
mapId [] = refl
mapId (x :> ss) rewrite mapId ss = refl
mapComp : {R S T : Set}(f : S -> T)(g : R -> S) ->
map f o map g =^= map (f o g)
mapComp f g [] = refl
mapComp f g (x :> ss) rewrite mapComp f g ss = refl
_>=_ : Nat -> Nat -> Set
m >= zero = One
zero >= suc n = Zero
suc m >= suc n = m >= n
geRefl : (n : Nat) -> n >= n
geRefl zero = <>
geRefl (suc x) = geRefl x
geTrans : (l m n : Nat) -> m >= n -> l >= m -> l >= n
geTrans l zero zero mn lm = <>
geTrans zero zero (suc x) mn lm = mn
geTrans (suc x) zero (suc zero) mn lm = <>
geTrans (suc x) zero (suc (suc x₁)) mn lm = geTrans x zero (suc x₁) mn <>
geTrans l (suc x) zero mn lm = <>
geTrans zero (suc x) (suc x₁) mn lm = lm
geTrans (suc x) (suc x₁) (suc x₂) mn lm = geTrans x x₁ x₂ mn lm
data Vec (X : Set) : Nat -> Set where
[] : Vec X zero
_,_ : forall {n} -> X -> Vec X n -> Vec X (suc n)
take : {X : Set}(m n : Nat) -> m >= n -> (Vec X m -> Vec X n)
take m zero mn xs = []
take .0 (suc n) () []
take ._ (suc n) mn (x , xs) = x , take _ n mn xs
data Tree (X : Set) : Set where
leaf : Tree X
node : Tree X -> X -> Tree X -> Tree X
treeMap : {S T : Set} -> (S -> T) -> (Tree S -> Tree T)
treeMap f leaf = leaf
treeMap f (node l s r) = node (treeMap f l) (f s) (treeMap f r)
From : Set -> Set -> Set
From A X = A -> X
fromMap : {A S T : Set} -> (S -> T) -> ((From A) S -> (From A) T)
fromMap f g = f o g
{-
To : Set -> Set -> Set
To B X = X -> B
toMap : {B S T : Set} -> (S -> T) -> ((To B) S -> (To B) T)
toMap {B}{S}{T} f g = {!!}
-}
NotNot : Set -> Set
NotNot X = (X -> Zero) -> Zero
nnMap : {S T : Set} -> (S -> T) -> (NotNot S -> NotNot T)
nnMap f nns = \ nt -> nns (\ s -> nt (f s))
good : Zero -> One
good ()
{-
bad : One -> Zero
bad = toMap good id
-}
Id : Set -> Set
Id X = X
idMap : {S T : Set} -> (S -> T) -> (Id S -> Id T)
idMap {S}{T} = id
Product : (F G : Set -> Set) -> Set -> Set
Product F G X = F X /*/ G X
prodMap : {F G : Set -> Set} ->
({S T : Set} -> (S -> T) -> (F S -> F T)) ->
({S T : Set} -> (S -> T) -> (G S -> G T)) ->
({S T : Set} -> (S -> T) -> ((Product F G) S -> (Product F G) T))
prodMap fmap gmap h (fs , gs) = fmap h fs , gmap h gs
ex1 : Product Id Id Nat
ex1 = 6 , 7
ex2 : Product Id Id Two
ex2 = prodMap idMap idMap (\ n -> n <= 6) ex1
Sum : (F G : Set -> Set) -> Set -> Set
Sum F G X = F X /+/ G X
sumMap : {F G : Set -> Set} ->
({S T : Set} -> (S -> T) -> (F S -> F T)) ->
({S T : Set} -> (S -> T) -> (G S -> G T)) ->
({S T : Set} -> (S -> T) -> ((Sum F G) S -> (Sum F G) T))
sumMap fmap gmap h (inl fs) = inl (fmap h fs)
sumMap fmap gmap h (inr gs) = inr (gmap h gs)
ex3 : Sum (Product Id Id) Id Two
ex3 = inl (tt , ff)
K : Set -> Set -> Set
K A X = A
kMap : {A S T : Set} -> (S -> T) -> (K A S -> K A T)
kMap f a = a
Mystery : Set -> Set
Mystery = Sum (K One) Id
mystery : Mystery Two
mystery = inl <>
data Kit : Set1 where
kK : Set -> Kit
kId : Kit
_k+_ : Kit -> Kit -> Kit
_k*_ : Kit -> Kit -> Kit
kFun : Kit -> (Set -> Set)
kFun (kK A) X = A
kFun kId X = X
kFun (f k+ g) X = kFun f X /+/ kFun g X
kFun (f k* g) X = kFun f X /*/ kFun g X
kitMap : (k : Kit){S T : Set} -> (S -> T) -> kFun k S -> kFun k T
kitMap (kK A) h a = a
kitMap kId h s = h s
kitMap (f k+ g) h (inl fs) = inl (kitMap f h fs)
kitMap (f k+ g) h (inr gs) = inr (kitMap g h gs)
kitMap (f k* g) h (fs , gs) = kitMap f h fs , kitMap g h gs
data Data (k : Kit) : Set where
[_] : kFun k (Data k) -> Data k
fold : (k : Kit){X : Set} -> (kFun k X -> X) -> Data k -> X
fold k {X} f [ kd ] = f (kitMapFold k kd) where
kitMapFold : (j : Kit) -> kFun j (Data k) -> kFun j X
kitMapFold (kK A) a = a
kitMapFold kId s = fold k f s
kitMapFold (f k+ g) (inl fs) = inl (kitMapFold f fs)
kitMapFold (f k+ g) (inr gs) = inr (kitMapFold g gs)
kitMapFold (f k* g) (fs , gs) = kitMapFold f fs , kitMapFold g gs
kMaybe : Kit
kMaybe = kK One k+ kId
pattern ze = inl <>
pattern su n = inr n
NAT = Data kMaybe
exNat : NAT
exNat = [ su [ su [ ze ] ] ]
_+'_ : NAT -> NAT -> NAT
x +' y = fold kMaybe p x where
p : kFun kMaybe NAT -> NAT
p ze = y
p (su x+y) = [ su x+y ]
{-
[ ze ] +' y = y
[ su x ] +' y = [ su (x +' y) ]
-}
kT : Kit
kT = kK One k+ (kId k* kId)
exTree : Data kT
exTree = [ inl <> ]
FreeMo : Kit -> Set -> Set
FreeMo k X = Data (k k+ kK X)
return : (k : Kit) -> {A : Set} -> A -> FreeMo k A
return k a = [ inr a ]
bind : (k : Kit){A B : Set} ->
FreeMo k A ->
(A -> FreeMo k B) ->
FreeMo k B
bind k {A} ma a2mb = fold (k k+ kK A)
(\ { (inl kb) -> [ inl kb ]
; (inr a) -> a2mb a
}) ma
Error : Set -> Set -> Set
Error E = FreeMo (kK E)
kBitWrite : Kit
kBitWrite = kK Two k* kId
kBitRead : Kit
kBitRead = kId k* kId
RWBit : Set -> Set
RWBit = FreeMo (kBitWrite k+ kBitRead)
run : {X : Set} -> RWBit X ->
List Two -> List Two /*/ Error One X
run [ inl (inl (b , p)) ] bs with run p bs
run [ inl (inl (b , p)) ] bs | bs' , ex
= (b :> bs') , ex
run [ inl (inr (tp , fp)) ] [] = [] , [ inl <> ]
run [ inl (inr (tp , fp)) ] (tt :> bs)
= run tp bs
run [ inl (inr (tp , fp)) ] (ff :> bs)
= run fp bs
run [ inr x ] bs = [] , [ inr x ]
record Container : Set1 where
constructor _<!_
field
Command : Set -- aka Shape
Response : Command -> Set -- aka Position
open Container public
record Sigma (S : Set)(T : S -> Set) : Set where
constructor _,_
field
fst : S
snd : T fst
open Sigma public
_*'_ : Set -> Set -> Set
S *' T = Sigma S \ _ -> T
_+s_ : Set -> Set -> Set
S +s T = Sigma Two \ { tt -> S ; ff -> T }
[[_]] : Container -> Set -> Set
[[ C <! R ]] Y = Sigma C (\ c -> R c -> Y)
cmap : (F : Container) -> {S T : Set} -> (S -> T) -> [[ F ]] S -> [[ F ]] T
cmap F f (c , k) = c , (\ r -> f (k r))
data GenMo (F : Container)
(X : Set) : Set where
ret : X -> GenMo F X
<_> : [[ F ]] (GenMo F X) -> GenMo F X
_>>=_ : {F : Container}
{A B : Set} -> GenMo F A -> (A -> GenMo F B)
-> GenMo F B
ret a >>= f = f a
< c , k > >>= f = < c , (\ r -> k r >>= f) >
data Fail : Set where
fail : Fail
FailR : Fail -> Set
FailR fail = Zero
Maybe : Container
Maybe = Fail <! FailR
! : {F : Container} ->
(c : Command F) -> GenMo F (Response F c)
! c = < c , ret >
_c+_ : Container -> Container -> Container
(C0 <! R0) c+ (C1 <! R1) = (C0 /+/ C1) <! (\ { (inl c0) -> R0 c0 ; (inr c1) -> R1 c1 })
inC : {F G : Container}{X : Set} -> [[ F ]] X /+/ [[ G ]] X -> [[ F c+ G ]] X
inC (inl (fc , fk)) = inl fc , fk
inC (inr (gc , gk)) = inr gc , gk
_c*_ : Container -> Container -> Container
(C0 <! R0) c* (C1 <! R1) = (C0 /*/ C1) <! (\ { (c0 , c1) -> R0 c0 /+/ R1 c1 })
pairC : {F G : Container}{X : Set} -> [[ F ]] X /*/ [[ G ]] X -> [[ F c* G ]] X
pairC ((fc , fk) , (gc , gk))
= (fc , gc) , (\ { (inl fr) -> fk fr ; (inr gr) -> gk gr })
kContainer : Kit -> Container
kContainer (kK A) = A <! (\ _ -> Zero)
kContainer kId = One <! (\ _ -> One)
kContainer (k k+ k') = kContainer k c+ kContainer k'
kContainer (k k* k') = kContainer k c* kContainer k'
tail : {X : Set} -> List X -> GenMo Maybe (List X)
tail [] = ! fail >>= (\ ())
tail (x :> xs) = ret xs
try : {X : Set} -> GenMo Maybe X -> X -> X
try (ret x) _ = x
try < fail , k > x = x
data State (S : Set) : Set where
get : State S
put : S -> State S
StateR : {S : Set} -> State S -> Set
StateR {S} get = S
StateR (put x) = One
StateC : Set -> Container
StateC S = State S <! StateR
c++ : GenMo (StateC Nat) Nat
c++ = ! get >>= \ c -> ! (put (suc c)) >>= \ _ -> ret c
runState : {S X : Set} -> GenMo (StateC S) X ->
S -> X /*/ S
runState (ret x) s = x , s
runState < get , k > s = runState (k s) s
runState < put s' , k > s = runState (k <>) s'
test : (Nat /*/ Nat) /*/ Nat
test = runState (c++ >>= \ x -> c++ >>= \ y -> ret (x , y)) 41
data Choose : Set where
choose : Choose
ChooseR : Choose -> Set
ChooseR choose = Two
ChooseC : Container
ChooseC = Choose <! ChooseR
truey : {X : Set} -> GenMo ChooseC X -> X
truey (ret x) = x
truey < choose , k > = truey (k tt)
streamy : {X : Set} ->
GenMo ChooseC X -> (Nat -> Two) -> X
streamy (ret x) s = x
streamy < choose , k > s = streamy (k (s zero)) (s o suc)
_++_ : {X : Set} -> List X -> List X -> List X
[] ++ ys = ys
x :> xs ++ ys = x :> (xs ++ ys)
infixr 3 _++_
pokemon : {X : Set} -> GenMo ChooseC X -> List X
pokemon (ret x) = x :> []
pokemon < choose , k > = pokemon (k tt) ++ pokemon (k ff)
FailOrChoose : Container
FailOrChoose = Maybe c+ ChooseC
answers : {X : Set} -> GenMo FailOrChoose X -> List X
answers (ret x) = x :> []
answers < inl fail , k > = []
answers < inr choose , k > = answers (k tt) ++ answers (k ff)
data Sender (X : Set) : Set where
send : X -> Sender X
SenderC : Set -> Container
SenderC X = Sender X <! \ _ -> One
data Receiver : Set where
receive : Receiver
ReceiverC : Set -> Container
ReceiverC X = Receiver <! \ _ -> X
TransducerC : Set -> Container
TransducerC X = ReceiverC X c+ SenderC X
FlakyTransducerC : Set -> Container
FlakyTransducerC X = Maybe c+ (ReceiverC X c+ SenderC X)
pipe : {X Y : Set} -> GenMo (TransducerC X) One -> GenMo (TransducerC X) Y ->
GenMo (FlakyTransducerC X) Y
pipe (ret <>) (ret y) = ret y
pipe (ret <>) < inl receive , k > = < inl fail , (\ ()) >
pipe < inl receive , k > q = < inr (inl receive) , (\ x -> pipe (k x) q) >
pipe < inr (send x) , k > (ret y) = ret y
pipe < inr (send x) , k > < inl receive , j > = pipe (k <>) (j x)
pipe p < inr (send x) , k > = < inr (inr (send x)) , (\ _ -> pipe p (k <>)) >
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module HuttonVar where
open import Ex1Prelude
data HExp (V : Set) : Set where
var : V -> HExp V
val : Nat -> HExp V
_+++_ : HExp V -> HExp V -> HExp V
eval : HExp Zero -> Nat
eval (var ())
eval (val n) = id n
eval (d +++ e) = eval d + eval e
subst : {U V : Set} -> HExp U -> (U -> HExp V) -> HExp V
subst (var x) s = s x
subst (val n) s = val n
subst (d +++ e) s = subst d s +++ subst e s
hMap : {U V : Set} -> (U -> V) -> (HExp U -> HExp V)
hMap f e = subst e (var o f)
eval' : {V : Set} -> HExp V -> (V -> Nat) -> Nat
eval' e g = eval (subst e (val o g))
mySubst : Two -> HExp One
mySubst tt = val 5
mySubst ff = var <> +++ val 3
myTest : HExp One
myTest = subst ((val 1 +++ var tt) +++ (var tt +++ var ff)) mySubst
Subst : Set -> Set -> Set
Subst U V = U -> HExp V
idSubst : (V : Set) -> Subst V V
idSubst V = var
compSubst : {U V W : Set} -> Subst V W -> Subst U V -> Subst U W
compSubst f g = \ u -> subst (g u) f
Envy : Set -> Set -> Set
Envy V X = (V -> Nat) -> X
envyRet : {V X : Set} -> X -> Envy V X
envyRet x g = x
_-envyThen-_ : {V X Y : Set} ->
Envy V X -> (X -> Envy V Y) -> Envy V Y
evx -envyThen- x2evy = \ g -> x2evy (evx g) g
gimme : {V : Set} -> V -> Envy V Nat
gimme v = \ g -> g v
eval2 : {V : Set} -> HExp V -> Envy V Nat
eval2 (var x) = gimme x
eval2 (val n) = envyRet n
eval2 (e +++ e') =
eval2 e -envyThen- \ v ->
eval2 e' -envyThen- \ v' ->
envyRet (v + v')
{-
leaves : HExp -> List Nat
leaves (val n) = n :> []
leaves (d +++ e) = {!leaves d ++ leaves e!}
data HCode : Nat -> Nat -> Set where
PUSH : {i : Nat} -> Nat -> HCode i (suc i)
ADD : {i : Nat} -> HCode (suc (suc i)) (suc i)
_-SEQ-_ : {i j k : Nat} -> HCode i j -> HCode j k -> HCode i k
infixr 3 _-SEQ-_
data Vec (X : Set) : Nat -> Set where
[] : Vec X zero
_,_ : forall {n} -> X -> Vec X n -> Vec X (suc n)
exec : {i j : Nat} -> HCode i j -> Vec Nat i -> Vec Nat j
exec (PUSH x) s = x , s
exec ADD (x , (y , s)) = (y + x) , s
exec (h -SEQ- k) s = exec k (exec h s)
exec' : (i j : Nat) -> HCode i j -> Vec Nat i -> Vec Nat j
exec' i .(suc i) (PUSH x) s = x , s
exec' .(suc (suc i)) .(suc i) (ADD {i}) s = {!!}
exec' i j (c -SEQ- c₁) s = {!!}
compile : HExp -> {i : Nat} -> HCode i (suc i)
compile (val n) = PUSH n
compile (d +++ e) = compile d -SEQ- compile e -SEQ- ADD
-}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex2Sol where
{-----------------------------------------------------------------------------
Name: Conor McSpecimen
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
CS410 Exercise 2, due 5pm on Monday of Week 6 (3 November 2014)
NOTE: I am well aware that week 6 is quite busy with deadlines,
what with CS408-related obligations and so on. I'd much prefer
you did things to the best of your ability rather than on time,
so I would be sympathetic to requests for some flexibility.
Still, your best bet is to make an early start rather than a
late finish.
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
This exercise is based around extending Hutton's razor with Boolean
values and conditional expressions. By introducing a second value
type, we acquire the risk of type mismatch. The idea here is to
explore different approaches to managing that risk.
-----------------------------------------------------------------------------}
{- Mark scheme
Each part is worth one mark each, apart from the four labelled
as worth two. The total number of marks available is 15.
-}
open import Ex1Prelude
open import Ex2Prelude
{- The extended Hutton's Razor syntax -}
data HExpIf : Set where
num : Nat -> HExpIf
boo : Two -> HExpIf
_+++_ : HExpIf -> HExpIf -> HExpIf
hif_then_else_ : HExpIf -> HExpIf -> HExpIf -> HExpIf
{- Note that an expression
hif eb then ex1 else ex2
makes sense only when
* eb produces a Boolean value
* ex1 and ex2 produce the same sort of value (numeric or Boolean)
-}
HValIf : Set
HValIf = Two /+/ Nat
{- We now have the risk of run time type errors. Let's introduce a type
for things which can go wrong. -}
data Error (E X : Set) : Set where
ok : X -> Error E X
error : E -> Error E X
{- 2.1 Add a constructor to the following datatype for each different
kind of run time error that can happen. (Come back to this exercise
when you're writing the evaluator in 2.3.) Make these error reports
as informative as you can.
-}
data EvalError : Set where
wantedANatButGotALousy : HExpIf -> EvalError
wantedATwoButGotALousy : HExpIf -> EvalError
-- your constructors here
{- 2.2 Write a little piece of "glue code" to make it easier to manage
errors. The idea is to combine error-prone process in *sequence*, where
the second process can depend on the value produced by the first if it
succeeds. The resulting process is, of course, also error-prone, failing
as soon as either component fails.
-}
_>>=_ : {E S T : Set}
-> Error E S -- process which tries to get an S
-> (S -> Error E T) -- given an S, process which tries for a T
-> Error E T -- combined in sequence
ok s >>= s2et = s2et s
error e >>= s2et = error e
{- 2.3 Implement an evaluator for HExpIf. Be sure to add only numbers and
to branch only on Booleans. Report type mismatches as errors. You should
use _>>=_ to help with the propagation of error messages.
(2 marks)
-}
natOrBust : {E : Set} -> E -> HValIf -> Error E Nat
natOrBust e (inl b) = error e
natOrBust e (inr n) = ok n
twoOrBust : {E : Set} -> E -> HValIf -> Error E Two
twoOrBust e (inl b) = ok b
twoOrBust e (inr n) = error e
eval : HExpIf -> Error EvalError HValIf
eval (num n) = ok (inr n)
eval (boo x) = ok (inl x)
eval (d +++ e) =
(eval d >>= natOrBust (wantedANatButGotALousy d)) >>= \ dn ->
(eval e >>= natOrBust (wantedANatButGotALousy e)) >>= \ en ->
ok (inr (dn + en))
eval (hif e then t else f) =
(eval e >>= twoOrBust (wantedATwoButGotALousy e)) >>= \ eb ->
if eb then eval t else eval f
{- Note that the type of eval is not specific about whether the value
expected is numeric or Boolean. It may help to introduce auxiliary
definitions of error-prone processes which are "ok" only for the
type that you really want.
-}
{- Next up, stack machine code, and its execution. -}
data HBCode : Set where
PUSHN : Nat -> HBCode
PUSHB : Two -> HBCode
ADD : HBCode
_SEQ_ : HBCode -> HBCode -> HBCode
_IFPOP_ : HBCode -> HBCode -> HBCode
{- The intended behaviour of (t IFPOP f) is as follows
* pop the (we hope) Boolean value from top of stack
* if it's tt, execute t, else execute f
* whichever branch is executed, it gets the popped stack to start
-}
{- 2.4 Populate the type of possible execution errors and implement the
execution behaviour of HBCode, operating on a stack represented as
a list of HValIf values. (2 marks)
-}
data ExecError : Set where
stackUnderflowInADD : ExecError
stackUnderflowInIFPOP : ExecError
addingATwo : HValIf -> ExecError
iffingANat : HValIf -> ExecError
-- your constructors here
exec : HBCode -> List HValIf -> Error ExecError (List HValIf)
exec (PUSHN n) s = ok (inr n :> s)
exec (PUSHB b) s = ok (inl b :> s)
exec ADD (y :> x :> s)
= natOrBust (addingATwo x) x >>= \ xn ->
natOrBust (addingATwo y) y >>= \ yn ->
ok (inr (xn + yn) :> s)
exec ADD _ = error stackUnderflowInADD
exec (c SEQ d) s = exec c s >>= exec d
exec (t IFPOP f) [] = error stackUnderflowInIFPOP
exec (t IFPOP f) (x :> s)
= twoOrBust (iffingANat x) x >>= \ xb ->
if xb then exec t s else exec f s
{- Next, we take a look at code generation and type safety. -}
data HTy : Set where -- we have two types in HExpIf
NUM BOOL : HTy
_=HTy=_ : HTy -> HTy -> Two -- we can test if two types are equal
NUM =HTy= NUM = tt
NUM =HTy= BOOL = ff
BOOL =HTy= NUM = ff
BOOL =HTy= BOOL = tt
{- 2.5 Write a type-synthesizing compiler, computing both the HTy type and
the HBCode executable for a given expression. Your compiler should
give an informative error report if the expression it receives is
ill typed. Your compiler should also ensure (at least informally) that
the code produced will never trigger any execution errors.
(2 marks)
-}
data CompileError : Set where
addingABool : HExpIf -> CompileError
iffingANumber : HExpIf -> CompileError
ifBranchesMismatchedTypes : (HExpIf /*/ HTy) -> (HExpIf /*/ HTy) -> CompileError
compile : HExpIf -> Error CompileError (HTy /*/ HBCode)
compile (num x) = ok (NUM , PUSHN x)
compile (boo x) = ok (BOOL , PUSHB x)
compile (e1 +++ e2) = compile e1 >>= \
{ (BOOL , _) -> error (addingABool e1)
; (NUM , c1) -> compile e2 >>= \
{ (BOOL , _) -> error (addingABool e2)
; (NUM , c2) -> ok (NUM , (c1 SEQ c2) SEQ ADD)
}
}
compile (hif e then t else f) = compile e >>= \
{ (NUM , _) -> error (iffingANumber e)
; (BOOL , c) -> compile t >>= \
{ (tty , tc) -> compile f >>= \
{ (fty , fc) ->
if tty =HTy= fty then ok (tty , c SEQ (tc IFPOP fc))
else error (ifBranchesMismatchedTypes (t , tty) (f , fty))
}
}
}
{- You have a little bit more room for creative problem-solving in what's
left of the exercise. The plan is to build the type system into expressions
and code, the same way we did with plain Hutton's Razor in class.
-}
{- If we *know* which HTy type we want, we can compute which Agda type we
expect our value to take. -}
HVal : HTy -> Set
HVal NUM = Nat
HVal BOOL = Two
{- 2.6 Finish the type of typed expressions. You should ensure that only
well HTy-typed expressions can be constructed. -}
data THExpIf : HTy -> Set where
val : {t : HTy} -> HVal t -> THExpIf t
_+++_ : THExpIf NUM -> THExpIf NUM -> THExpIf NUM
hif_then_else_ : {t : HTy} -> THExpIf BOOL -> THExpIf t -> THExpIf t -> THExpIf t
-- you fill in addition and if-then-else
{- 2.7 Implement a type-safe evaluator. -}
teval : {t : HTy} -> THExpIf t -> HVal t
teval (val x) = x
teval (d +++ e) = teval d + teval e
teval (hif e then t else f) = if teval e then teval t else teval f
{- 2.8 Implement a type checker. (2 marks) -}
data TypeError : Set where
wanted_got_ : HTy -> HExpIf -> TypeError
-- your constructors here
tcheck : (t : HTy) -> HExpIf -> Error TypeError (THExpIf t)
tcheck NUM (num x) = ok (val x)
tcheck BOOL (num x) = error (wanted BOOL got num x)
tcheck NUM (boo x) = error (wanted NUM got boo x)
tcheck BOOL (boo x) = ok (val x)
tcheck NUM (d +++ e) = tcheck NUM d >>= \ dt -> tcheck NUM e >>= \ et -> ok (dt +++ et)
tcheck BOOL (d +++ e) = error (wanted BOOL got (d +++ e))
tcheck t (hif e then th else el) =
tcheck BOOL e >>= \ et ->
tcheck t th >>= \ tht ->
tcheck t el >>= \ elt -> ok (hif et then tht else elt)
{- 2.9 Adapt the technique from Hutton.agda to give a type-safe underflow-free
version of HBCode. You will need to think what is a good type to represent
the "shape" of a stack: before, we just used Nat to represent the *height* of
the stack, but now we must worry about types. See next question for a hint. -}
data THBCode : List HTy -> List HTy -> Set where
PUSHV : {t : HTy}{s : List HTy} -> HVal t -> THBCode s (t :> s)
ADD : {s : List HTy} -> THBCode (NUM :> NUM :> s) (NUM :> s)
_SEQ_ : {i j k : List HTy} -> THBCode i j -> THBCode j k -> THBCode i k
_IFPOP_ : {i j : List HTy} -> THBCode i j -> THBCode i j -> THBCode (BOOL :> i) j
{- 2.10 Implement the execution semantics for your code. You will need to think
about how to represent a stack. The Ex2Prelude.agda file contains a very
handy piece of kit for this purpose. You write the type, too. -}
Stack : List HTy → Set
Stack i = All HVal i
-- forward composition
_followedBy_ : {A B C : Set} (f : A → B) (g : B → C) → A → C
f followedBy g = λ z → g (f z)
tsemantics : {i j : List HTy} (c : THBCode i j) (s : Stack i) → Stack j
tsemantics (PUSHV x) s = x , s
tsemantics ADD (m , n , s) = m + n , s
tsemantics (c SEQ d) s = (tsemantics c followedBy tsemantics d) s
tsemantics (t IFPOP f) (b , s) = if b then tsemantics t s else tsemantics f s
{- 2.11 Write the compiler from well typed expressions to safe code. -}
tcompile : {t : HTy} -> THExpIf t -> {s : List HTy} -> THBCode s (t :> s)
tcompile (val x) = PUSHV x
tcompile (d +++ e) = (tcompile d SEQ tcompile e) SEQ ADD
tcompile (hif e then t else f) = tcompile e SEQ (tcompile t IFPOP tcompile f)
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
\chapter{Introduction}
\section{Language and Tools}
For the most part, we'll be using the experimental language,
Agda~\cite{DBLP:conf/afp/Norell08}, which is a bit like Haskell
(and implemented in Haskell), but has a more expressive type system
and a rather fabulous environment for typed programming. Much of what
we learn here can be ported back to Haskell with a bit of bodging and
fudging (and perhaps some stylish twists), but it's the programming
environment that makes it worth exploring the ideas in this class via
Agda.
The bad news, for some of you at any rate, is that the Agda programming
environment is tightly coupled to the Emacs editor. If you don't like
Emacs, tough luck. You may have a job getting all this stuff to work on
whatever machines you use outside the department, but the toolchain all
works fine on departmental machines.
Teaching materials, exercise files, lecture scripts, and so on, will
all pile up in the repository
\url{https://github.com/pigworker/CS410-14}, so you'll need to get
with the git programme. We'll fix it so you each have your own place
to put your official branch of the repo where I can get at it. All
work and feedback will be mediated via your git repository.
\section{Lectures, Lab, Tutorials}
\textbf{Monday:~} Lecture 11am--12pm, JA326; Lab, 3--5pm LT1301
\textbf{Tuesday:~} Tutorial, 4--5pm, AR401a
\textbf{Friday:~} Lecture, 1--2pm, LT210
\section{Twitter @@CS410afp}
This class has a twitter feed. Largely, this is so that I can post
pictures of the whiteboard. I don't use it for essential
communications about class business, so you need neither join twitter
nor follow this user. You can access all the relevant stuff just by
surfing into \url{http://twitter.com/CS410afp}. This user, unlike my
personal account, will follow back all class members who follow it,
unless you ask it not to.
\section{Hoop Jumping}
CS410 Advanced Functional Programming is a level 4 class worth 20
credits. It is assessed \emph{entirely} by coursework. Departmental
policy requires class convenors to avoid deadline collisions by
polite negotiation, so I've agreed the following dates for handins,
as visible on the 4th year noticeboard.
\begin{itemize}
\item Monday week 3
\item Monday week 6
\item Monday week 9
\item Monday week 12
\item Monday week 15
\item final assignment, issued as soon as possible after fourth year project
deadline, to be submitted as late as I consider practicable
before the exam board
\end{itemize}
Marking will happen `live' and one-to-one, in office hours on a sign-up basis.
\section{Getting Agda Going on Departmental Machines}
Step 1. Use Linux. Get yourself a shell. (It's going to be that sort
of a deal, all the way along. Welcome back to the 1970s.)
Step 2 for \emph{bash} users. Ensure that your \texttt{PATH} environment variable includes
the directory where Haskell's \texttt{cabal} build manager puts
executables. Under normal circumstances, this is readily achieved by
ensuring that your \texttt{.profile} file contains the line:
\[
\mbox{\texttt{export PATH=\$HOME/.cabal/bin:\$PATH}}
\]
After you've edited \texttt{.profile}, grab a fresh shell window before
continuing.
Step 2 for \emph{tcsh} users. Ensure that your \texttt{path} environment variable includes
the directory where Haskell's \texttt{cabal} build manager puts
executables. Under normal circumstances, this is readily achieved by
ensuring that your \texttt{.cshrc} file contains the line:
\[
\mbox{\texttt{set path = (\$home/.cabal/bin \$path)}}
\]
After you've edited \texttt{.cshrc}, grab a fresh shell window before
continuing.
Step 3. Ensure that you are in sync with the Haskell package database
by issuing the command:
\[
\mbox{\texttt{cabal update}}
\]
Some people found that this bombs out with a missing library. Asking
\texttt{which cabal} revealed that they had a spurious \texttt{\~{}/.cabal/bin/cabal}
file which took precedence over the regular \texttt{/usr/bin/cabal}. Simply delete
\texttt{\~{}/.cabal/bin/cabal} to fix this problem.
Step 4. Install Agda by issuing the command:
\[
\mbox{\texttt{cabal install agda}}
\]
Yes, that's a lower case 'a' in 'agda'. In some situations, it may not manage the full
installation in one go, delivering an error message about which package or version it has
failed to install. We've found that it's sometimes necessary to do
\texttt{cabal install happy} separately, and to do \texttt{cabal install alex-3.0},
requesting a specific older version, as required by another package.
Step 5. Wait.
Step 6. Wait some more.
Step 7. Assuming all of that worked just fine, set up the Emacs interactive environment with the command:
\[
\mbox{\texttt{agda-mode setup; agda-mode compile}}
\]
Step 8. Get this repository. Navigate to where in your file system you want
to keep it and do
\[
\mbox{\texttt{git clone https://github.com/pigworker/CS410-14.git}}
\]
Step 9. Navigate into the repo.
\[
\mbox{\texttt{cd CS410-14}}
\]
Step 10. Start an emacs session involving an Agda file, e.g., by the command:
\[
\mbox{\texttt{emacs Hello.agda \&}}
\]
The file should appear highlighted, and the mode line should say that the buffer is in
Agda mode. In at least one case, this has proven problematic. To check what is going
on, load the configuration file \texttt{\~{}/.emacs} and find the LISP command which
refers to \texttt{agda-mode locate}. Try executing that command: select it with the
mouse, then type ESC x, which should get you a prompt at which you can type
\texttt{eval-region}, which will execute the selected command. If you get a message
about not being able to find \texttt{agda-mode}, then edit the LISP command to give
\texttt{agda-mode} the full path returned by asking \texttt{which agda-mode} in a shell.
And if you get a bad response to \texttt{which agda-mode}, go back to step 2.
Step 11. When you're done, please confirm by posting a message on the class discussion
forum.
\section{Making These Notes}
The sources for these notes are included in the repo along with
everything else. They're built using the excellent \texttt{lhs2TeX}
tool, developed by Andres L\"oh and Ralf Hinze. This, also, can be
summoned via the Haskell package manager.
\[
\mbox{\texttt{cabal install lhs2tex}}
\]
With that done, the default action of \texttt{make} is to build
these notes as \texttt{CS410.pdf}.
\section{What's in \texttt{Hello.agda}?}
It starts with a \texttt{module} declaration, which should and does
match the filename.
\begin{verbatim}
module Hello where
\end{verbatim}
Then, as in Haskell, we have comments-to-end-of-line, as signalled by
\texttt{ --~} with a space.
\begin{verbatim}
-- Oh, you made it! Well done! This line is a comment.
-- In the beginning, Agda knows nothing, but we can teach it about numbers.
\end{verbatim}
Indeed, this module has not \texttt{import}ed any others, and unlike in
Haskell, there is no implicit `Prelude', so at this stage, the only thing
we have is the notion of a \texttt{Set}. The following \texttt{data}
declaration creates three new things---a new \texttt{Set}, populated
with just the values generated by its constructors.
\begin{verbatim}
data Nat : Set where
zero : Nat
suc : Nat -> Nat
\end{verbatim}
We see some key differences with Haskell. Firstly, \emph{one} colon
means `has type', rather than `list cons'. Secondly, rather than
writing `templates' for data, we just state directly the types of the
constructors. Thirdly, there's a lot of space: Agda has very simple
rules for splitting text into tokens, so space is often necessary,
e.g., around \texttt{:} or \texttt{ ->}. It is my habit to use even
more space than is necessary for disambiguation, because I like to
keep things in alignment.
Speaking of alignment, we do have the similarity with Haskell that
indentation after \texttt{where} indicates subordination, showing that
the declarations of the \texttt{zero} and \texttt{suc} value
constructors belong to the declaration of the \texttt{Nat} type
constructor.
Another difference is that I have chosen to begin the names of
\texttt{zero} and \texttt{suc} in \emph{lower} case. Agda enforces no
typographical convention to distinguish constructors from other things,
so we can choose whatever names we like. It is conventional in Agda to
name data-like things in lower case and type-like things in upper case.
Crucially, \texttt{zero}, \texttt{suc}, \texttt{Nat} and \texttt{Set}
all live in the \emph{same} namespace. The distinction between different
kinds of things is achieved by referring back to their declaration, which
is the basis for the colour scheme in the emacs interface.
The declaration of \texttt{Nat} tells us exactly which values the new set
has. When we declare a function, we create new \emph{expressions} in a
type, but \emph{no new values}. Rather, we explain which value should
be returned for every possible combination of inputs.
\begin{verbatim}
-- Now we can say how to add numbers.
_+_ : Nat -> Nat -> Nat
zero + n = n
suc m + n = suc (m + n)
\end{verbatim}
What's in a name? When a name includes \emph{underscores}, they stand
for places you can put arguments in an application. The unspaced
\texttt{\_+\_} is the name of the function, and can be used as an
ordinary identifier in prefix notation, e.g. \texttt{\_+\_ m n} for
\texttt{m + n}. When we use \texttt{+} as an infix operator (with
arguments in the places suggested by the underscores), the spaces
around it are necessary. If we wrote \texttt{m+n} by accident, we would
find that it is treated as a whole other symbol.
Meanwhile, because there are no values in \texttt{Nat} other than
those built by \texttt{zero} and \texttt{suc}, we can be sure that
the definition of \texttt{+} covers all the possibilities for the
inputs. Moreover, or rather, lessunder, the recursive call in the
\texttt{suc} case has as its first argument a smaller number than
in the pattern on the left hand side, so the recursive call is
strictly simpler. Assuming (rightly, in Agda), that \emph{values}
are not recursive structures, we must eventually reach \texttt{zero},
so that every addition of values is bound to yield a value.
\begin{verbatim}
-- Now we can try adding some numbers.
four : Nat
four = (suc (suc zero)) + (suc (suc zero))
-- To make it go, select "Evaluate term to normal form" from the
-- Agda menu, then type "four", without the quotes, and press return.
-- Hopefully, you should get a response
-- suc (suc (suc (suc zero)))
\end{verbatim}
Evaluation shows us that although we have enriched our expression
language with things like $2+2$, the values in \texttt{Nat} are exactly
what we said they were: there are no new numbers, no error cases, no
`undefined's, no recursive black holes, just the values we declared.
That is to say, Agda is a language of \emph{total} programs. You can
approach it on the basis that things mean what they say, and---unusually
for programming languages---you will usually be right.
\section{Where are we going?}
Agda is a language honest, expressive and precise. We shall use it to
explore and model fundamental concepts in computation, working from
concrete examples to the general structures that show up time and time
again. We'll look at examples like parsers, interpreters, editors, and
servers. We'll implement algorithms like arithmetic, sorting, search
and unification. We'll see structures like monoids, functors, algebras
and monads. The purpose is not just to teach a new language for
instructing computers to do things, but to equip you with a deeper
perception of structure and the articulacy to exploit that structure.
Agda is a dependently typed language, meaning that types can mention
values and thus describe their intended properties directly. If we are
to be honest and ensure that we mean what we say, we had better be
able to say more precisely what we do mean. This is not intended to be
a course in dependently typed programming, although precision is
habit-forming, so a certain amount of the serious business is
inevitable. We'll also be in a position to state and prove that the
programs we write are in various ways sensible. What would it take to
convince you that the \texttt{+} operator we constructed above really
does addition?
I'm using Agda rather than Haskell for four reasons, two selfish, two
less so.
\begin{itemize}
\item I am curious to see what happens.
\item Using Agda brings my teaching a lot closer to my research and
obliges me to generate introductory material which will help
make this area more accessible. (The benefit for you is that I have
lots of motivation to write thorough notes.)
\item Agda's honesty will help us see things as they really are: we cannot
push trouble under the rug without saying what sort of rug it is.
Other languages are much more casual about run time failure or other
forms of external interaction.
\item Agda's editing environment gives strong and useful feedback during
the programming process, encouraging a type-centred method of development,
hopefully providing the cues to build good mental models of data and
computation. We do write programs with computers: we don't just type
them in.
\end{itemize}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
default : CS410.pdf
CS410.tex : CS410.lagda Introduction.lagda BasicPrelude.lagda EmacsCheatSheet.lagda Logic.lagda Razor.lagda
lhs2TeX --agda CS410.lagda > CS410.tex
CS410.aux : CS410.tex
latex CS410
CS410.blg : CS410.aux CS410.bib
bibtex CS410
CS410.dvi : CS410.tex CS410.blg
latex CS410
latex CS410
CS410.pdf : CS410.tex CS410.blg
pdflatex CS410
# Ex2
EX2=Ex2
REPLACE=replace
ex2: $(EX2).pdf
$(EX2).pdf: latex/$(EX2).tex
cd latex/ && \
latexmk -pdf -use-make $(EX2).tex && \
mv $(EX2).pdf ..
latex/%.tex: %.lagda
agda --allow-unsolved-metas -i . --latex $<
sed -f $(REPLACE).sed $@ > [email protected]
mv [email protected] $@ | {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module NBE where
open import Ex1Prelude
data Ty : Set where
base : Ty
_>>_ : Ty -> Ty -> Ty
data Cx : Set where
C0 : Cx
_/_ : Cx -> Ty -> Cx
infixl 4 _/_
infixl 3 _<:_
data _<:_ (T : Ty) : Cx -> Set where
zero : {G : Cx} -> T <: G / T
suc : {G : Cx}{S : Ty} -> T <: G -> T <: G / S
data Term (G : Cx) : Ty -> Set where
lam : {S T : Ty} ->
Term (G / S) T -> Term G (S >> T)
var : {S : Ty} -> S <: G -> Term G S
_$_ : {S T : Ty} -> Term G (S >> T) ->
Term G S -> Term G T
data Form : Set where normal neutral : Form
data Result (G : Cx) : Form -> Ty -> Set where
lam : {S T : Ty} ->
Result (G / S) normal T -> Result G normal (S >> T)
[_] : {T : Ty} -> Result G neutral T -> Result G normal T
var : {S : Ty} -> S <: G -> Result G neutral S
_$_ : {S T : Ty} -> Result G neutral (S >> T) ->
Result G normal S -> Result G neutral T
Renaming : Cx -> Cx -> Set
Renaming G G' = {T : Ty} -> T <: G -> T <: G'
pushRen : {G G' : Cx}{S : Ty} ->
Renaming G G' -> Renaming (G / S) (G' / S)
pushRen r zero = zero
pushRen r (suc x) = suc (r x)
Semantics : Cx -> Ty -> Set
Computing : Cx -> Ty -> Set
Semantics G T = Result G neutral T /+/ Computing G T
Computing G base = Zero
Computing G (S >> T) = {G' : Cx} -> Renaming G G' ->
Semantics G' S -> Semantics G' T
wkRes : {G G' : Cx}{f : Form} -> Renaming G G' -> {T : Ty} ->
Result G f T -> Result G' f T
wkRes r (lam t) = lam (wkRes (pushRen r) t)
wkRes r [ t ] = [ wkRes r t ]
wkRes r (var x) = var (r x)
wkRes r (f $ s) = wkRes r f $ wkRes r s
wkSem : {G G' : Cx} -> Renaming G G' -> (T : Ty) ->
Semantics G T -> Semantics G' T
wkSem r T (inl e) = inl (wkRes r e)
wkSem r base (inr ())
wkSem r (S >> T) (inr f) = inr \ r' -> f (r' o r)
Env : Cx -> Cx -> Set
Env G G' = {T : Ty} -> T <: G -> Semantics G' T
wkEnv : {G0 G1 G2 : Cx} -> Renaming G1 G2 -> Env G0 G1 -> Env G0 G2
wkEnv r g x = wkSem r _ (g x)
_//_ : {G G' : Cx}{T : Ty} -> Env G G' -> Semantics G' T ->
Env (G / T) G'
_//_ g v zero = v
_//_ g v (suc x) = g x
_$$_ : {G : Cx}{S T : Ty} -> Semantics G (S >> T) ->
Semantics G S -> Semantics G T
stop : {G : Cx}(S : Ty) -> Semantics G S -> Result G normal S
inl e $$ s = inl (e $ stop _ s)
inr f $$ s = f id s
stop base (inl e) = [ e ]
stop base (inr ())
stop (S >> T) v = lam (stop T
(wkSem suc (S >> T) v $$ inl (var zero)))
semantics : {G G' : Cx}{T : Ty} ->
({T : Ty} -> T <: G -> Semantics G' T) ->
Term G T -> Semantics G' T
semantics g (lam t) = inr \ r s -> semantics (wkEnv r g // s) t
semantics g (var x) = g x
semantics g (f $ s) = semantics g f $$ semantics g s
value : {G : Cx}{T : Ty} -> Term G T -> Result G normal T
value {G}{T} t = stop T (semantics (inl o var) t)
myTerm : Term (C0 / base) base
myTerm = lam (var zero $ (var zero $ var (suc zero))) $ lam (var zero)
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module FunctorKit where
open import BasicPrelude
record Functor (F : Set{-type of elements-} -> Set{-type of structures-})
: Set1 where
field
map : {S T : Set} -> (S -> T) {- operation on elements-}
-> F S -> F T {- operation on structures -}
mapI : {X : Set}(xs : F X) -> map id xs == xs
mapC : {R S T : Set}(f : S -> T)(g : R -> S)(xs : F R) ->
map f (map g xs) == map (f o g) xs
open Functor public
ListFunctor : Functor List
ListFunctor = record { map = mapList; mapI = mapIList; mapC = mapCList } where
mapList : {S T : Set} -> (S -> T) -> List S -> List T
mapList f [] = []
mapList f (x :> xs) = f x :> mapList f xs
mapIList : {X : Set} (xs : List X) -> mapList id xs == xs
mapIList [] = refl
mapIList (x :> xs) rewrite mapIList xs = refl
mapCList : {R S T : Set} (f : S -> T) (g : R -> S) (xs : List R) ->
mapList f (mapList g xs) == mapList (f o g) xs
mapCList f g [] = refl
mapCList f g (x :> xs) rewrite mapCList f g xs = refl
Label : Set -> (Set -> Set) -- no elements
Label A X = A
LabelFunctor : (A : Set) -> Functor (Label A)
LabelFunctor A = record
{ map = \ _ a -> a; mapI = \ _ -> refl; mapC = \ _ _ _ -> refl }
Id : Set -> Set -- one element
Id X = X
IdFunctor : Functor Id
IdFunctor = record {
map = id;
mapI = \ _ -> refl;
mapC = \ _ _ _ -> refl }
PairFunctor : {F G : Set -> Set} -> Functor F -> Functor G ->
Functor \ X -> F X /*/ G X
PairFunctor {F}{G} FunF FunG = record { map = mapP ; mapI = mapPI ; mapC = mapPC }
where
mapP : {S T : Set} -> (S -> T) -> (F S /*/ G S) -> (F T /*/ G T)
mapP f (xF , xG) = map FunF f xF , map FunG f xG
mapPI : forall {X : Set}(xs : F X /*/ G X) -> mapP id xs == xs
mapPI (xF , xG) rewrite mapI FunF xF | mapI FunG xG = refl
mapPC : {R S T : Set} (f : S -> T) (g : R -> S) (xs : F R /*/ G R) ->
mapP f (mapP g xs) == mapP (f o g) xs
mapPC f g (xF , xG) rewrite mapC FunF f g xF | mapC FunG f g xG = refl
SumFunctor : {F G : Set -> Set} -> Functor F -> Functor G ->
Functor \ X -> F X /+/ G X
SumFunctor {F}{G} FunF FunG = record { map = mapS ; mapI = mapSI; mapC = mapSC }
where
mapS : {S T : Set} -> (S -> T) -> (F S /+/ G S) -> (F T /+/ G T)
mapS f (inl xF) = inl (map FunF f xF)
mapS f (inr xG) = inr (map FunG f xG)
mapSI : {X : Set} (xs : F X /+/ G X) -> mapS id xs == xs
mapSI (inl xF) rewrite mapI FunF xF = refl
mapSI (inr xG) rewrite mapI FunG xG = refl
mapSC : {R S T : Set} (f : S -> T) (g : R -> S) (xs : F R /+/ G R) ->
mapS f (mapS g xs) == mapS (f o g) xs
mapSC f g (inl xF) rewrite mapC FunF f g xF = refl
mapSC f g (inr xG) rewrite mapC FunG f g xG = refl
data Kit : Set1 where
zeroK oneK : Kit
idK : Kit
dataK : Kit -> Kit
_*K_ : Kit -> Kit -> Kit
_+K_ : Kit -> Kit -> Kit
infixr 4 _+K_
infixr 5 _*K_
Fun : Kit -> Set -> Set
data DATA (f : Kit) : Set where
[_] : Fun f (DATA f) -> DATA f
Fun zeroK X = Zero
Fun oneK X = One
Fun idK X = Id X
Fun (dataK f) X = DATA f
Fun (f *K g) X = Fun f X /*/ Fun g X
Fun (f +K g) X = Fun f X /+/ Fun g X
FunFunctor : (f : Kit) -> Functor (Fun f)
FunFunctor zeroK = LabelFunctor Zero
FunFunctor oneK = LabelFunctor One
FunFunctor (dataK f) = LabelFunctor (DATA f)
FunFunctor idK = IdFunctor
FunFunctor (f *K g) = PairFunctor (FunFunctor f) (FunFunctor g)
FunFunctor (f +K g) = SumFunctor (FunFunctor f) (FunFunctor g)
twoK : Kit
twoK = oneK +K oneK
pattern true = [ inl <> ]
pattern false = [ inr <> ]
natK : Kit
natK = oneK +K idK
pattern ze = [ inl <> ]
pattern su n = [ inr n ]
toNatK : Nat -> DATA natK
toNatK zero = ze
toNatK (suc n) = su (toNatK n)
listK : Kit -> Kit
listK f = oneK +K (dataK f *K idK)
pattern nil = [ inl <> ]
pattern cons x xs = [ inr (x , xs) ]
treeK : Kit -> Kit
treeK f = oneK +K (idK *K dataK f *K idK)
leaf' : {f : Kit} -> DATA (treeK f)
pattern leaf = [ inl <> ]
leaf' = leaf
pattern node l x r = [ inr (l , x , r) ]
node' : {f : Kit} -> DATA (treeK f) -> DATA f -> DATA (treeK f) -> DATA (treeK f)
node' l x r = node l x r
leK : DATA natK -> DATA natK -> DATA twoK
leK ze n = true
leK (su m) ze = false
leK (su m) (su n) = leK m n
{-
noLabels : (f : Kit) -> DATA f -> Zero
noLabels' : (r f : Kit) -> Fun f (DATA r) -> Zero
noLabels' r idK x = noLabels r x
noLabels' r (f *K g) (xf , xg) = noLabels' r f xf
noLabels' r (f +K g) (inl x) = noLabels' r f x
noLabels' r (f +K g) (inr x) = noLabels' r g x
noLabels f [ x ] = noLabels' f f x
-}
{-
mysteryf : Kit
mysteryf = (labelK One) +K idK
MYSTERY : Set
MYSTERY = DATA mysteryf
{- -- ask Agsy to try making some elements of the MYSTERY type
mystery : MYSTERY
mystery = {!-l!} -- do [C-c C-a] with -l in the braces
-}
-- Aha! It's a copy of the natural numbers!
zeroM : MYSTERY
zeroM = [ inl <> ]
sucM : MYSTERY -> MYSTERY
sucM n = [ inr n ]
-- Now how about this...
treef : Set -> Kit
treef X = labelK One +K idK *K labelK X *K idK
pattern leaf = [ inl <> ]
pattern node l x r = [ inr (l , x , r) ]
flatten : {X : Set} -> DATA (treef X) -> List X
flatten leaf = []
flatten (node l x r) = flatten l ++ x :> flatten r
insert : Nat -> DATA (treef Nat) -> DATA (treef Nat)
insert n leaf = node leaf n leaf
insert n (node l x r) with n <= x
insert n (node l x r) | tt = node (insert n l) x r
insert n (node l x r) | ff = node l x (insert n r)
StuffINeed : Kit -> Set
StuffINeed (labelK A) = A -> A -> Two
StuffINeed idK = One
StuffINeed (f *K g) = StuffINeed f /*/ StuffINeed g
StuffINeed (f +K g) = StuffINeed f /*/ StuffINeed g
-}
kitEq : {f : Kit} -> DATA f -> DATA f -> DATA twoK
nodeEq : (r f : Kit) -> Fun f (DATA r) -> Fun f (DATA r) -> DATA twoK
nodeEq r zeroK () y
nodeEq r oneK <> <> = true
nodeEq r idK x y = kitEq x y -- here's where r is used
nodeEq r (dataK f) x y = kitEq x y
nodeEq r (f *K g) (xf , xg) (yf , yg) with nodeEq r f xf yf | nodeEq r g xg yg
nodeEq r (f *K g) (xf , xg) (yf , yg) | true | true = true
nodeEq r (f *K g) (xf , xg) (yf , yg) | qf | qg = false
nodeEq r (f +K g) (inl x) (inl y) = nodeEq r f x y
nodeEq r (f +K g) (inl x) (inr y) = false
nodeEq r (f +K g) (inr x) (inl y) = false
nodeEq r (f +K g) (inr x) (inr y) = nodeEq r g x y
kitEq {f} [ x ] [ y ] = nodeEq f f x y
delOne : Kit -> Kit
delOne zeroK = zeroK
delOne oneK = zeroK
delOne idK = oneK
delOne (dataK f) = zeroK
delOne (f *K g) = delOne f *K g +K f *K delOne g
delOne (f +K g) = delOne f +K delOne g
{-
nodeEq r sr (labelK A) s a a' = s a a'
nodeEq r sr idK s x y = kitEq sr x y
nodeEq r sr (f *K g) (sf , sg) (xf , xg) (yf , yg)
with nodeEq r sr f sf xf yf | nodeEq r sr g sg xg yg
nodeEq r sr (f *K g) (sf , sg) (xf , xg) (yf , yg) | tt | tt = tt
nodeEq r sr (f *K g) (sf , sg) (xf , xg) (yf , yg) | qf | qg = ff
nodeEq r sr (f +K g) s (inl xf) (inl yf) = nodeEq r sr f (outl s) xf yf
nodeEq r sr (f +K g) s (inl xf) (inr yg) = ff
nodeEq r sr (f +K g) s (inr xg) (inl yf) = ff
nodeEq r sr (f +K g) s (inr xg) (inr yg) = nodeEq r sr g (outr s) xg yg
kitEq {f} s [ x ] [ y ] = nodeEq f s f s x y
myGo : Two
myGo = kitEq ((\ _ _ -> tt) , _) (sucM (sucM (sucM zeroM))) (sucM (sucM (sucM zeroM)))
-} | {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex3Sol where
{- Mark Scheme
3.1 is work 3; 3.2 is worth 4; 3.3 is worth 3; 3.4 is worth 5
The total number of marks available is 15.
See below for individual mark breakdown.
-}
open import Ex1Prelude
open import FuncKit
{- 3.1 Numbers in the Kit (3 marks) -}
{- We can define the type of natural numbers using the tools
from the functor kit like this: -}
kNat : Kit
kNat = kK One k+ kId
NAT : Set
NAT = Data kNat
-- Define the function which sends "ordinary" numbers to
-- the corresponding kit-encoded numbers. (1 mark)
Nat2NAT : Nat -> NAT
Nat2NAT zero = [ inl <> ]
Nat2NAT (suc n) = [ inr (Nat2NAT n) ]
-- Use fold to define the function which sends them back. (1 mark)
NAT2Nat : NAT -> Nat
NAT2Nat = fold (kK One k+ kId) (\
{ (inl <>) -> zero
; (inr NAT2Nat_n) -> suc NAT2Nat_n
})
-- Show that you get the "round trip" property (by writing
-- recursive functions that use rewrite. (1 mark)
Nat2NAT2Nat : NAT2Nat o Nat2NAT =^= id
Nat2NAT2Nat zero = refl
Nat2NAT2Nat (suc n) rewrite Nat2NAT2Nat n = refl
NAT2Nat2NAT : Nat2NAT o NAT2Nat =^= id
NAT2Nat2NAT [ inl <> ] = refl
NAT2Nat2NAT [ inr x ] rewrite NAT2Nat2NAT x = refl
{- 3.2 Lists in the Kit (4 marks) -}
-- find the code which gives you lists with a given element
-- type (note that the kId constructor marks the place for
-- recursive *sublists* not for list elements (1 mark)
kLIST : Set -> Kit
kLIST A = kK One k+ (kK A k* kId)
LIST : Set -> Set
LIST A = Data (kLIST A)
-- define nil and cons for your lists (1 mark)
nil : {A : Set} -> LIST A
nil = [ inl <> ]
cons : {A : Set} -> A -> LIST A -> LIST A
cons a as = [ inr (a , as) ]
-- use fold to define concatenation (1 mark)
conc : {A : Set} -> LIST A -> LIST A -> LIST A
conc {A} xs ys = fold (kLIST A)
(\ { (inl <>) -> ys
; (inr (a , conc_as_ys)) -> cons a conc_as_ys
})
xs
-- prove the following (the yellow bits should disappear when
-- you define kLIST); (1 mark)
-- maddeningly, "rewrite" won't do it, but this piece of kit
-- (which is like a manual version of rewrite) will do it
cong : {S T : Set}(f : S -> T){a b : S} -> a == b -> f a == f b
cong f refl = refl
concNil : {A : Set}(as : LIST A) -> conc as nil == as
concNil [ inl <> ] = refl
concNil [ inr (a , as) ] = cong (cons a) (concNil as)
concAssoc : {A : Set}(as bs cs : LIST A) ->
conc (conc as bs) cs == conc as (conc bs cs)
concAssoc [ inl <> ] bs cs = refl
concAssoc [ inr (a , as) ] bs cs = cong (cons a) (concAssoc as bs cs)
{- 3.3 Trees in the Kit (3 marks) -}
-- give a kit code for binary trees with unlabelled leaves
-- and nodes labelled with elements of NAT (1 mark)
kTREE : Kit
kTREE = kK One k+ (kId k* (kK NAT k* kId))
TREE : Set
TREE = Data kTREE
-- give the constructors (1 mark)
leaf : TREE
leaf = [ inl <> ]
node : TREE -> NAT -> TREE -> TREE
node l n r = [ inr (l , n , r) ]
-- implement flattening (slow flattening is ok) as a fold (1 mark)
flatten : TREE -> LIST NAT
flatten = fold kTREE (\
{ (inl <>) -> nil
; (inr (flatten_l , n , flatten_r)) -> conc flatten_l (cons n flatten_r)
})
{- 3.4 "rec" from "fold" (5 marks) -}
-- The recursor is a variation on the theme of fold, but you
-- get a wee bit more information at each step. In particular,
-- in each recursive position, you get the original substructure
-- *as well as* the value that is computed from it.
rec : (k : Kit){X : Set} ->
(kFun k (Data k /*/ X) -> X) ->
-- ^^^^^^ ^
-- substructure value
Data k -> X
-- Demonstrate that rec is no more powerful than fold by constructing
-- rec from fold. The trouble is that fold throws away the original
-- substructures. But you can compensate by computing something extra
-- as well as the value you actually want. (1 mark)
rec k {X} f d = outr (fold k {Data k /*/ X}
(\ kdx -> [ kitMap k outl kdx ] , f kdx) d)
-- use rec to implement "insList", being the function which inserts
-- a number in a list, such that if the input list is in increasing
-- order, so is the output list; you may assume that "lessEq" exists (1 mark)
lessEq : NAT -> NAT -> Two
insList : NAT -> LIST NAT -> LIST NAT
insList n = rec (kLIST NAT) (\
{ (inl <>) -> cons n nil
; (inr (a , (as , insList_n_as))) ->
if lessEq n a
then cons n (cons a as)
else cons a insList_n_as
})
-- justify the assumption by defining "lessEq"; do not use explicit
-- recursion; do use "rec kNat" once more to take numbers apart
-- (2 marks, one for each "rec")
lessEq x y = rec kNat {NAT -> Two}
(\ { (inl <>) -> \ y -> {- lessEq zero y -} tt
; (inr (x , lessEq_x)) -> rec kNat (\
{ (inl <>) -> {- lessEq (suc x) zero -} ff
; (inr (y , lessEq_[suc_x]_y)) -> {- lessEq (suc x) (suc y) -} lessEq_x y
})
})
x y
-- implement insertion for binary search trees using "rec" (1 mark)
insTree : NAT -> TREE -> TREE
insTree n = rec kTREE (\
{ (inl <>) -> node leaf n leaf
; (inr ((l , insTree_n_l) , y , (r , insTree_n_r))) ->
if lessEq n y then node insTree_n_l y r else node l y insTree_n_r
})
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module IxCon where
open import Ex1Prelude
record Sigma (S : Set)(T : S -> Set) : Set where
constructor _,_
field
fst : S
snd : T fst
open Sigma public
record _=>_ (I J : Set) : Set1 where
constructor _<!_/_
field
Command : J -> Set
Response : (j : J) -> Command j -> Set
next : (j : J)(c : Command j) -> Response j c -> I
open _=>_ public
_-:>_ : {I : Set}(S T : I -> Set) -> Set
S -:> T = {i : _} -> S i -> T i
record FunctorIx (I J : Set) : Set1 where
field
FObj : (I -> Set) -> J -> Set
FArr : {S T : I -> Set} -> (S -:> T) -> FObj S -:> FObj T
open FunctorIx public
[[_]] : {I J : Set} -> I => J -> FunctorIx I J
[[ Command <! Response / next ]] = record
{ FObj = \ Goal j -> Sigma (Command j) \ c -> (r : Response j c) -> Goal (next j c r)
; FArr = \ { f {j} (c , k) -> c , (\ r -> f (k r)) }
}
data Game {I : Set}(C : I => I)(Win : I -> Set)(i : I) : Set where
win : Win i -> Game C Win i
<_> : FObj [[ C ]] (Game C Win) i -> Game C Win i
VCon : Set -> (Nat => Nat)
VCon A = (\ { zero -> Zero ; (suc n) -> A })
<! (\ _ _ -> One)
/ \ { zero () _
; (suc n) a <> -> n
}
Vector : Set -> Nat -> Set
Vector A n = Game (VCon A) (\ { zero -> One ; (suc n) -> Zero }) n
vnil : {A : Set} -> Vector A zero
vnil = win <>
vcons : {A : Set}{n : Nat} -> A -> Vector A n -> Vector A (suc n)
vcons a as = < a , (\ { <> -> as }) >
data Bound : Set where
bot : Bound
# : Nat -> Bound
top : Bound
TGame : (Bound /*/ Bound) => (Bound /*/ Bound)
TGame = (\ _ -> Nat) <! (\ _ _ -> Two)
/ (\ { (l , u) n tt -> (l , # n)
; (l , u) n ff -> (# n , u)
})
Le : Nat -> Nat -> Set
Le zero y = One
Le (suc x) zero = Zero
Le (suc x) (suc y) = Le x y
LeB : Bound /*/ Bound -> Set
LeB (bot , _) = One
LeB (# x , # y) = Le x y
LeB (_ , top) = One
LeB _ = Zero
MyTree : Set
MyTree = Game TGame LeB (bot , top)
leaf : {l u : Bound} -> LeB (l , u) -> Game TGame LeB (l , u)
leaf = win
node : {l u : Bound}(n : Nat) -> Game TGame LeB (l , # n) -> Game TGame LeB (# n , u) ->
Game TGame LeB (l , u)
node n ln nu = < n , (\ { tt -> ln ; ff -> nu }) >
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module L1 where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
{-# BUILTIN NATURAL Nat #-}
-- data Nat = Zero | Suc Nat
_+_ : Nat -> Nat -> Nat
zero + y = y
suc x + y = suc (x + y)
data List (X : Set) : Nat -> Set where
[] : List X zero
_,_ : forall {n} -> X -> List X n -> List X (suc n)
_++_ : forall {X m n} -> List X m -> List X n -> List X (m + n)
[] ++ ys = ys
(x₁ , x₂) ++ ys = x₁ , (x₂ ++ ys)
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex2 where
{-----------------------------------------------------------------------------
Name:
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
CS410 Exercise 2, due 5pm on Monday of Week 6 (3 November 2014)
NOTE: I am well aware that week 6 is quite busy with deadlines,
what with CS408-related obligations and so on. I'd much prefer
you did things to the best of your ability rather than on time,
so I would be sympathetic to requests for some flexibility.
Still, your best bet is to make an early start rather than a
late finish.
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
This exercise is based around extending Hutton's razor with Boolean
values and conditional expressions. By introducing a second value
type, we acquire the risk of type mismatch. The idea here is to
explore different approaches to managing that risk.
-----------------------------------------------------------------------------}
open import Ex1Prelude
open import Ex2Prelude
{- The extended Hutton's Razor syntax -}
data HExpIf : Set where
num : Nat -> HExpIf
boo : Two -> HExpIf
_+++_ : HExpIf -> HExpIf -> HExpIf
hif_then_else_ : HExpIf -> HExpIf -> HExpIf -> HExpIf
{- Note that an expression
hif eb then ex1 else ex2
makes sense only when
* eb produces a Boolean value
* ex1 and ex2 produce the same sort of value (numeric or Boolean)
-}
HValIf : Set
HValIf = Two /+/ Nat
{- We now have the risk of run time type errors. Let's introduce a type
for things which can go wrong. -}
data Error (E X : Set) : Set where
ok : X -> Error E X
error : E -> Error E X
{- 2.1 Add a constructor to the following datatype for each different
kind of run time error that can happen. (Come back to this exercise
when you're writing the evaluator in 2.3.) Make these error reports
as informative as you can.
-}
data EvalError : Set where
-- your constructors here
{- 2.2 Write a little piece of "glue code" to make it easier to manage
errors. The idea is to combine error-prone process in *sequence*, where
the second process can depend on the value produced by the first if it
succeeds. The resulting process is, of course, also error-prone, failing
as soon as either component fails.
-}
_>>=_ : {E S T : Set}
-> Error E S -- process which tries to get an S
-> (S -> Error E T) -- given an S, process which tries for a T
-> Error E T -- combined in sequence
es >>= s2et = {!!}
{- 2.3 Implement an evaluator for HExpIf. Be sure to add only numbers and
to branch only on Booleans. Report type mismatches as errors. You should
use _>>=_ to help with the propagation of error messages.
-}
eval : HExpIf -> Error EvalError HValIf
eval e = {!!}
{- Note that the type of eval is not specific about whether the value
expected is numeric or Boolean. It may help to introduce auxiliary
definitions of error-prone processes which are "ok" only for the
type that you really want.
-}
{- Next up, stack machine code, and its execution. -}
data HBCode : Set where
PUSHN : Nat -> HBCode
PUSHB : Two -> HBCode
ADD : HBCode
_SEQ_ : HBCode -> HBCode -> HBCode
_IFPOP_ : HBCode -> HBCode -> HBCode
{- The intended behaviour of (t IFPOP f) is as follows
* pop the (we hope) Boolean value from top of stack
* if it's tt, execute t, else execute f
* whichever branch is executed, it gets the popped stack to start
-}
{- 2.4 Populate the type of possible execution errors and implement the
execution behaviour of HBCode, operating on a stack represented as
a list of HValIf values.
-}
data ExecError : Set where
-- your constructors here
exec : HBCode -> List HValIf -> Error ExecError (List HValIf)
exec c s = {!!}
{- Next, we take a look at code generation and type safety. -}
data HTy : Set where -- we have two types in HExpIf
NUM BOOL : HTy
_=HTy=_ : HTy -> HTy -> Two -- we can test if two types are equal
NUM =HTy= NUM = tt
NUM =HTy= BOOL = ff
BOOL =HTy= NUM = ff
BOOL =HTy= BOOL = tt
{- 2.5 Write a type-synthesizing compiler, computing both the HTy type and
the HBCode executable for a given expression. Your compiler should
give an informative error report if the expression it receives is
ill typed. Your compiler should also ensure (at least informally) that
the code produced will never trigger any execution errors.
-}
data CompileError : Set where
-- your constructors here
compile : HExpIf -> Error CompileError (HTy /*/ HBCode)
compile (num x) = {!!}
compile (boo x) = {!!}
compile (e1 +++ e2) = compile e1 >>= \
{ (BOOL , c1) -> error {!!}
; (NUM , c1) -> {!!}
}
compile (hif e then e₁ else e₂) = {!!}
{- You have a little bit more room for creative problem-solving in what's
left of the exercise. The plan is to build the type system into expressions
and code, the same way we did with plain Hutton's Razor in class.
-}
{- If we *know* which HTy type we want, we can compute which Agda type we
expect our value to take. -}
HVal : HTy -> Set
HVal NUM = Nat
HVal BOOL = Two
{- 2.6 Finish the type of typed expressions. You should ensure that only
well HTy-typed expressions can be constructed. -}
data THExpIf : HTy -> Set where
val : {t : HTy} -> HVal t -> THExpIf t
-- you fill in addition and if-then-else
{- 2.7 Implement a type-safe evaluator. -}
teval : {t : HTy} -> THExpIf t -> HVal t
teval e = {!!}
{- 2.8 Implement a type checker. -}
data TypeError : Set where
-- your constructors here
tcheck : (t : HTy) -> HExpIf -> Error TypeError (THExpIf t)
tcheck t e = {!!}
{- 2.9 Adapt the technique from Hutton.agda to give a type-safe underflow-free
version of HBCode. You will need to think what is a good type to represent
the "shape" of a stack: before, we just used Nat to represent the *height* of
the stack, but now we must worry about types. See next question for a hint. -}
data THBCode : {- your indices here -} Set where
-- your constructors here
{- 2.10 Implement the execution semantics for your code. You will need to think
about how to represent a stack. The Ex2Prelude.agda file contains a very
handy piece of kit for this purpose. You write the type, too. -}
-- your code here
{- 2.11 Write the compiler from well typed expressions to safe code. -}
tcompile : {t : HTy} -> THExpIf t -> {!!}
tcompile e = {!!}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
\chapter{Logic via Types}
The inescapable honesty of Agda makes it possible for us to
treat values as \emph{evidence} for something. We gain a
logical interpretation of types.
%format Logic = "\M{Logic}"
\begin{code}
module Logic where
open import BasicPrelude
\end{code}
One way of looking at logical formulae is to consider what constitutes
evidence that they hold. We can look at the connectives systematically.
What constitutes `evidence for A or B'? Either `evidence for A'
or `evidence for B'. If we have a type, |A|, representing `evidence for A'
and another, |B| representing `evidence for B', then |A /+/ B| represents
`evidence for A or B'.
What constitutes `evidence for A and B'? We need both `evidence for A'
and `evidence for B'. If we have a type, |A|, representing `evidence for A'
and another, |B| representing `evidence for B', then |A /*/ B| represents
`evidence for A and B'.
What constitutes `evidence that A implies B'? We need to be sure that,
given `evidence for A', we can produce `evidence for B'. If we have a
type, |A|, representing `evidence for A' and another, |B| representing
`evidence for B', then |A -> B| represents `evidence for A and B'.
There will be more to say here, after exercise 1 is completed, but the basic
message is:
\begin{center}
propositions are types; types are propositions\\
proofs are programs; programs are proofs
\end{center}
Types like |Nat| are rather boring propositions. Types like |2 + 2 == 4| are
slightly more interesting.
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex4Tut where
{- I'm sorry I haven't quite finished setting this exercise yet, but by
the joy of version control, the rest of it can be merged in later
(quite soon). At least you can get cracking: I promise not to break
anything, just to add a bit more on the end.
The deadline for this is midnight on the Monday of Week 12 (15 Dec).
It'd be good to get the marks in before Christmas, but if the end of
term is looking deadlinetastic, please open negotiations.
-}
open import Ex1Prelude
open import IxCon
_>>=_ : {I : Set}{CRn : I => I}{A B : I -> Set} ->
{i : I} -> Game CRn A i ->
({i' : I} -> A i' -> Game CRn B i') ->
Game CRn B i
_>>=_ (win a) a2gb = a2gb a
_>>=_ < c , k > a2gb = < c , (\ r -> k r >>= a2gb) >
{-# BUILTIN BOOL Two #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #-}
{-# BUILTIN CONS _:>_ #-}
postulate -- this means that we just suppose the following things exist...
Char : Set
String : Set
{-# BUILTIN CHAR Char #-}
{-# BUILTIN STRING String #-}
primitive -- these are baked in; they even work!
primCharEquality : Char -> Char -> Two
primStringAppend : String -> String -> String
primStringToList : String -> List Char
primStringFromList : List Char -> String
---------------------------------------------------------------------------
-- WRITING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- If you possess the ability to open a file for writing, you might
have the following interface. -}
-- States
data WriteState : Set where
opened closed : WriteState -- do you currently have a file open or not?
-- Commands
data WriteC : WriteState -> Set where
openWrite : (fileName : String) -> WriteC closed
writeChar : Char -> WriteC opened
closeWrite : WriteC opened
-- Responses
WriteR : (j : WriteState)(c : WriteC j) -> Set
WriteR .closed (openWrite fileName) = WriteState -- we get told whether it worked
WriteR .opened (writeChar x) = One -- always works
WriteR .opened closeWrite = One -- always works
{- 4.1 Implement the following operation which determines the next
state. You should ensure that you can write characters only to
a successfully opened file, and that you can write as many as
you want. It should also be possible to insist that a process
closes its file. -}
writeNext : (j : WriteState)(c : WriteC j) -> WriteR j c -> WriteState
writeNext j c r = {!!}
-- the file writing interface, assembled as an indexed container
WRITE : WriteState => WriteState
WRITE = WriteC <! WriteR / writeNext
---------------------------------------------------------------------------
-- READING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- To read from a file, it should be open, and you shouldn't be at the
end of it. -}
-- States
data ReadState : Set where
opened : (eof : Two) -> ReadState -- eof is tt if we're at end of file
closed : ReadState
{- 4.2 Finish the READ implementation, in accordance with the description. -}
-- Commands
data ReadC : ReadState -> Set where
openRead : {- your stuff -} ReadC {!!} -- needs a filename; might not open successfully;
-- might open an empty file
readChar : {- your stuff -} ReadC {!!} -- makes sense only if we're not at end of file
-- and might take us to end of file
closeRead : {- your stuff -} ReadC {!!} -- makes sense only if the file is open
-- Responses
ReadR : (j : ReadState)(c : ReadC j) -> Set
ReadR j c = {!!}
-- next State; you need to make sure the response gives enough info
readNext : (j : ReadState)(c : ReadC j) -> ReadR j c -> ReadState
readNext j c r = {!!}
READ : ReadState => ReadState
READ = ReadC <! ReadR / readNext
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SHARED STATE
---------------------------------------------------------------------------
{- 4.3 Let's suppose we have two command-response interfaces which offer
different functionality for the same system. Correspondingly, we'll
have two indexed containers for the same index set. Show that you
can combine them into one indexed container which lets you choose a
command from either menu and evolves the state as specified by
whichever interface offered the chosen command.
-}
_=+=_ : {I : Set} -> I => I -> I => I -> I => I
CRn0 =+= CRn1 = {!!}
---------------------------------------------------------------------------
-- WHEN IGNORANCE IS BLISS, BIS
---------------------------------------------------------------------------
{- 4.4 If we have a command-response interface with index I representing
states of the system, show that we can index basically the same
commands and responses over a state, I /*/ J, where the J is just
useless information which never changes. (This operation isn't
super-useful on its own, but it's handy in combination with other
things. -}
GrowR : {I J : Set} -> I => I -> (I /*/ J) => (I /*/ J)
GrowR CRn = {!!}
-- do the same for "growing the index on the left"
GrowL : {I J : Set} -> I => I -> (J /*/ I) => (J /*/ I)
GrowL CRn = {!!}
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SEPARATE STATE
---------------------------------------------------------------------------
{- 4.5 Making use of 4.4 and 4.5, show how to combine two interfaces which
operate independently on separate state: commands from one should
not affect the state of the other.
-}
_<+>_ : {I0 I1 : Set} -> I0 => I0 -> I1 => I1 -> (I0 /*/ I1) => (I0 /*/ I1)
CRn0 <+> CRn1 = {!!}
---------------------------------------------------------------------------
-- ERROR REPORTING, AN INTERFACE
---------------------------------------------------------------------------
{- I'm building the next bit for you.
When things go wrong, we need to trigger an error condition and abort
mission. However, if we have other stuff going on (open files, etc),
it may not always be ok to drop everything and run away. There will
be some states in which it is safe to escape (and deliver a suitable
error message, perhaps) and other states in which escape should be
impossible.
If it is safe to issue an error message, we should be able to do so
without fear of any response from the environment that would oblige
us to carry on.
-}
data ErrorC {I : Set}(SafeMessage : I -> Set)(i : I) : Set where
error : SafeMessage i -> ErrorC SafeMessage i
-- the SafeMessage parameter tells us what is an acceptable
-- error message in any given state; in states where this gives
-- Zero, it will be impossible to trigger an error!
ErrorR : {I : Set}{SafeMessage : I -> Set}(i : I)(c : ErrorC SafeMessage i) -> Set
ErrorR _ _ = Zero -- there's no comeback
errorNext : {I : Set}{SafeMessage : I -> Set}
(i : I)(c : ErrorC SafeMessage i) -> ErrorR i c -> I
errorNext i c () -- so we don't have to say how the state will evolve
ERROR : {I : Set}(SafeMessage : I -> Set) -> I => I
ERROR SafeMessage = ErrorC SafeMessage <! ErrorR / errorNext
---------------------------------------------------------------------------
-- COPY A FILE
---------------------------------------------------------------------------
{- 4.6 Implement a process which, given access to suitable interfaces, will
give the process for copying a named source file to a named target
file. This goes in two phases.
-}
{- 4.6.1 Firstly, you should identify the command-reponse interface within
which you need to work. You will need to be able to read and write files,
but also to signal errors (in case a file fails to open for some reason).
You must ensure that it is impossible for any process using your interface
to escape with an error leaving a file open. You must also make it
possible to guarantee that your copying process will, error or not, leave
all files closed.
-}
CPState : Set
CPState = {!!}
CPInterface : CPState => CPState
CPInterface = {!!}
{- 4.6.2 Secondly, you should implement your copying process, working to your
interface. I will let you switch off the termination checker: you cannot
predict in advance how long the copying process will go on, as you have
not seen the source file yet. (Later, we'll learn how to be honest about
things which might go on for ever, but for now, let's cheat.)
-}
{-# NO_TERMINATION_CHECK #-}
cp : (sourceFile targetFile : String) -> Game CPInterface {!!} {!!}
cp sourceFile targetFile = {!!}
{- HINTS
You will certainly need to build some extra bits and pieces.
You have the components for reading, writing and error handling, and
suitable kit with which to combine them. Reading and writing don't
interfere with each other, but it's important to make sure that you
can't bomb out with an error, so some shared state seems important.
There are really two phases to the process:
(1) getting the files open -- this may go wrong
(2) copying from one to the other -- this will work if we reach it
You might want to split these phases apart.
-}
---------------------------------------------------------------------------
-- SCRIPTING INTERACTION
---------------------------------------------------------------------------
{- 4.7.1 Show how to take a command-response interface and deliver its
"scripted" version, where a script command consists of any permitted
(possibly empty) sequence of the given commands. -}
SCRIPT : {I : Set} -> I => I -> I => I
SCRIPT {I} CRn = Game CRn (\ I -> One) <! Rs / ns where
Rs : (i : I) -> Game CRn (\ I -> One) i -> Set
Rs i cs = {!!}
ns : (i : I)(cs : Game CRn (\ I -> One) i) -> Rs i cs -> I
ns i cs rs = {!!}
{- 4.7.2 Show how to take a strategy for scripted interaction and turn
it into a strategey for unscripted interaction, by running the scripts
one command at a time. You may find it useful to build a helper function
to process one script. -}
unScript : {I : Set}(CRn : I => I){X : I -> Set}{i : I} ->
Game (SCRIPT CRn) X i -> Game CRn X i
unScript CRn g = {!!}
-- HINT doing recursion in the "fold" pattern may help
---------------------------------------------------------------------------
-- INDEXED CONTAINER DRIVERS(*)
-- (*) The researchers who invented this stuff are fans of The Fall
-- (by which I mean the group led my Mark E Smith who wrote the song
-- The Container Drivers, not some johnny-come-lately Northern Irish
-- serial killer drama).
---------------------------------------------------------------------------
record Driver {I J : Set}(Sync : I -> J -> Set)
(Hi : I => I)(Lo : J => J) : Set where
-- Hi is a high-level command-response interface
-- Lo is a low-level command-response interface
-- Sync specifies which high and low level states are compatible
-- and what you expect to know at the time
field
-- assuming states are in sync; it should be possible to map
-- high-level commands to low-level commands...
hiClo : (i : I)(j : J) -> Sync i j ->
Command Hi i -> Command Lo j
-- ...and afterwards to translate the low-level response to that
-- command back up to the high-level
loRhi : (i : I)(j : J)(s : Sync i j)(c : Command Hi i) ->
Response Lo j (hiClo i j s c) -> Response Hi i c
-- moreover, the resulting states should be in sync
nSync : (i : I)(j : J)(s : Sync i j)(c : Command Hi i)
(r : Response Lo j (hiClo i j s c)) ->
Sync (next Hi i c (loRhi i j s c r)) (next Lo j (hiClo i j s c) r)
open Driver public
---------------------------------------------------------------------------
-- A DANGEROUS HASKELL IO COMMAND-RESPONSE SYSTEM
---------------------------------------------------------------------------
data Maybe (X : Set) : Set where
yes : X -> Maybe X
no : Maybe X
data IOMode : Set where
readMode writeMode appendMode readWriteMode : IOMode
postulate Handle : Set
data HaskellIOCommand (_ : One) : Set where
hOpen : String -> IOMode -> HaskellIOCommand <>
hClose hIsEOF hGetChar : Handle -> HaskellIOCommand <>
hPutChar : Handle -> Char -> HaskellIOCommand <>
hError : String -> HaskellIOCommand <>
HaskellIOResponse : (i : One) -> HaskellIOCommand i -> Set
HaskellIOResponse i (hOpen f m) = Maybe Handle
HaskellIOResponse i (hClose h) = One
HaskellIOResponse i (hIsEOF h) = Two
HaskellIOResponse i (hGetChar h) = Char
HaskellIOResponse i (hPutChar h c) = One
HaskellIOResponse i (hError e) = Zero
HASKELLIO : One => One
HASKELLIO = HaskellIOCommand <! HaskellIOResponse / _
---------------------------------------------------------------------------
-- SCRIPTING INTERACTION
---------------------------------------------------------------------------
{- 4.8 Your mission is to translate your lovely, safe characterisation
of reading and writing into its dodgy Haskell counterpart. Of course,
your code shouldn't do anything dodgy. You will need to think what
information must be available when you are in each state.
-}
safe2unsafe : Driver (\ i j -> {!!}) CPInterface (SCRIPT HASKELLIO)
safe2unsafe = {!!}
---------------------------------------------------------------
-- TO BE CONTINUED... BUT NOT WITH ANY MORE CODING OBLIGATIONS
---------------------------------------------------------------
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
\chapter{Agda Mode Cheat Sheet}
I use standard emacs keystroke descriptions. E.g., `C-c' means control-c.
I delimit keystrokes with square brackets, but don't type the brackets or the
spaces between the individual key descriptions.
\section{Managing the buffer}
\subsection*{[C-c C-l] load buffer}
This keystroke tells Agda to resynchronize with the buffer contents, typechecking
everything. It will also make sure everything is displayed in the correct colour.
\subsection*{[C-c C-x C-d] deactivate goals}
This keystroke deactivates Agda's goal machinery.
\subsection*{[C-c C-x C-r] restart Agda}
This keystroke restarts Agda.
\section{Working in a goal}
The following apply only when the cursor is sitting inside the braces of a goal.
\subsection*{[C-c C-,] what's going on?}
If you select a goal and type this keystroke, the information buffer
will tell you the type of the goal and the types of everything in the
context. Some things in the context are not in scope, because you
haven't bound them with a name anywhere. These show up with names
Agda chooses, beginning with a dot: you cannot refer to these things,
but they do exist.
\subsection*{[C-c C-.] more on what's going on?}
This is a variant of the above which in addition also shows you the type
of the expression currently typed into the hole. This is useful for
trying different constructions out before giving/refining them!
\subsection*{[C-c C-spc] give expression}
If you think you know which expression belongs in a goal, type the expression
between its braces, then use this keystroke. The expression can include |?|
symbols, which become subgoals.
\subsection*{[C-c C-c] case split}
If your goal is immediately to the right of |=|, then you're still building your
program's decision tree, so you can ask for a case analysis. Type the name of
a variable in the goal, then make this keystroke. Agda will try to split that
variable into its possible constructor patterns. Amusingly, if you type several
variables names and ask for a case analysis, you will get all the possible
combinations from splitting each of the variables.
\subsection*{[C-c C-r] refine}
If there's only one constructor which fits in the hole, Agda deploys
it. If there's a choice, Agda tells you the options.
\subsection*{[C-c C-a] ask Agsy (a.k.a. I feel lucky)}
If you make this keystroke, Agda will use a search mechanism called
`Agsy' to try and guess something with the right type. Agsy may not
succeed. Even if it does, the guess may not be the right answer.
Sometimes, however, there's obviously only one sensible thing to do,
and then Agsy is your bezzy mate! It can be an incentive to make your
types precise!
\section{Checking and Testing things}
\subsection*{[C-c C-d] deduce type of expression}
If you type this keystroke, you will be prompted for an expression. If
the expression you supply makes sense, you will be told its type.
If you are working in a goal and have typed an expression already, Agda will
assume that you want the type of that expression.
\subsection*{[C-c C-n] normalize expression}
If you type this keystroke, you will be prompted for an expression. If
the expression you supply makes sense, you will be told its value.
If you are working in a goal and have typed an expression already, Agda will
assume that you want to normalize (i.e. compute as far as possible)
that expression. The normal form might not be a value, because there
might be some variables in your expression, getting in the way of
computation. When there are no free variables present, the normal form
is sure to be a value.
\section{Moving around}
\subsection*{[C-c C-f]/[C-c C-b] move to next/previous goal}
A quick way to get to where the action is to use these two keystrokes,
which takes you to the next and previous goal respectively.
\subsection*{[M-.] go to definition}
If you find yourself wondering what the definition of some identifier
is, then you can put the cursor at it and use this keystroke -- it will
make Agda take you there.
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Zipper where
open import Ex1Prelude
open import FuncKit
data Tree (X : Set) : Set where
leaf : Tree X
_<[_]>_ : Tree X -> X -> Tree X -> Tree X
data Context (X : Set) : Set where
root : Context X
lefty : Context X -> X -> Tree X -> Context X
righty : Tree X -> X -> Context X -> Context X
data Layer (X : Set) : Set where
lefty : One -> X -> Tree X -> Layer X
righty : Tree X -> X -> One -> Layer X
-- take Context X = List (Layer X)
TreeZipper : Set -> Set
TreeZipper X = Context X /*/ Tree X
getOutHelp : {X : Set} -> Context X -> Tree X -> Tree X
getOutHelp root t = t
getOutHelp (lefty c x r) t = getOutHelp c (t <[ x ]> r)
getOutHelp (righty l x c) t = getOutHelp c (l <[ x ]> t)
getOut : {X : Set} -> TreeZipper X -> Tree X
getOut (c , t) = getOutHelp c t
{- -- termination checker says no
getOut (root , t) = t
getOut (lefty c x r , t) = getOut (c , (t <[ x ]> r))
getOut (righty l x c , t) = getOut (c , (l <[ x ]> t))
-}
Maybe : Set -> Set
Maybe X = One /+/ X
goLeft : {X : Set} -> TreeZipper X -> Maybe (TreeZipper X)
goLeft (c , leaf) = inl <>
goLeft (c , l <[ x ]> r) = inr (lefty c x r , l)
layer : Kit -> Kit
layer (kK A) = kK Zero
layer kId = kK One
layer (j k+ k) = layer j k+ layer k
layer (j k* k) = (layer j k* k) k+ (j k* layer k)
plug : (k : Kit) -> {X : Set} -> kFun (layer k) X -> X -> kFun k X
plug (kK A) () x
plug kId <> x = x
plug (j k+ k) (inl j') x = inl (plug j j' x)
plug (j k+ k) (inr k') x = inr (plug k k' x)
plug (j k* k) (inl (j' , k')) x = plug j j' x , k'
plug (j k* k) (inr (j' , k')) x = j' , plug k k' x
KLayer : Kit -> Set
KLayer k = kFun (layer k) (Data k)
kOut1 : (k : Kit) -> KLayer k -> Data k -> Data k
kOut1 k l d = [ plug k l d ]
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module CoInd where
open import Ex1Prelude
open import FuncKit
open import IxCon
postulate
Delay : {a : _} -> Set a -> Set a
delay : {a : _}{A : Set a} -> A -> Delay A
force : {a : _}{A : Set a} -> Delay A -> A
{-# BUILTIN INFINITY Delay #-}
{-# BUILTIN SHARP delay #-}
{-# BUILTIN FLAT force #-}
data Stream (X : Set) : Set where
_:>_ : X -> Delay (Stream X) -> Stream X
repeat : {X : Set} -> X -> Stream X
repeat x = x :> delay (repeat x)
natsFrom : Nat -> Stream Nat
natsFrom n = n :> delay (natsFrom (suc n))
takeUpto : {X : Set} -> (n : Nat) -> Stream X -> Vec X n
takeUpto zero xs = []
takeUpto (suc n) (x :> xs) = x , takeUpto n (force xs)
data Codata (k : Kit) : Set where
[_] : kFun k (Delay (Codata k)) -> Codata k
unfold : {k : Kit}{S : Set} ->
(S -> kFun k S) ->
S -> Codata k
unfold {k}{S} f s = [ mapunfoldf k (f s) ] where
mapunfoldf : (j : Kit) -> kFun j S -> kFun j (Delay (Codata k))
mapunfoldf (kK A) a = a
mapunfoldf kId s' = delay (unfold f s')
mapunfoldf (j k+ j') (inl x) = inl (mapunfoldf j x)
mapunfoldf (j k+ j') (inr x) = inr (mapunfoldf j' x)
mapunfoldf (j k* j') (x , y) = mapunfoldf j x , mapunfoldf j' y
STREAM : Set -> Set
STREAM X = Codata (kK X k* kId)
REPEAT : {X : Set} -> X -> STREAM X
REPEAT x = unfold (\ _ -> x , <>) <>
NATSFROM : Nat -> STREAM Nat
NATSFROM n = unfold (\ k -> k , suc k) n
PERHAPS : Set -> Set
PERHAPS X = Codata (kK X k+ kId)
never : {X : Set} -> PERHAPS X
never = unfold (\ s -> inr s) <>
now : {X : Set} -> X -> PERHAPS X
now x = unfold (\ s -> inl x) <>
wait : {X : Set} -> PERHAPS X -> PERHAPS X
wait p = [ inr (delay p) ]
-- PERHAPS is a monad; its bind operator combines the delays in sequence
-- at each step, we're either still working on getting the X, or
-- we're trying to get the Y;
-- we should ensure that the delay for the whole process is the sum of
-- the delays for each part
bind : {X Y : Set} -> PERHAPS X -> (X -> PERHAPS Y) -> PERHAPS Y
bind {X}{Y} px x2py = unfold coalgebra (inl px) where
workOnY : PERHAPS Y -> Y /+/ (PERHAPS X /+/ PERHAPS Y)
workOnY [ inl y ] = inl y
workOnY [ inr py ] = inr (inr (force py))
workOnX : PERHAPS X -> Y /+/ (PERHAPS X /+/ PERHAPS Y)
workOnX [ inl x ] = workOnY (x2py x)
workOnX [ inr px ] = inr (inl (force px))
coalgebra : (PERHAPS X /+/ PERHAPS Y) -> Y /+/ (PERHAPS X /+/ PERHAPS Y)
coalgebra (inl px) = workOnX px
coalgebra (inr py) = workOnY py
myTest : PERHAPS Nat
myTest = bind (wait (now 2)) \ x ->
bind (wait (now 3)) \ y ->
wait (now (x + y))
-- you can test PERHAPS processes with a "boredom threshold"
-- saying how long you're willing to wait; you get either the
-- answer, or a process which has evolved by the indicated
-- number of steps
runFor : {X : Set} -> Nat -> PERHAPS X -> X /+/ PERHAPS X
runFor _ [ inl x ] = inl x
runFor (suc n) [ inr px ] = runFor n (force px)
runFor zero px = inr px
{-
data Game {I : Set}(C : I => I)(Win : I -> Set)(i : I) : Set where
win : Win i -> Game C Win i
<_> : FObj [[ C ]] (Game C Win) i -> Game C Win i
-}
data Oppo {I : Set}(C : I => I)(i : I) : Set where
oppo : ((c : Command C i) ->
Sigma (Response C i c) \ r ->
Delay (Oppo C (next C i c r))) ->
Oppo C i
runGame : {I : Set}{C : I => I}{Win : I -> Set}{i : I} ->
Game C Win i -> Oppo C i ->
Sigma I \ i' -> Win i' /*/ Oppo C i'
runGame {i = i'} (win x) o = i' , (x , o)
runGame < c , k > (oppo f) with f c
runGame < c , k > (oppo f) | r , o = runGame (k r) (force o)
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module HuttonFail where
open import Ex1Prelude
data HExp : Set where
fail : HExp
val : Nat -> HExp
_+++_ : HExp -> HExp -> HExp
data Maybe (X : Set) : Set where
yes : X -> Maybe X
no : Maybe X
eval : HExp -> Maybe Nat
eval fail = no
eval (val x) = yes x
eval (e +++ e') with eval e
eval (e +++ e') | yes x with eval e'
eval (e +++ e') | yes x | yes x' = yes (x + x')
eval (e +++ e') | yes x | no = no
eval (e +++ e') | no = no
_-then-_ : {S T : Set} -> Maybe S -> (S -> Maybe T) -> Maybe T
yes x -then- s2mt = s2mt x
no -then- s2mt = no
eval2 : HExp -> Maybe Nat
eval2 fail = no
eval2 (val x) = yes x
eval2 (e +++ e') =
eval2 e -then- \ v ->
eval2 e' -then- \ v' ->
yes (v + v')
_-?>_ : Set -> Set -> Set
S -?> T = S -> Maybe T
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
#CS410-14#
This repository contains the materials for CS410 Advanced Functional
Programming in the 2014-15 session. The class runs through semesters
1 and 2, with most of its teaching and assessment activity completed
already in semester 1. Accordingly, for ease of reference, this page
includes the exercises so far, and is intended to be a reasonably
self-contained account of how the class works.
CS410 is assessed entirely by coursework. It runs for all 15 weeks of
semester 1, in which there are 5 exercises, each lasting 3 weeks and
worth 15% of the class score, then it suspends for the 10 "project"
weeks of semester 2, before resuming in the last 5 weeks of semester 2
for a single "capstone" exercise worth 25% of the class score.
The class is about programming in the advanced functional language,
Agda. Teaching is largely show-and-tell: I introduce concepts and
illustrate them with "live programming" in the classroom. Agda
supports development by interactive type-directed refinement---filling
in "holes". Exercises thus consist of incomplete programs, to be
finished appropriately by each student. They are distributed via this
public code repository on GitHub. The students work in lab sessions
which I supervise: often, the discussion which breaks out in the lab
once they are hands-on with a problem is how the real learning
happens. The students each have their own private branch of the
repository on BitBucket, to which they invite me as a "collaborator"
whilst keeping everyone else out. After each deadline, the students
make individual appointments to see me, where we work through their
code. I quiz them about it, grade it, and issue oral feedback.
This is a challenging class, but the students are bright and
enthusiastic for a challenge, having done well at the corresponding
third year Haskell class. The precise direction and choice of material
is informed by the progress the class makes as we go. This year, I was
pleasantly surprised by their willingness to engage with some quite
deep concepts.
The semester 1 exercises were as follows.
1. *an introduction to propositions-as-types and programming by
refinement* This exercise is as much an orientation in driving
the tools as it is an introduction to the basic concepts.
2. *a study of a simple interpreter, once with monadic error
propagation, and again with a typesafe representation ensuring
error-free execution* This exercise introduces basic techniques of
programming with monads, but also the idea of imposing strong
invariants by indexing datatypes.
3. *a study of polynomial datatypes, and their generic recursion
schemes* This exercise revisits some examples from exercise 1, but
encourages the students to recognize the types and programs as
instances of a general scheme.
4. *a study of interaction with an external environment* The students
develop the basic building blocks of command-response systems
contingent on some sort of state. They develop an approach to
file-handling which is statically guaranteed to be safe, and then
implement a file-copying program within that discipline.
5. *a text editor with verified update* A mostly dysfunctional text
editor is provided. The students repair it and extend it with
useful behaviour by implementing the behaviour of keystrokes,
estimating the severity of the change each makes. They are obliged
to prove that they overestimate change, thus ensuring that
necessary updates happen.
The exercise files, mark schemes and specimen solutions for exercises
1-4 are included below. For exercise 5, the main exercise file and the
mark scheme is included.
At time of writing, exercise 6 is under construction. It will be
issued to students at the start of the Easter break, giving them some
chance of a head start. It will amount to
* building a basic library for working with lists indexed by length (5
marks)
* developing the theory of rectangular tilings indexed by length and
height: these have monadic structure, and when you include
transparent tiles, a monoidal "overlaying" structure, with a clear
visual intuition (10 marks)
* developing a simple window manager for rectangular overlapping
windows, runnning in a shell: what sort of content goes in the
windows will leave room for creativity (10 marks)
The exercises tend to be quite structured, designed to promote the
grasping of key concepts. How far they get depends on their ability
and determination to struggle to an understanding. They get out what
they put in.
Below are the relevant files for the first 5 exercises.
##Exercise 1##
**problem file**
```
module Ex1 where
open import Ex1Prelude
{----------------------------------------------------------------------------}
{- Name: -}
{----------------------------------------------------------------------------}
{----------------------------------------------------------------------------}
{- DEADLINE: Week 3 Monday 13 October 23:59 (preferably by BitBucket) -}
{----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
TOP TIP: if you have annoyingly many open goals, comment out big chunks of the
file with a multi-line comment a bit like this one.
-----------------------------------------------------------------------------}
{----------------------------------------------------------------------------}
{- 1.1: Tree Sort -}
{----------------------------------------------------------------------------}
-- 1.1.1 implement concatenation for lists
_++_ : {X : Set} -> List X -> List X -> List X
xs ++ ys = {!!}
infixr 3 _++_
-- a datatype of node-labelled binary trees is given as follows
data Tree (X : Set) : Set where
leaf : Tree X
_<[_]>_ : Tree X -> X -> Tree X -> Tree X
{-
data Tree x = Leaf | Node (Tree X) X (Tree X)
Leaf :: Tree x
Node :: Tree x -> x -> Tree x -> Tree x
-}
demoTree : Tree Nat
demoTree = ({!!} <[ 3 ]> {!!}) <[ 5 ]> {!!}
-- 1.1.2 implement the insertion of a number into a tree, ensuring that
-- the numbers in the tree are in increasing order from left to right;
-- make sure to retain duplicates
insertTree : Nat -> Tree Nat -> Tree Nat
insertTree x t = {!!}
-- 1.1.3 implement the function which takes the elements of a list and
-- builds an ordered tree from them, using insertTree
makeTree : List Nat -> Tree Nat
makeTree xs = {!!}
-- 1.1.4 implement the function which flattens a tree to a list,
-- using concatenation
flatten : {X : Set} -> Tree X -> List X
flatten t = {!!}
-- 1.1.5 using the above components, implement a sorting algorithm which
-- works by building a tree and then flattening it
treeSort : List Nat -> List Nat
treeSort = {!!}
-- 1.1.6 give a collection of unit tests which cover every program line
-- from 1.1.1 to 1.1.5
-- 1.1.7 implement a fast version of flatten, taking an accumulating parameter,
-- never using ++. and ensuring that the law
--
-- fastFlatten t xs == flatten t ++ xs
--
-- is true; for an extra style point, ensure that the accumulating parameter
-- is never given a name in your program
fastFlatten : {X : Set} -> Tree X -> List X -> List X
fastFlatten t = {!!}
-- 1.1.8 use fastFlatten to build a fast version of tree sort
fastTreeSort : List Nat -> List Nat
fastTreeSort xs = {!!}
-- 1.1.9 again, give unit tests which cover every line of code
{----------------------------------------------------------------------------}
{- 1.2: Shooting Propositional Logic Fish In A Barrel -}
{----------------------------------------------------------------------------}
-- 1.2.1 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
orCommute : {A B : Set} -> A /+/ B -> B /+/ A
orCommute x = {!!}
orAbsorbL : {A : Set} -> Zero /+/ A -> A
orAbsorbL x = {!!}
orAbsorbR : {A : Set} -> A /+/ Zero -> A
orAbsorbR x = {!!}
orAssocR : {A B C : Set} -> (A /+/ B) /+/ C -> A /+/ (B /+/ C)
orAssocR x = {!!}
orAssocL : {A B C : Set} -> A /+/ (B /+/ C) -> (A /+/ B) /+/ C
orAssocL x = {!!}
-- 1.2.2 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
andCommute : {A B : Set} -> A /*/ B -> B /*/ A
andCommute x = {!!}
andAbsorbL : {A : Set} -> A -> One /*/ A
andAbsorbL x = {!!}
andAbsorbR : {A : Set} -> A -> A /*/ One
andAbsorbR x = {!!}
andAssocR : {A B C : Set} -> (A /*/ B) /*/ C -> A /*/ (B /*/ C)
andAssocR x = {!!}
andAssocL : {A B C : Set} -> A /*/ (B /*/ C) -> (A /*/ B) /*/ C
andAssocL x = {!!}
-- how many times is [C-c C-c] really needed?
-- 1.2.3 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
distribute : {A B C : Set} -> A /*/ (B /+/ C) -> (A /*/ B) /+/ (A /*/ C)
distribute x = {!!}
factor : {A B C : Set} -> (A /*/ B) /+/ (A /*/ C) -> A /*/ (B /+/ C)
factor x = {!!}
-- 1.2.4 try to implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]; at least one of them will prove to be
-- impossible, in which case you should comment it out and explain
-- why it's impossible
Not : Set -> Set
Not X = X -> Zero
deMorgan1 : {A B : Set} -> (Not A /+/ Not B) -> Not (A /*/ B)
deMorgan1 x y = {!!}
deMorgan2 : {A B : Set} -> Not (A /*/ B) -> (Not A /+/ Not B)
deMorgan2 x = {!!}
deMorgan3 : {A B : Set} -> (Not A /*/ Not B) -> Not (A /+/ B)
deMorgan3 x y = {!!}
deMorgan4 : {A B : Set} -> Not (A /+/ B) -> (Not A /*/ Not B)
deMorgan4 x = {!!}
-- 1.2.5 try to implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]; at least one of them will prove to be
-- impossible, in which case you should comment it out and explain
-- why it's impossible
dnegI : {X : Set} -> X -> Not (Not X)
dnegI = {!!}
dnegE : {X : Set} -> Not (Not X) -> X
dnegE = {!!}
neg321 : {X : Set} -> Not (Not (Not X)) -> Not X
neg321 = {!!}
hamlet : {B : Set} -> B /+/ Not B
hamlet = {!!}
nnHamlet : {B : Set} -> Not (Not (B /+/ Not B))
nnHamlet = {!!}
```
**specimen solution and mark scheme**
```
module Ex1Sol where
open import Ex1Prelude
{----------------------------------------------------------------------------}
{- Name: Conor McSpecimen -}
{----------------------------------------------------------------------------}
{----------------------------------------------------------------------------}
{- DEADLINE: Week 3 Monday 13 October 23:59 (preferably by BitBucket) -}
{----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
TOP TIP: if you have annoyingly many open goals, comment out big chunks of the
file with a multi-line comment a bit like this one.
-----------------------------------------------------------------------------}
{- Mark scheme:
The programming for each part is worth one mark.
the explanation of why the impossible cases are impossible is worth
one mark.
The total number of available marks is 15.
-}
{----------------------------------------------------------------------------}
{- 1.1: Tree Sort -}
{----------------------------------------------------------------------------}
-- 1.1.1 implement concatenation for lists
_++_ : {X : Set} -> List X -> List X -> List X
[] ++ ys = ys
x :> xs ++ ys = x :> (xs ++ ys)
infixr 3 _++_
-- a datatype of node-labelled binary trees is given as follows
data Tree (X : Set) : Set where
leaf : Tree X
_<[_]>_ : Tree X -> X -> Tree X -> Tree X
{-
data Tree x = Leaf | Node (Tree X) X (Tree X)
Leaf :: Tree x
Node :: Tree x -> x -> Tree x -> Tree x
-}
demoTree : Tree Nat
demoTree = (leaf <[ 3 ]> leaf) <[ 5 ]> leaf
-- 1.1.2 implement the insertion of a number into a tree, ensuring that
-- the numbers in the tree are in increasing order from left to right;
-- make sure to retain duplicates
insertTree : Nat -> Tree Nat -> Tree Nat
insertTree x leaf = leaf <[ x ]> leaf
insertTree x (l <[ y ]> r) with x <= y -- or use if_then_else_
insertTree x (l <[ y ]> r) | tt = insertTree x l <[ y ]> r
insertTree x (l <[ y ]> r) | ff = l <[ y ]> insertTree x r
-- 1.1.3 implement the function which takes the elements of a list and
-- builds an ordered tree from them, using insertTree
makeTree : List Nat -> Tree Nat
makeTree [] = leaf
makeTree (x :> xs) = insertTree x (makeTree xs)
-- 1.1.4 implement the function which flattens a tree to a list,
-- using concatenation
flatten : {X : Set} -> Tree X -> List X
flatten leaf = []
flatten (l <[ x ]> r) = flatten l ++ x :> flatten r
-- 1.1.5 using the above components, implement a sorting algorithm which
-- works by building a tree and then flattening it
treeSort : List Nat -> List Nat
treeSort = flatten o makeTree
-- 1.1.6 give a collection of unit tests which cover every program line
-- from 1.1.1 to 1.1.5
treeSortTest : treeSort (1 :> 5 :> 2 :> 4 :> 3 :> [])
== (1 :> 2 :> 3 :> 4 :> 5 :> [])
treeSortTest = refl
-- 1.1.7 implement a fast version of flatten, taking an accumulating parameter,
-- never using ++. and ensuring that the law
--
-- fastFlatten t xs == flatten t ++ xs
--
-- is true;
{-
fastFlatten : {X : Set} -> Tree X -> (List X -> List X)
fastFlatten leaf xs
-- = flatten leaf ++ xs -- by specification
-- = [] ++ xs -- definition of flatten
= xs -- definition of ++
fastFlatten (l <[ x ]> r) xs
-- = flatten (l <[ x ]> r) ++ xs -- by specification
-- = (flatten l ++ x :> flatten r) ++ xs -- definition of flatten
-- = flatten l ++ x :> flatten r ++ xs -- ++ is associative
-- = flatten l ++ x :> fastFlatten r xs -- by specification
= fastFlatten l (x :> fastFlatten r xs) -- by specification
-}
-- for an extra style point, ensure that the accumulating parameter
-- is never given a name in your program
fastFlatten : {X : Set} -> Tree X -> (List X -> List X)
fastFlatten leaf = id
fastFlatten (l <[ x ]> r) = (fastFlatten l) o (_:>_ x) o (fastFlatten r)
-- 1.1.8 use fastFlatten to build a fast version of tree sort
fastTreeSort : List Nat -> List Nat
fastTreeSort xs = fastFlatten (makeTree xs) []
-- 1.1.9 again, give unit tests which cover every line of code
fastTreeSortTest : fastTreeSort (1 :> 5 :> 2 :> 4 :> 3 :> [])
== (1 :> 2 :> 3 :> 4 :> 5 :> [])
fastTreeSortTest = refl
{----------------------------------------------------------------------------}
{- 1.2: Shooting Propositional Logic Fish In A Barrel -}
{----------------------------------------------------------------------------}
-- 1.2.1 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
orCommute : {A B : Set} -> A /+/ B -> B /+/ A
orCommute (inl a) = inr a
orCommute (inr b) = inl b
orAbsorbL : {A : Set} -> Zero /+/ A -> A
orAbsorbL (inl ())
orAbsorbL (inr a) = a
orAbsorbR : {A : Set} -> A /+/ Zero -> A
orAbsorbR (inl a) = a
orAbsorbR (inr ())
orAssocR : {A B C : Set} -> (A /+/ B) /+/ C -> A /+/ (B /+/ C)
orAssocR (inl (inl a)) = inl a
orAssocR (inl (inr b)) = inr (inl b)
orAssocR (inr c) = inr (inr c)
orAssocL : {A B C : Set} -> A /+/ (B /+/ C) -> (A /+/ B) /+/ C
orAssocL (inl a) = inl (inl a)
orAssocL (inr (inl b)) = inl (inr b)
orAssocL (inr (inr c)) = inr c
-- 1.2.2 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
andCommute : {A B : Set} -> A /*/ B -> B /*/ A
andCommute (a , b) = b , a
andAbsorbL : {A : Set} -> A -> One /*/ A
andAbsorbL a = <> , a
andAbsorbR : {A : Set} -> A -> A /*/ One
andAbsorbR a = a , <>
andAssocR : {A B C : Set} -> (A /*/ B) /*/ C -> A /*/ (B /*/ C)
andAssocR ((a , b) , c) = a , (b , c)
andAssocL : {A B C : Set} -> A /*/ (B /*/ C) -> (A /*/ B) /*/ C
andAssocL (a , (b , c)) = (a , b) , c
-- how many times is [C-c C-c] really needed?
-- NEVER, but I'd rather use patterns than projections
-- 1.2.3 implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]
distribute : {A B C : Set} -> A /*/ (B /+/ C) -> (A /*/ B) /+/ (A /*/ C)
distribute (a , inl b) = inl (a , b)
distribute (a , inr c) = inr (a , c)
factor : {A B C : Set} -> (A /*/ B) /+/ (A /*/ C) -> A /*/ (B /+/ C)
factor (inl (a , b)) = (a , inl b)
factor (inr (a , c)) = (a , inr c)
-- 1.2.4 try to implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]; at least one of them will prove to be
-- impossible, in which case you should comment it out and explain
-- why it's impossible
Not : Set -> Set
Not X = X -> Zero
deMorgan1 : {A B : Set} -> (Not A /+/ Not B) -> Not (A /*/ B)
deMorgan1 (inl na) (a , b) = na a
deMorgan1 (inr nb) (a , b) = nb b
{-
All I know is that A and B are not both true. That does not tell
me which of the two is false. To give a value in S /+/ T, I must
come off the fence and choose either the inl constructor and give
an S value or the inr constructor with a T. I can't just say "well,
I'm sure it isn't neither of those".
deMorgan2 : {A B : Set} -> Not (A /*/ B) -> (Not A /+/ Not B)
deMorgan2 x = inl (\ a -> {!!})
Closer to the detail, a value of type Not (A /*/ B) is really a
function of type (A /*/ B) -> Zero, so I can never get any actual
data out of it that would help me come off the fence. If I plump
for one side (inl, above), I get offered an A, but that isn't
enough to make use of the hypoothesis.
-}
deMorgan3 : {A B : Set} -> (Not A /*/ Not B) -> Not (A /+/ B)
deMorgan3 (na , nb) (inl a) = na a
deMorgan3 (na , nb) (inr b) = nb b
deMorgan4 : {A B : Set} -> Not (A /+/ B) -> (Not A /*/ Not B)
deMorgan4 n = (\ a -> n (inl a)) , (\ b -> n (inr b))
-- 1.2.5 try to implement the following operations; try to use only
-- [C-c C-c] and [C-c C-a]; at least one of them will prove to be
-- impossible, in which case you should comment it out and explain
-- why it's impossible
dnegI : {X : Set} -> X -> Not (Not X)
dnegI = \ x nx → nx x
{-
dnegE : {X : Set} -> Not (Not X) -> X
dnegE = {!!}
Just because you can't prove that X's don't exist, it doesn't mean
you actually know how to compute an X.
-}
neg321 : {X : Set} -> Not (Not (Not X)) -> Not X
neg321 = λ nnx x → nnx \ nx -> nx x
{-
hamlet : {B : Set} -> B /+/ Not B
hamlet = {!!}
For any proposition (e.g., the halting of a Turing machine), that
we can encode as a Set, hamlet promises to compute whether or not
it has a proof. That's far cleverer than a real computer.
-}
nnHamlet : {B : Set} -> Not (Not (B /+/ Not B))
nnHamlet z = z (inr (\ b -> z (inl b)))
{- Just for fun... -}
DEMORGAN2 : Set1
DEMORGAN2 = {A B : Set} -> Not (A /*/ B) -> (Not A /+/ Not B)
DNEGE : Set1
DNEGE = {X : Set} -> Not (Not X) -> X
HAMLET : Set1 -- also known as "the law of the excluded middle"
HAMLET = {B : Set} -> B /+/ Not B -- or "tertium non datur" (third (way) not given)
-- and one more variation, Peirce's Law, also a classical truth
PEIRCE : Set1
PEIRCE = {P Q : Set} -> ((P -> Q) -> P) -> P
-- DNEGE, PEIRCE and HAMLET are equivalent
imp1 : DNEGE -> HAMLET
imp1 dne = dne nnHamlet
imp2 : HAMLET -> PEIRCE
imp2 h {P} {Q} pqp with h {P}
imp2 h pqp | inl p = p
imp2 h pqp | inr np = pqp (\ p -> magic (np p)) where
imp3 : PEIRCE -> DNEGE
imp3 peirce nnx = peirce (\ nx -> magic (nnx nx))
-- they all imply DEMORGAN2
impDeMorgan : DNEGE -> DEMORGAN2
impDeMorgan dne nab = dne (\ z -> z (inl (\ a -> z (inr (\ b → nab (a , b))))))
-- but (and sorry if I led some of you to believe the opposite)
-- DEMORGAN2 is weaker than the others, because you can only
-- get one bit at at time
{- So, the business of constructing values as evidence for
propositions corresponds to functional programming in a "total"
language, but it doesn't give us quite the same logic as the
Boolean logic we teach you when you start. That logic (aka
"classical logic") makes "true" some things which do not correspond
to computations.
The logic you get here is sometimes called "constructive logic"
because we ask not "is it true?" but "can you make the evidence?".
FUN FACT (due to Kurt Goedel): if something is true, classically,
you can prove that it's not false, constructively.
WEIRD POSSIBILITY: there are such things as "anti-classical" logics
which are even more constructive, in which things like HAMLET are
actually false; these logics build in the idea that the *only*
truths arise by construction.
-}
```
##Exercise 2##
**problem file**
```
module Ex2 where
{-----------------------------------------------------------------------------
Name:
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
CS410 Exercise 2, due 5pm on Monday of Week 6 (3 November 2014)
NOTE: I am well aware that week 6 is quite busy with deadlines,
what with CS408-related obligations and so on. I'd much prefer
you did things to the best of your ability rather than on time,
so I would be sympathetic to requests for some flexibility.
Still, your best bet is to make an early start rather than a
late finish.
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
This exercise is based around extending Hutton's razor with Boolean
values and conditional expressions. By introducing a second value
type, we acquire the risk of type mismatch. The idea here is to
explore different approaches to managing that risk.
-----------------------------------------------------------------------------}
open import Ex1Prelude
open import Ex2Prelude
{- The extended Hutton's Razor syntax -}
data HExpIf : Set where
num : Nat -> HExpIf
boo : Two -> HExpIf
_+++_ : HExpIf -> HExpIf -> HExpIf
hif_then_else_ : HExpIf -> HExpIf -> HExpIf -> HExpIf
{- Note that an expression
hif eb then ex1 else ex2
makes sense only when
* eb produces a Boolean value
* ex1 and ex2 produce the same sort of value (numeric or Boolean)
-}
HValIf : Set
HValIf = Two /+/ Nat
{- We now have the risk of run time type errors. Let's introduce a type
for things which can go wrong. -}
data Error (E X : Set) : Set where
ok : X -> Error E X
error : E -> Error E X
{- 2.1 Add a constructor to the following datatype for each different
kind of run time error that can happen. (Come back to this exercise
when you're writing the evaluator in 2.3.) Make these error reports
as informative as you can.
-}
data EvalError : Set where
-- your constructors here
{- 2.2 Write a little piece of "glue code" to make it easier to manage
errors. The idea is to combine error-prone process in *sequence*, where
the second process can depend on the value produced by the first if it
succeeds. The resulting process is, of course, also error-prone, failing
as soon as either component fails.
-}
_>>=_ : {E S T : Set}
-> Error E S -- process which tries to get an S
-> (S -> Error E T) -- given an S, process which tries for a T
-> Error E T -- combined in sequence
es >>= s2et = {!!}
{- 2.3 Implement an evaluator for HExpIf. Be sure to add only numbers and
to branch only on Booleans. Report type mismatches as errors. You should
use _>>=_ to help with the propagation of error messages.
-}
eval : HExpIf -> Error EvalError HValIf
eval e = {!!}
{- Note that the type of eval is not specific about whether the value
expected is numeric or Boolean. It may help to introduce auxiliary
definitions of error-prone processes which are "ok" only for the
type that you really want.
-}
{- Next up, stack machine code, and its execution. -}
data HBCode : Set where
PUSHN : Nat -> HBCode
PUSHB : Two -> HBCode
ADD : HBCode
_SEQ_ : HBCode -> HBCode -> HBCode
_IFPOP_ : HBCode -> HBCode -> HBCode
{- The intended behaviour of (t IFPOP f) is as follows
* pop the (we hope) Boolean value from top of stack
* if it's tt, execute t, else execute f
* whichever branch is executed, it gets the popped stack to start
-}
{- 2.4 Populate the type of possible execution errors and implement the
execution behaviour of HBCode, operating on a stack represented as
a list of HValIf values.
-}
data ExecError : Set where
-- your constructors here
exec : HBCode -> List HValIf -> Error ExecError (List HValIf)
exec c s = {!!}
{- Next, we take a look at code generation and type safety. -}
data HTy : Set where -- we have two types in HExpIf
NUM BOOL : HTy
_=HTy=_ : HTy -> HTy -> Two -- we can test if two types are equal
NUM =HTy= NUM = tt
NUM =HTy= BOOL = ff
BOOL =HTy= NUM = ff
BOOL =HTy= BOOL = tt
{- 2.5 Write a type-synthesizing compiler, computing both the HTy type and
the HBCode executable for a given expression. Your compiler should
give an informative error report if the expression it receives is
ill typed. Your compiler should also ensure (at least informally) that
the code produced will never trigger any execution errors.
-}
data CompileError : Set where
-- your constructors here
compile : HExpIf -> Error CompileError (HTy /*/ HBCode)
compile (num x) = {!!}
compile (boo x) = {!!}
compile (e1 +++ e2) = compile e1 >>= \
{ (BOOL , c1) -> error {!!}
; (NUM , c1) -> {!!}
}
compile (hif e then e₁ else e₂) = {!!}
{- You have a little bit more room for creative problem-solving in what's
left of the exercise. The plan is to build the type system into expressions
and code, the same way we did with plain Hutton's Razor in class.
-}
{- If we *know* which HTy type we want, we can compute which Agda type we
expect our value to take. -}
HVal : HTy -> Set
HVal NUM = Nat
HVal BOOL = Two
{- 2.6 Finish the type of typed expressions. You should ensure that only
well HTy-typed expressions can be constructed. -}
data THExpIf : HTy -> Set where
val : {t : HTy} -> HVal t -> THExpIf t
-- you fill in addition and if-then-else
{- 2.7 Implement a type-safe evaluator. -}
teval : {t : HTy} -> THExpIf t -> HVal t
teval e = {!!}
{- 2.8 Implement a type checker. -}
data TypeError : Set where
-- your constructors here
tcheck : (t : HTy) -> HExpIf -> Error TypeError (THExpIf t)
tcheck t e = {!!}
{- 2.9 Adapt the technique from Hutton.agda to give a type-safe underflow-free
version of HBCode. You will need to think what is a good type to represent
the "shape" of a stack: before, we just used Nat to represent the *height* of
the stack, but now we must worry about types. See next question for a hint. -}
data THBCode : {- your indices here -} Set where
-- your constructors here
{- 2.10 Implement the execution semantics for your code. You will need to think
about how to represent a stack. The Ex2Prelude.agda file contains a very
handy piece of kit for this purpose. You write the type, too. -}
-- your code here
{- 2.11 Write the compiler from well typed expressions to safe code. -}
tcompile : {t : HTy} -> THExpIf t -> {!!}
tcompile e = {!!}
```
**specimen solution and mark scheme**
```
module Ex2Sol where
{-----------------------------------------------------------------------------
Name: Conor McSpecimen
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
CS410 Exercise 2, due 5pm on Monday of Week 6 (3 November 2014)
NOTE: I am well aware that week 6 is quite busy with deadlines,
what with CS408-related obligations and so on. I'd much prefer
you did things to the best of your ability rather than on time,
so I would be sympathetic to requests for some flexibility.
Still, your best bet is to make an early start rather than a
late finish.
-----------------------------------------------------------------------------}
{-----------------------------------------------------------------------------
This exercise is based around extending Hutton's razor with Boolean
values and conditional expressions. By introducing a second value
type, we acquire the risk of type mismatch. The idea here is to
explore different approaches to managing that risk.
-----------------------------------------------------------------------------}
{- Mark scheme
Each part is worth one mark each, apart from the four labelled
as worth two. The total number of marks available is 15.
-}
open import Ex1Prelude
open import Ex2Prelude
{- The extended Hutton's Razor syntax -}
data HExpIf : Set where
num : Nat -> HExpIf
boo : Two -> HExpIf
_+++_ : HExpIf -> HExpIf -> HExpIf
hif_then_else_ : HExpIf -> HExpIf -> HExpIf -> HExpIf
{- Note that an expression
hif eb then ex1 else ex2
makes sense only when
* eb produces a Boolean value
* ex1 and ex2 produce the same sort of value (numeric or Boolean)
-}
HValIf : Set
HValIf = Two /+/ Nat
{- We now have the risk of run time type errors. Let's introduce a type
for things which can go wrong. -}
data Error (E X : Set) : Set where
ok : X -> Error E X
error : E -> Error E X
{- 2.1 Add a constructor to the following datatype for each different
kind of run time error that can happen. (Come back to this exercise
when you're writing the evaluator in 2.3.) Make these error reports
as informative as you can.
-}
data EvalError : Set where
wantedANatButGotALousy : HExpIf -> EvalError
wantedATwoButGotALousy : HExpIf -> EvalError
-- your constructors here
{- 2.2 Write a little piece of "glue code" to make it easier to manage
errors. The idea is to combine error-prone process in *sequence*, where
the second process can depend on the value produced by the first if it
succeeds. The resulting process is, of course, also error-prone, failing
as soon as either component fails.
-}
_>>=_ : {E S T : Set}
-> Error E S -- process which tries to get an S
-> (S -> Error E T) -- given an S, process which tries for a T
-> Error E T -- combined in sequence
ok s >>= s2et = s2et s
error e >>= s2et = error e
{- 2.3 Implement an evaluator for HExpIf. Be sure to add only numbers and
to branch only on Booleans. Report type mismatches as errors. You should
use _>>=_ to help with the propagation of error messages.
(2 marks)
-}
natOrBust : {E : Set} -> E -> HValIf -> Error E Nat
natOrBust e (inl b) = error e
natOrBust e (inr n) = ok n
twoOrBust : {E : Set} -> E -> HValIf -> Error E Two
twoOrBust e (inl b) = ok b
twoOrBust e (inr n) = error e
eval : HExpIf -> Error EvalError HValIf
eval (num n) = ok (inr n)
eval (boo x) = ok (inl x)
eval (d +++ e) =
(eval d >>= natOrBust (wantedANatButGotALousy d)) >>= \ dn ->
(eval e >>= natOrBust (wantedANatButGotALousy e)) >>= \ en ->
ok (inr (dn + en))
eval (hif e then t else f) =
(eval e >>= twoOrBust (wantedATwoButGotALousy e)) >>= \ eb ->
if eb then eval t else eval f
{- Note that the type of eval is not specific about whether the value
expected is numeric or Boolean. It may help to introduce auxiliary
definitions of error-prone processes which are "ok" only for the
type that you really want.
-}
{- Next up, stack machine code, and its execution. -}
data HBCode : Set where
PUSHN : Nat -> HBCode
PUSHB : Two -> HBCode
ADD : HBCode
_SEQ_ : HBCode -> HBCode -> HBCode
_IFPOP_ : HBCode -> HBCode -> HBCode
{- The intended behaviour of (t IFPOP f) is as follows
* pop the (we hope) Boolean value from top of stack
* if it's tt, execute t, else execute f
* whichever branch is executed, it gets the popped stack to start
-}
{- 2.4 Populate the type of possible execution errors and implement the
execution behaviour of HBCode, operating on a stack represented as
a list of HValIf values. (2 marks)
-}
data ExecError : Set where
stackUnderflowInADD : ExecError
stackUnderflowInIFPOP : ExecError
addingATwo : HValIf -> ExecError
iffingANat : HValIf -> ExecError
-- your constructors here
exec : HBCode -> List HValIf -> Error ExecError (List HValIf)
exec (PUSHN n) s = ok (inr n :> s)
exec (PUSHB b) s = ok (inl b :> s)
exec ADD (y :> x :> s)
= natOrBust (addingATwo x) x >>= \ xn ->
natOrBust (addingATwo y) y >>= \ yn ->
ok (inr (xn + yn) :> s)
exec ADD _ = error stackUnderflowInADD
exec (c SEQ d) s = exec c s >>= exec d
exec (t IFPOP f) [] = error stackUnderflowInIFPOP
exec (t IFPOP f) (x :> s)
= twoOrBust (iffingANat x) x >>= \ xb ->
if xb then exec t s else exec f s
{- Next, we take a look at code generation and type safety. -}
data HTy : Set where -- we have two types in HExpIf
NUM BOOL : HTy
_=HTy=_ : HTy -> HTy -> Two -- we can test if two types are equal
NUM =HTy= NUM = tt
NUM =HTy= BOOL = ff
BOOL =HTy= NUM = ff
BOOL =HTy= BOOL = tt
{- 2.5 Write a type-synthesizing compiler, computing both the HTy type and
the HBCode executable for a given expression. Your compiler should
give an informative error report if the expression it receives is
ill typed. Your compiler should also ensure (at least informally) that
the code produced will never trigger any execution errors.
(2 marks)
-}
data CompileError : Set where
addingABool : HExpIf -> CompileError
iffingANumber : HExpIf -> CompileError
ifBranchesMismatchedTypes : (HExpIf /*/ HTy) -> (HExpIf /*/ HTy) -> CompileError
compile : HExpIf -> Error CompileError (HTy /*/ HBCode)
compile (num x) = ok (NUM , PUSHN x)
compile (boo x) = ok (BOOL , PUSHB x)
compile (e1 +++ e2) = compile e1 >>= \
{ (BOOL , _) -> error (addingABool e1)
; (NUM , c1) -> compile e2 >>= \
{ (BOOL , _) -> error (addingABool e2)
; (NUM , c2) -> ok (NUM , (c1 SEQ c2) SEQ ADD)
}
}
compile (hif e then t else f) = compile e >>= \
{ (NUM , _) -> error (iffingANumber e)
; (BOOL , c) -> compile t >>= \
{ (tty , tc) -> compile f >>= \
{ (fty , fc) ->
if tty =HTy= fty then ok (tty , c SEQ (tc IFPOP fc))
else error (ifBranchesMismatchedTypes (t , tty) (f , fty))
}
}
}
{- You have a little bit more room for creative problem-solving in what's
left of the exercise. The plan is to build the type system into expressions
and code, the same way we did with plain Hutton's Razor in class.
-}
{- If we *know* which HTy type we want, we can compute which Agda type we
expect our value to take. -}
HVal : HTy -> Set
HVal NUM = Nat
HVal BOOL = Two
{- 2.6 Finish the type of typed expressions. You should ensure that only
well HTy-typed expressions can be constructed. -}
data THExpIf : HTy -> Set where
val : {t : HTy} -> HVal t -> THExpIf t
_+++_ : THExpIf NUM -> THExpIf NUM -> THExpIf NUM
hif_then_else_ : {t : HTy} -> THExpIf BOOL -> THExpIf t -> THExpIf t -> THExpIf t
-- you fill in addition and if-then-else
{- 2.7 Implement a type-safe evaluator. -}
teval : {t : HTy} -> THExpIf t -> HVal t
teval (val x) = x
teval (d +++ e) = teval d + teval e
teval (hif e then t else f) = if teval e then teval t else teval f
{- 2.8 Implement a type checker. (2 marks) -}
data TypeError : Set where
wanted_got_ : HTy -> HExpIf -> TypeError
-- your constructors here
tcheck : (t : HTy) -> HExpIf -> Error TypeError (THExpIf t)
tcheck NUM (num x) = ok (val x)
tcheck BOOL (num x) = error (wanted BOOL got num x)
tcheck NUM (boo x) = error (wanted NUM got boo x)
tcheck BOOL (boo x) = ok (val x)
tcheck NUM (d +++ e) = tcheck NUM d >>= \ dt -> tcheck NUM e >>= \ et -> ok (dt +++ et)
tcheck BOOL (d +++ e) = error (wanted BOOL got (d +++ e))
tcheck t (hif e then th else el) =
tcheck BOOL e >>= \ et ->
tcheck t th >>= \ tht ->
tcheck t el >>= \ elt -> ok (hif et then tht else elt)
{- 2.9 Adapt the technique from Hutton.agda to give a type-safe underflow-free
version of HBCode. You will need to think what is a good type to represent
the "shape" of a stack: before, we just used Nat to represent the *height* of
the stack, but now we must worry about types. See next question for a hint. -}
data THBCode : List HTy -> List HTy -> Set where
PUSHV : {t : HTy}{s : List HTy} -> HVal t -> THBCode s (t :> s)
ADD : {s : List HTy} -> THBCode (NUM :> NUM :> s) (NUM :> s)
_SEQ_ : {i j k : List HTy} -> THBCode i j -> THBCode j k -> THBCode i k
_IFPOP_ : {i j : List HTy} -> THBCode i j -> THBCode i j -> THBCode (BOOL :> i) j
{- 2.10 Implement the execution semantics for your code. You will need to think
about how to represent a stack. The Ex2Prelude.agda file contains a very
handy piece of kit for this purpose. You write the type, too. -}
Stack : List HTy → Set
Stack i = All HVal i
-- forward composition
_followedBy_ : {A B C : Set} (f : A → B) (g : B → C) → A → C
f followedBy g = λ z → g (f z)
tsemantics : {i j : List HTy} (c : THBCode i j) (s : Stack i) → Stack j
tsemantics (PUSHV x) s = x , s
tsemantics ADD (m , n , s) = m + n , s
tsemantics (c SEQ d) s = (tsemantics c followedBy tsemantics d) s
tsemantics (t IFPOP f) (b , s) = if b then tsemantics t s else tsemantics f s
{- 2.11 Write the compiler from well typed expressions to safe code. -}
tcompile : {t : HTy} -> THExpIf t -> {s : List HTy} -> THBCode s (t :> s)
tcompile (val x) = PUSHV x
tcompile (d +++ e) = (tcompile d SEQ tcompile e) SEQ ADD
tcompile (hif e then t else f) = tcompile e SEQ (tcompile t IFPOP tcompile f)
```
##Exercise 3##
**problem file**
```
module Ex3 where
open import Ex1Prelude
open import FuncKit
{- 3.1 Numbers in the Kit -}
{- We can define the type of natural numbers using the tools
from the functor kit like this: -}
kNat : Kit
kNat = kK One k+ kId
NAT : Set
NAT = Data kNat
-- Define the function which sends "ordinary" numbers to
-- the corresponding kit-encoded numbers.
Nat2NAT : Nat -> NAT
Nat2NAT n = {!!}
-- Use fold to define the function which sends them back.
NAT2Nat : NAT -> Nat
NAT2Nat = fold (kK One k+ kId) {!!}
-- Show that you get the "round trip" property (by writing
-- recursive functions that use rewrite.
Nat2NAT2Nat : NAT2Nat o Nat2NAT =^= id
Nat2NAT2Nat n = {!!}
NAT2Nat2NAT : Nat2NAT o NAT2Nat =^= id
NAT2Nat2NAT n = {!!}
{- 3.2 Lists in the Kit -}
-- find the code which gives you lists with a given element
-- type (note that the kId constructor marks the place for
-- recursive *sublists* not for list elements
kLIST : Set -> Kit
kLIST A = {!!}
LIST : Set -> Set
LIST A = Data (kLIST A)
-- define nil and cons for your lists
nil : {A : Set} -> LIST A
nil = {!!}
cons : {A : Set} -> A -> LIST A -> LIST A
cons a as = {!!}
-- use fold to define concatenation
conc : {A : Set} -> LIST A -> LIST A -> LIST A
conc {A} xs ys = fold (kLIST A) {!!} xs
-- prove the following (the yellow bits should disappear when
-- you define kLIST);
-- maddeningly, "rewrite" won't do it, but this piece of kit
-- (which is like a manual version of rewrite) will do it
cong : {S T : Set}(f : S -> T){a b : S} -> a == b -> f a == f b
cong f refl = refl
concNil : {A : Set}(as : LIST A) -> conc as nil == as
concNil as = {!!}
concAssoc : {A : Set}(as bs cs : LIST A) ->
conc (conc as bs) cs == conc as (conc bs cs)
concAssoc as bs cs = {!!}
{- 3.3 Trees in the Kit -}
-- give a kit code for binary trees with unlabelled leaves
-- and nodes labelled with elements of NAT
kTREE : Kit
kTREE = {!!}
TREE : Set
TREE = Data kTREE
-- give the constructors
leaf : TREE
leaf = {!!}
node : TREE -> NAT -> TREE -> TREE
node l n r = {!!}
-- implement flattening (slow flattening is ok) as a fold
flatten : TREE -> LIST NAT
flatten = fold kTREE {!!}
{- 3.4 "rec" from "fold" -}
-- The recursor is a variation on the theme of fold, but you
-- get a wee bit more information at each step. In particular,
-- in each recursive position, you get the original substructure
-- *as well as* the value that is computed from it.
rec : (k : Kit){X : Set} ->
(kFun k (Data k /*/ X) -> X) ->
-- ^^^^^^ ^
-- substructure value
Data k -> X
-- Demonstrate that rec is no more powerful than fold by constructing
-- rec from fold. The trouble is that fold throws away the original
-- substructures. But you can compensate by computing something extra
-- as well as the value you actually want.
rec k {X} f d = outr (fold k {{!!} /*/ X} {!!} d)
-- use rec to implement "insList", being the function which inserts
-- a number in a list, such that if the input list is in increasing
-- order, so is the output list; you may assume that "lessEq" exists
lessEq : NAT -> NAT -> Two
insList : NAT -> LIST NAT -> LIST NAT
insList n = rec (kLIST NAT) {!!}
-- justify the assumption by defining "lessEq"; do not use explicit
-- recursion;
-- note that the thing we build for each number is its less-or-equal
-- test;
-- do use "rec kNat" once more to take numbers apart
lessEq x y = rec kNat {NAT -> Two} {!!} x y
-- implement insertion for binary search trees using "rec"
insTree : NAT -> TREE -> TREE
insTree n = rec kTREE {!!}
```
**specimen solution and mark scheme**
```
module Ex3Sol where
{- Mark Scheme
3.1 is work 3; 3.2 is worth 4; 3.3 is worth 3; 3.4 is worth 5
The total number of marks available is 15.
See below for individual mark breakdown.
-}
open import Ex1Prelude
open import FuncKit
{- 3.1 Numbers in the Kit (3 marks) -}
{- We can define the type of natural numbers using the tools
from the functor kit like this: -}
kNat : Kit
kNat = kK One k+ kId
NAT : Set
NAT = Data kNat
-- Define the function which sends "ordinary" numbers to
-- the corresponding kit-encoded numbers. (1 mark)
Nat2NAT : Nat -> NAT
Nat2NAT zero = [ inl <> ]
Nat2NAT (suc n) = [ inr (Nat2NAT n) ]
-- Use fold to define the function which sends them back. (1 mark)
NAT2Nat : NAT -> Nat
NAT2Nat = fold (kK One k+ kId) (\
{ (inl <>) -> zero
; (inr NAT2Nat_n) -> suc NAT2Nat_n
})
-- Show that you get the "round trip" property (by writing
-- recursive functions that use rewrite. (1 mark)
Nat2NAT2Nat : NAT2Nat o Nat2NAT =^= id
Nat2NAT2Nat zero = refl
Nat2NAT2Nat (suc n) rewrite Nat2NAT2Nat n = refl
NAT2Nat2NAT : Nat2NAT o NAT2Nat =^= id
NAT2Nat2NAT [ inl <> ] = refl
NAT2Nat2NAT [ inr x ] rewrite NAT2Nat2NAT x = refl
{- 3.2 Lists in the Kit (4 marks) -}
-- find the code which gives you lists with a given element
-- type (note that the kId constructor marks the place for
-- recursive *sublists* not for list elements (1 mark)
kLIST : Set -> Kit
kLIST A = kK One k+ (kK A k* kId)
LIST : Set -> Set
LIST A = Data (kLIST A)
-- define nil and cons for your lists (1 mark)
nil : {A : Set} -> LIST A
nil = [ inl <> ]
cons : {A : Set} -> A -> LIST A -> LIST A
cons a as = [ inr (a , as) ]
-- use fold to define concatenation (1 mark)
conc : {A : Set} -> LIST A -> LIST A -> LIST A
conc {A} xs ys = fold (kLIST A)
(\ { (inl <>) -> ys
; (inr (a , conc_as_ys)) -> cons a conc_as_ys
})
xs
-- prove the following (the yellow bits should disappear when
-- you define kLIST); (1 mark)
-- maddeningly, "rewrite" won't do it, but this piece of kit
-- (which is like a manual version of rewrite) will do it
cong : {S T : Set}(f : S -> T){a b : S} -> a == b -> f a == f b
cong f refl = refl
concNil : {A : Set}(as : LIST A) -> conc as nil == as
concNil [ inl <> ] = refl
concNil [ inr (a , as) ] = cong (cons a) (concNil as)
concAssoc : {A : Set}(as bs cs : LIST A) ->
conc (conc as bs) cs == conc as (conc bs cs)
concAssoc [ inl <> ] bs cs = refl
concAssoc [ inr (a , as) ] bs cs = cong (cons a) (concAssoc as bs cs)
{- 3.3 Trees in the Kit (3 marks) -}
-- give a kit code for binary trees with unlabelled leaves
-- and nodes labelled with elements of NAT (1 mark)
kTREE : Kit
kTREE = kK One k+ (kId k* (kK NAT k* kId))
TREE : Set
TREE = Data kTREE
-- give the constructors (1 mark)
leaf : TREE
leaf = [ inl <> ]
node : TREE -> NAT -> TREE -> TREE
node l n r = [ inr (l , n , r) ]
-- implement flattening (slow flattening is ok) as a fold (1 mark)
flatten : TREE -> LIST NAT
flatten = fold kTREE (\
{ (inl <>) -> nil
; (inr (flatten_l , n , flatten_r)) -> conc flatten_l (cons n flatten_r)
})
{- 3.4 "rec" from "fold" (5 marks) -}
-- The recursor is a variation on the theme of fold, but you
-- get a wee bit more information at each step. In particular,
-- in each recursive position, you get the original substructure
-- *as well as* the value that is computed from it.
rec : (k : Kit){X : Set} ->
(kFun k (Data k /*/ X) -> X) ->
-- ^^^^^^ ^
-- substructure value
Data k -> X
-- Demonstrate that rec is no more powerful than fold by constructing
-- rec from fold. The trouble is that fold throws away the original
-- substructures. But you can compensate by computing something extra
-- as well as the value you actually want. (1 mark)
rec k {X} f d = outr (fold k {Data k /*/ X}
(\ kdx -> [ kitMap k outl kdx ] , f kdx) d)
-- use rec to implement "insList", being the function which inserts
-- a number in a list, such that if the input list is in increasing
-- order, so is the output list; you may assume that "lessEq" exists (1 mark)
lessEq : NAT -> NAT -> Two
insList : NAT -> LIST NAT -> LIST NAT
insList n = rec (kLIST NAT) (\
{ (inl <>) -> cons n nil
; (inr (a , (as , insList_n_as))) ->
if lessEq n a
then cons n (cons a as)
else cons a insList_n_as
})
-- justify the assumption by defining "lessEq"; do not use explicit
-- recursion; do use "rec kNat" once more to take numbers apart
-- (2 marks, one for each "rec")
lessEq x y = rec kNat {NAT -> Two}
(\ { (inl <>) -> \ y -> {- lessEq zero y -} tt
; (inr (x , lessEq_x)) -> rec kNat (\
{ (inl <>) -> {- lessEq (suc x) zero -} ff
; (inr (y , lessEq_[suc_x]_y)) -> {- lessEq (suc x) (suc y) -} lessEq_x y
})
})
x y
-- implement insertion for binary search trees using "rec" (1 mark)
insTree : NAT -> TREE -> TREE
insTree n = rec kTREE (\
{ (inl <>) -> node leaf n leaf
; (inr ((l , insTree_n_l) , y , (r , insTree_n_r))) ->
if lessEq n y then node insTree_n_l y r else node l y insTree_n_r
})
```
##Exercise 4##
**problem file**
```
module Ex4 where
{- I'm sorry I haven't quite finished setting this exercise yet, but by
the joy of version control, the rest of it can be merged in later
(quite soon). At least you can get cracking: I promise not to break
anything, just to add a bit more on the end.
The deadline for this is midnight on the Monday of Week 12 (15 Dec).
It'd be good to get the marks in before Christmas, but if the end of
term is looking deadlinetastic, please open negotiations.
-}
open import Ex1Prelude
open import IxCon
{-# BUILTIN BOOL Two #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #-}
{-# BUILTIN CONS _:>_ #-}
postulate -- this means that we just suppose the following things exist...
Char : Set
String : Set
{-# BUILTIN CHAR Char #-}
{-# BUILTIN STRING String #-}
primitive -- these are baked in; they even work!
primCharEquality : Char -> Char -> Two
primStringAppend : String -> String -> String
primStringToList : String -> List Char
primStringFromList : List Char -> String
---------------------------------------------------------------------------
-- WRITING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- If you possess the ability to open a file for writing, you might
have the following interface. -}
-- States
data WriteState : Set where
opened closed : WriteState -- do you currently have a file open or not?
-- Commands
data WriteC : WriteState -> Set where
openWrite : (fileName : String) -> WriteC closed
writeChar : Char -> WriteC opened
closeWrite : WriteC opened
-- Responses
WriteR : (j : WriteState)(c : WriteC j) -> Set
WriteR .closed (openWrite fileName) = WriteState -- we get told whether it worked
WriteR .opened (writeChar x) = One -- always works
WriteR .opened closeWrite = One -- always works
{- 4.1 Implement the following operation which determines the next
state. You should ensure that you can write characters only to
a successfully opened file, and that you can write as many as
you want. It should also be possible to insist that a process
closes its file. -}
writeNext : (j : WriteState)(c : WriteC j) -> WriteR j c -> WriteState
writeNext j c r = {!!}
-- the file writing interface, assembled as an indexed container
WRITE : WriteState => WriteState
WRITE = WriteC <! WriteR / writeNext
---------------------------------------------------------------------------
-- READING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- To read from a file, it should be open, and you shouldn't be at the
end of it. -}
-- States
data ReadState : Set where
opened : (eof : Two) -> ReadState -- eof is tt if we're at end of file
closed : ReadState
{- 4.2 Finish the READ implementation, in accordance with the description. -}
-- Commands
data ReadC : ReadState -> Set where
openRead : {- your stuff -} ReadC {!!} -- needs a filename; might not open successfully;
-- might open an empty file
readChar : {- your stuff -} ReadC {!!} -- makes sense only if we're not at end of file
-- and might take us to end of file
closeRead : {- your stuff -} ReadC {!!} -- makes sense only if the file is open
-- Responses
ReadR : (j : ReadState)(c : ReadC j) -> Set
ReadR j c = {!!}
-- next State; you need to make sure the response gives enough info
readNext : (j : ReadState)(c : ReadC j) -> ReadR j c -> ReadState
readNext j c r = {!!}
READ : ReadState => ReadState
READ = ReadC <! ReadR / readNext
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SHARED STATE
---------------------------------------------------------------------------
{- 4.3 Let's suppose we have two command-response interfaces which offer
different functionality for the same system. Correspondingly, we'll
have two indexed containers for the same index set. Show that you
can combine them into one indexed container which lets you choose a
command from either menu and evolves the state as specified by
whichever interface offered the chosen command.
-}
_=+=_ : {I : Set} -> I => I -> I => I -> I => I
CRn0 =+= CRn1 = {!!}
---------------------------------------------------------------------------
-- WHEN IGNORANCE IS BLISS, BIS
---------------------------------------------------------------------------
{- 4.4 If we have a command-response interface with index I representing
states of the system, show that we can index basically the same
commands and responses over a state, I /*/ J, where the J is just
useless information which never changes. (This operation isn't
super-useful on its own, but it's handy in combination with other
things. -}
GrowR : {I J : Set} -> I => I -> (I /*/ J) => (I /*/ J)
GrowR CRn = {!!}
-- do the same for "growing the index on the left"
GrowL : {I J : Set} -> I => I -> (J /*/ I) => (J /*/ I)
GrowL CRn = {!!}
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SEPARATE STATE
---------------------------------------------------------------------------
{- 4.5 Making use of 4.4 and 4.5, show how to combine two interfaces which
operate independently on separate state: commands from one should
not affect the state of the other.
-}
_<+>_ : {I0 I1 : Set} -> I0 => I0 -> I1 => I1 -> (I0 /*/ I1) => (I0 /*/ I1)
CRn0 <+> CRn1 = {!!}
---------------------------------------------------------------------------
-- ERROR REPORTING, AN INTERFACE
---------------------------------------------------------------------------
{- I'm building the next bit for you.
When things go wrong, we need to trigger an error condition and abort
mission. However, if we have other stuff going on (open files, etc),
it may not always be ok to drop everything and run away. There will
be some states in which it is safe to escape (and deliver a suitable
error message, perhaps) and other states in which escape should be
impossible.
If it is safe to issue an error message, we should be able to do so
without fear of any response from the environment that would oblige
us to carry on.
-}
data ErrorC {I : Set}(SafeMessage : I -> Set)(i : I) : Set where
error : SafeMessage i -> ErrorC SafeMessage i
-- the SafeMessage parameter tells us what is an acceptable
-- error message in any given state; in states where this gives
-- Zero, it will be impossible to trigger an error!
ErrorR : {I : Set}{SafeMessage : I -> Set}(i : I)(c : ErrorC SafeMessage i) -> Set
ErrorR _ _ = Zero -- there's no comeback
errorNext : {I : Set}{SafeMessage : I -> Set}
(i : I)(c : ErrorC SafeMessage i) -> ErrorR i c -> I
errorNext i c () -- so we don't have to say how the state will evolve
ERROR : {I : Set}(SafeMessage : I -> Set) -> I => I
ERROR SafeMessage = ErrorC SafeMessage <! ErrorR / errorNext
---------------------------------------------------------------------------
-- COPY A FILE
---------------------------------------------------------------------------
{- 4.6 Implement a process which, given access to suitable interfaces, will
give the process for copying a named source file to a named target
file. This goes in two phases.
-}
{- 4.6.1 Firstly, you should identify the command-reponse interface within
which you need to work. You will need to be able to read and write files,
but also to signal errors (in case a file fails to open for some reason).
You must ensure that it is impossible for any process using your interface
to escape with an error leaving a file open. You must also make it
possible to guarantee that your copying process will, error or not, leave
all files closed.
-}
CPState : Set
CPState = {!!}
CPInterface : CPState => CPState
CPInterface = {!!}
{- 4.6.2 Secondly, you should implement your copying process, working to your
interface. I will let you switch off the termination checker: you cannot
predict in advance how long the copying process will go on, as you have
not seen the source file yet. (Later, we'll learn how to be honest about
things which might go on for ever, but for now, let's cheat.)
-}
{-# NO_TERMINATION_CHECK #-}
cp : (sourceFile targetFile : String) -> Game CPInterface {!!} {!!}
cp sourceFile targetFile = {!!}
{- HINTS
You will certainly need to build some extra bits and pieces.
You have the components for reading, writing and error handling, and
suitable kit with which to combine them. Reading and writing don't
interfere with each other, but it's important to make sure that you
can't bomb out with an error, so some shared state seems important.
There are really two phases to the process:
(1) getting the files open -- this may go wrong
(2) copying from one to the other -- this will work if we reach it
You might want to split these phases apart.
-}
---------------------------------------------------------------------------
-- SCRIPTING INTERACTION
---------------------------------------------------------------------------
{- 4.7.1 Show how to take a command-response interface and deliver its
"scripted" version, where a script command consists of any permitted
(possibly empty) sequence of the given commands. -}
SCRIPT : {I : Set} -> I => I -> I => I
SCRIPT {I} CRn = Game CRn (\ I -> One) <! Rs / ns where
Rs : (i : I) -> Game CRn (\ I -> One) i -> Set
Rs i cs = {!!}
ns : (i : I)(cs : Game CRn (\ I -> One) i) -> Rs i cs -> I
ns i cs rs = {!!}
{- 4.7.2 Show how to take a strategy for scripted interaction and turn
it into a strategey for unscripted interaction, by running the scripts
one command at a time. You may find it useful to build a helper function
to process one script. -}
unScript : {I : Set}(CRn : I => I){X : I -> Set}{i : I} ->
Game (SCRIPT CRn) X i -> Game CRn X i
unScript CRn g = {!!}
-- HINT doing recursion in the "fold" pattern may help
---------------------------------------------------------------------------
-- INDEXED CONTAINER DRIVERS(*)
-- (*) The researchers who invented this stuff are fans of The Fall
-- (by which I mean the group led my Mark E Smith who wrote the song
-- The Container Drivers, not some johnny-come-lately Northern Irish
-- serial killer drama).
---------------------------------------------------------------------------
record Driver {I J : Set}(Sync : I -> J -> Set)
(Hi : I => I)(Lo : J => J) : Set where
-- Hi is a high-level command-response interface
-- Lo is a low-level command-response interface
-- Sync specifies which high and low level states are compatible
-- and what you expect to know at the time
field
-- assuming states are in sync; it should be possible to map
-- high-level commands to low-level commands...
hiClo : (i : I)(j : J) -> Sync i j ->
Command Hi i -> Command Lo j
-- ...and afterwards to translate the low-level response to that
-- command back up to the high-level
loRhi : (i : I)(j : J)(s : Sync i j)(c : Command Hi i) ->
Response Lo j (hiClo i j s c) -> Response Hi i c
-- moreover, the resulting states should be in sync
nSync : (i : I)(j : J)(s : Sync i j)(c : Command Hi i)
(r : Response Lo j (hiClo i j s c)) ->
Sync (next Hi i c (loRhi i j s c r)) (next Lo j (hiClo i j s c) r)
open Driver public
---------------------------------------------------------------------------
-- A DANGEROUS HASKELL IO COMMAND-RESPONSE SYSTEM
---------------------------------------------------------------------------
data Maybe (X : Set) : Set where
yes : X -> Maybe X
no : Maybe X
data IOMode : Set where
readMode writeMode appendMode readWriteMode : IOMode
postulate Handle : Set
data HaskellIOCommand (_ : One) : Set where
hOpen : String -> IOMode -> HaskellIOCommand <>
hClose hIsEOF hGetChar : Handle -> HaskellIOCommand <>
hPutChar : Handle -> Char -> HaskellIOCommand <>
hError : String -> HaskellIOCommand <>
HaskellIOResponse : (i : One) -> HaskellIOCommand i -> Set
HaskellIOResponse i (hOpen f m) = Maybe Handle
HaskellIOResponse i (hClose h) = One
HaskellIOResponse i (hIsEOF h) = Two
HaskellIOResponse i (hGetChar h) = Char
HaskellIOResponse i (hPutChar h c) = One
HaskellIOResponse i (hError e) = Zero
HASKELLIO : One => One
HASKELLIO = HaskellIOCommand <! HaskellIOResponse / _
---------------------------------------------------------------------------
-- SCRIPTING INTERACTION
---------------------------------------------------------------------------
{- 4.8 Your mission is to translate your lovely, safe characterisation
of reading and writing into its dodgy Haskell counterpart. Of course,
your code shouldn't do anything dodgy. You will need to think what
information must be available when you are in each state.
-}
safe2unsafe : Driver (\ i j -> {!!}) CPInterface (SCRIPT HASKELLIO)
safe2unsafe = {!!}
---------------------------------------------------------------
-- TO BE CONTINUED... BUT NOT WITH ANY MORE CODING OBLIGATIONS
---------------------------------------------------------------
```
**specimen solution and mark scheme**
```
module Ex4Sol where
{- Mark Scheme
as indicated, below, totalling 15
-}
open import Ex1Prelude
open import IxCon
{-# BUILTIN BOOL Two #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #-}
{-# BUILTIN CONS _:>_ #-}
postulate -- this means that we just suppose the following things exist...
Char : Set
String : Set
{-# BUILTIN CHAR Char #-}
{-# BUILTIN STRING String #-}
primitive -- these are baked in; they even work!
primCharEquality : Char -> Char -> Two
primStringAppend : String -> String -> String
primStringToList : String -> List Char
primStringFromList : List Char -> String
---------------------------------------------------------------------------
-- WRITING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- If you possess the ability to open a file for writing, you might
have the following interface. -}
-- States
data WriteState : Set where
opened closed : WriteState -- do you currently have a file open or not?
-- Commands
data WriteC : WriteState -> Set where
openWrite : (fileName : String) -> WriteC closed
writeChar : Char -> WriteC opened
closeWrite : WriteC opened
-- Responses
WriteR : (j : WriteState)(c : WriteC j) -> Set
WriteR .closed (openWrite fileName) = WriteState
WriteR .opened (writeChar x) = One
WriteR .opened closeWrite = One
{- 4.1 Implement the following operation which determines the next
state. You should ensure that you can write characters only to
a successfully opened file, and that you can write as many as
you want. It should also be possible to insist that a process
closes its file. (1 mark) -}
{-
writeNext : (j : WriteState)(c : WriteC j) -> WriteR j c -> WriteState
writeNext j c r = {!!}
-}
writeNext : (j : WriteState)(c : WriteC j) -> WriteR j c -> WriteState
writeNext ._ (openWrite fileName) j = j
writeNext .opened (writeChar x) r = opened
writeNext .opened closeWrite r = closed
-- the file writing interface, assembled as an indexed container
WRITE : WriteState => WriteState
WRITE = WriteC <! WriteR / writeNext
---------------------------------------------------------------------------
-- READING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- To read from a file, it should be open, and you shouldn't be at the
end of it. -}
-- States
data ReadState : Set where
opened : (eof : Two) -> ReadState -- eof is tt if we're at end of file
closed : ReadState
{- 4.2 Finish the READ implementation, in accordance with the description.
(3 marks, for commands, responses and next) -}
{-
-- Commands
data ReadC : ReadState -> Set where
openRead : {- your stuff -} ReadC {!!} -- needs a filename; might not open successfully;
-- might open an empty file
readChar : {- your stuff -} ReadC {!!} -- makes sense only if we're not at end of file
-- and might take us to end of file
closeRead : {- your stuff -} ReadC {!!} -- makes sense only if the file is open
-- but you should not be forced to read the whole file
-- Responses
ReadR : (j : ReadState)(c : ReadC j) -> Set
ReadR j c = {!!}
-- next State; you need to make sure the response gives enough info
readNext : (j : ReadState)(c : ReadC j) -> ReadR j c -> ReadState
readNext j c r = {!!}
-}
-- Commands
data ReadC : ReadState -> Set where
openRead : String -> ReadC closed -- needs a filename; might not open successfully;
-- might open an empty file
readChar : ReadC (opened ff) -- makes sense only if we're not at end of file
-- and might take us to end of file
closeRead : {b : Two} -> ReadC (opened b) -- makes sense only if the file is open
-- Responses
ReadR : (j : ReadState)(c : ReadC j) -> Set
ReadR .closed (openRead x) = ReadState
ReadR .(opened ff) readChar = Char /*/ Two
ReadR ._ closeRead = One
-- next State; you need to make sure the resonse gives enough info
readNext : (j : ReadState)(c : ReadC j) -> ReadR j c -> ReadState
readNext .closed (openRead x) s = s
readNext .(opened ff) readChar (c , b) = opened b
readNext ._ closeRead r = closed
-- the file reading interface, assembled as an indexed container
READ : ReadState => ReadState
READ = ReadC <! ReadR / readNext
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SHARED STATE
---------------------------------------------------------------------------
{- 4.3 Let's suppose we have two command-response interfaces which offer
different functionality for the same system. Correspondingly, we'll
have two indexed containers for the same index set. Show that you
can combine them into one indexed container which lets you choose a
command from either menu and evolves the state as specified by
whichever interface offered the chosen command.
(2 marks, one for commands, one for the rest)
-}
_=+=_ : {I : Set} -> I => I -> I => I -> I => I
(C0 <! R0 / n0) =+= (C1 <! R1 / n1)
= (\ i -> C0 i /+/ C1 i)
<! (\ { i (inl c0) -> R0 i c0 ; i (inr c1) -> R1 i c1 })
/ (\ { i (inl c0) r0 -> n0 i c0 r0 ; i (inr c1) r1 -> n1 i c1 r1 })
---------------------------------------------------------------------------
-- WHEN IGNORANCE IS BLISS, BIS
---------------------------------------------------------------------------
{- 4.4 If we have a command-response interface with index I representing
states of the system, show that we can index basically the same
commands and responses over a state, I /*/ J, where the J is just
useless information which never changes. (This operation isn't
super-useful on its own, but it's handy in combination with other
things. (2 marks; half each for C, R, n, half for deploying
symmetry) -}
GrowR : {I J : Set} -> I => I -> (I /*/ J) => (I /*/ J)
GrowR (C <! R / n)
= (\ { (i , j) -> C i })
<! (\ { (i , j) c -> R i c })
/ (\ { (i , j) c r -> n i c r , j })
-- do the same for "growing the index on the left"
GrowL : {I J : Set} -> I => I -> (J /*/ I) => (J /*/ I)
GrowL (C <! R / n)
= (\ { (j , i) -> C i })
<! (\ { (j , i) c -> R i c })
/ (\ { (j , i) c r -> j , n i c r })
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SEPARATE STATE
---------------------------------------------------------------------------
{- 4.5 Making use of 4.4 and 4.5, show how to combine two interfaces which
operate independently on separate state: commands from one should
not affect the state of the other. (1 mark)
-}
{-
_<+>_ : {I0 I1 : Set} -> I0 => I0 -> I1 => I1 -> (I0 /*/ I1) => (I0 /*/ I1)
C0 <+> C1 = {!!}
-}
_<+>_ : {I0 I1 : Set} -> I0 => I0 -> I1 => I1 -> (I0 /*/ I1) => (I0 /*/ I1)
C0 <+> C1 = GrowR C0 =+= GrowL C1
---------------------------------------------------------------------------
-- ERROR REPORTING, AN INTERFACE
---------------------------------------------------------------------------
{- I'm building the next bit for you.
When things go wrong, we need to trigger an error condition and abort
mission. However, if we have other stuff going on (open files, etc),
it may not always be ok to drop everything and run away. There will
be some states in which it is safe to escape (and deliver a suitable
error message, perhaps) and other states in which escape should be
impossible.
If it is safe to issue an error message, we should be able to do so
without fear of any response from the environment that would oblige
us to carry on.
-}
data ErrorC {I : Set}(SafeMessage : I -> Set)(i : I) : Set where
error : SafeMessage i -> ErrorC SafeMessage i
-- the SafeMessage parameter tells us what is an acceptable
-- error message in any given state; in states where this gives
-- Zero, it will be impossible to trigger an error!
ErrorR : {I : Set}{SafeMessage : I -> Set}(i : I)(c : ErrorC SafeMessage i) -> Set
ErrorR _ _ = Zero -- there's no comeback
errorNext : {I : Set}{SafeMessage : I -> Set}
(i : I)(c : ErrorC SafeMessage i) -> ErrorR i c -> I
errorNext i c () -- so we don't have to say how the state will evolve
ERROR : {I : Set}(SafeMessage : I -> Set) -> I => I
ERROR SafeMessage = ErrorC SafeMessage <! ErrorR / errorNext
---------------------------------------------------------------------------
-- COPY A FILE
---------------------------------------------------------------------------
{- 4.6 Implement a process which, given access to suitable interfaces, will
give the process for copying a named source file to a named target
file. You should:
(1) construct the appropriate combination of interfaces
(2) ensure that errors are appropriately signalled, including the
text of any relevant filenames
(3) ensure that all files are guaranteed by typechecking to be closed,
whether or not there is an error
(4) buffer as little data in memory as possible (so write early,
write often)
-}
IndexCP : Set
IndexCP = (ReadState /*/ WriteState)
BothClosed : IndexCP -> Set
BothClosed (closed , closed) = String
BothClosed _ = Zero
InterfaceCP : IndexCP => IndexCP -- (1 mark)
InterfaceCP = ERROR BothClosed =+= (READ <+> WRITE)
SuccessCP : IndexCP -> Set
SuccessCP (closed , closed) = One
SuccessCP _ = Zero
initialCP : IndexCP
initialCP = (closed , closed)
concat : List String -> String
concat [] = ""
concat (s :> ss) = primStringAppend s (concat ss)
{-# NO_TERMINATION_CHECK #-}
copyOpen : (b : Two) -> Game InterfaceCP SuccessCP (opened b , opened)
copyOpen tt = < inr (inl closeRead) , ( \ _ -> < inr (inr closeWrite) , ( \ _ -> win <> ) > ) >
copyOpen ff = < inr (inl readChar) , ( \ { (c , b) -> < inr (inr (writeChar c)) , (\ _ -> copyOpen b) > } ) >
-- (3 marks for beginning, middle, end)
cp : (sourceFile targetFile : String) -> Game InterfaceCP SuccessCP initialCP
cp sourceFile targetFile
= < inr (inl (openRead sourceFile)) , (\
{ (opened b) ->
< inr (inr (openWrite targetFile)) , ((\
{ opened -> copyOpen b
; closed -> < inr (inl closeRead) , (\ _ ->
< inl (error (concat ("Could not open " :> targetFile :> []))) , (\ ()) > ) >
})) >
; closed -> < inl (error (concat ("Could not open " :> sourceFile :> []))) , (\ ()) >
}) >
-- (1 mark)
SCRIPT : {I : Set} -> I => I -> I => I
SCRIPT {I} CRn = Game CRn (\ I -> One) <! Rs / ns where
Rs : (i : I) -> Game CRn (\ I -> One) i -> Set
Rs i (win x) = One
Rs i < c , k > = Sigma (Response CRn i c) \ r -> Rs (next CRn i c r) (k r)
ns : (i : I)(cs : Game CRn (\ I -> One) i) -> Rs i cs -> I
ns i (win x) rs = i
ns i < c , k > (r , rs) = ns (next CRn i c r) (k r) rs
-- (1 mark)
unScript : {I : Set}(CRn : I => I){X : I -> Set}{i : I} ->
Game (SCRIPT CRn) X i -> Game CRn X i
runScript : {I : Set}(CRn : I => I){X : I -> Set}{i : I} ->
(cs : Command (SCRIPT CRn) i)
(k : (rs : Response (SCRIPT CRn) i cs) ->
Game CRn X (next (SCRIPT CRn) i cs rs))
-> Game CRn X i
unScript CRn (win x) = win x
unScript CRn {X}{i} < cs , k > = runScript CRn cs \ rs -> unScript CRn (k rs)
runScript CRn (win x) k = k <>
runScript CRn < c , f > k = < c , (\ r -> runScript CRn (f r) \ rs -> k (r , rs)) >
-- the rest was for fun
data Maybe (X : Set) : Set where
yes : X -> Maybe X
no : Maybe X
data IOMode : Set where
readMode writeMode appendMode readWriteMode : IOMode
postulate Handle : Set
data HaskellIOCommand (_ : One) : Set where
hOpen : String -> IOMode -> HaskellIOCommand <>
hClose hIsEOF hGetChar : Handle -> HaskellIOCommand <>
hPutChar : Handle -> Char -> HaskellIOCommand <>
hError : String -> HaskellIOCommand <>
HaskellIOResponse : (i : One) -> HaskellIOCommand i -> Set
HaskellIOResponse i (hOpen f m) = Maybe Handle
HaskellIOResponse i (hClose h) = One
HaskellIOResponse i (hIsEOF h) = Two
HaskellIOResponse i (hGetChar h) = Char
HaskellIOResponse i (hPutChar h c) = One
HaskellIOResponse i (hError e) = Zero
HASKELLIO : One => One
HASKELLIO = HaskellIOCommand <! HaskellIOResponse / _
record Driver {I J : Set}(Sync : I -> J -> Set)
(Hi : I => I)(Lo : J => J) : Set where
field
hiClo : (i : I)(j : J) -> Sync i j ->
Command Hi i -> Command Lo j
loRhi : (i : I)(j : J)(s : Sync i j)(c : Command Hi i) ->
Response Lo j (hiClo i j s c) -> Response Hi i c
nSync : (i : I)(j : J)(s : Sync i j)(c : Command Hi i)
(r : Response Lo j (hiClo i j s c)) ->
Sync (next Hi i c (loRhi i j s c r)) (next Lo j (hiClo i j s c) r)
open Driver public
RH : ReadState -> Set
RH (opened eof) = Handle
RH closed = One
WH : WriteState -> Set
WH opened = Handle
WH closed = One
hC : (i : IndexCP) (j : One) ->
RH (outl i) /*/ WH (outr i) ->
Command InterfaceCP i -> Command (SCRIPT HASKELLIO) j
hC (.closed , w) j (rh , wh) (inr (inl (openRead x)))
= < hOpen x readMode , (\ { no -> win <> ;
(yes h) -> < hIsEOF h , (\ b -> win <>) > }) >
hC (.(opened ff) , w) j (rh , wh) (inr (inl readChar))
= < hGetChar rh , (\ c -> < hIsEOF rh , (\ b -> win <>) >) >
hC (._ , w) j (rh , wh) (inr (inl closeRead))
= < hClose rh , (\ _ -> win <>) >
hC (r , .closed) j (rh , wh) (inr (inr (openWrite fileName)))
= < hOpen fileName writeMode , (\ _ -> win <>) >
hC (r , .opened) j (rh , wh) (inr (inr (writeChar x)))
= < hPutChar wh x , (\ _ -> win <>) >
hC (r , .opened) j (rh , wh) (inr (inr closeWrite))
= < hClose wh , (\ _ -> win <>) >
hC (opened eof , opened) j (rh , wh) (inl (error ()))
hC (opened eof , closed) j (rh , wh) (inl (error ()))
hC (closed , opened) j (rh , wh) (inl (error ()))
hC (closed , closed) j (rh , wh) (inl (error e)) = < hError e , (\ ()) >
hR : (i : IndexCP) (j : One) (s : RH (outl i) /*/ WH (outr i))
(c : Command InterfaceCP i) ->
Response (SCRIPT HASKELLIO) j (hC i j s c) ->
Response InterfaceCP i c
hR (.closed , w) j (<> , wh) (inr (inl (openRead x))) (yes rh , b , <>)
= opened b
hR (.closed , w) j (<> , wh) (inr (inl (openRead x))) (no , <>)
= closed
hR (.(opened ff) , w) j (rh , wh) (inr (inl readChar)) (c , b , <>) = c , b
hR (._ , w) j (rh , wh) (inr (inl closeRead)) rs = <>
hR (r , .closed) j (rh , <>) (inr (inr (openWrite fileName))) (yes wh , <>)
= opened
hR (r , .closed) j (rh , <>) (inr (inr (openWrite fileName))) (no , <>)
= closed
hR (r , .opened) j (rh , wh) (inr (inr (writeChar x))) rs = <>
hR (r , .opened) j (rh , wh) (inr (inr closeWrite)) rs = <>
hR (opened eof , opened) j (rh , wh) (inl (error ())) rs
hR (opened eof , closed) j (rh , wh) (inl (error ())) rs
hR (closed , opened) j (rh , wh) (inl (error ())) rs
hR (closed , closed) j (rh , wh) (inl (error x)) (() , snd)
hnS : (i : IndexCP) (j : One) (s : RH (outl i) /*/ WH (outr i))
(c : Command InterfaceCP i)
(r : Response (SCRIPT HASKELLIO) j (hC i j s c)) ->
RH (outl (next InterfaceCP i c (hR i j s c r))) /*/
WH (outr (next InterfaceCP i c (hR i j s c r)))
hnS (.closed , w) j (<> , wh) (inr (inl (openRead x))) (yes rh , snd) = rh , wh
hnS (.closed , w) j (<> , wh) (inr (inl (openRead x))) (no , snd) = <> , wh
hnS (.(opened ff) , w) j (rh , wh) (inr (inl readChar)) rs = rh , wh
hnS (._ , w) j (rh , wh) (inr (inl closeRead)) rs = <> , wh
hnS (r , .closed) j (rh , <>) (inr (inr (openWrite fileName))) (yes wh , snd)
= rh , wh
hnS (r , .closed) j (rh , <>) (inr (inr (openWrite fileName))) (no , snd) = rh , <>
hnS (r , .opened) j (rh , wh) (inr (inr (writeChar x))) rs = rh , wh
hnS (r , .opened) j (rh , wh) (inr (inr closeWrite)) rs = rh , <>
hnS (opened eof , opened) j (rh , wh) (inl (error ())) rs
hnS (opened eof , closed) j (rh , wh) (inl (error ())) rs
hnS (closed , opened) j (rh , wh) (inl (error ())) rs
hnS (closed , closed) j (rh , wh) (inl (error x)) (() , snd)
safe2unsafe : Driver {IndexCP}{One} (\ { (r , w) j -> RH r /*/ WH w })
InterfaceCP (SCRIPT HASKELLIO)
safe2unsafe = record
{ hiClo = hC
; loRhi = hR
; nSync = hnS
}
```
##Exercise 5##
**problem file and mark scheme** `Ex5/Edit.agda`
```
module Edit where
{- This is the file where you should work. -}
open import AgdaSetup
{- The key editor data structure is the cursor. A Cursor M X represents
being somewhere in the middle of a sequence of X values, holding an M. -}
record Cursor (M X : Set) : Set where
constructor _<[_]>_
field
beforeMe : Bwd X
atMe : M
afterMe : List X
infix 4 _<[_]>_
{- An editor buffer is a nested cursor: we're in the middle of a bunch of
*lines*, holding a cursor for the current line, which puts us in the
middle of a bunch of characters, holding the element of One. -}
Buffer : Set
Buffer = Cursor (Cursor One Char) (List Char)
{- This operator, called "chips", shuffles the elements from a backward list
on to the start of a forward list, keeping them in the same order. -}
_<>>_ : {X : Set} -> Bwd X -> List X -> List X
[] <>> xs = xs
(xz <: x) <>> xs = xz <>> (x :> xs)
{- The "fish" operator goes the other way. -}
_<><_ : {X : Set} -> Bwd X -> List X -> Bwd X
xz <>< [] = xz
xz <>< (x :> xs) = (xz <: x) <>< xs
{- You can turn a buffer into a list of lines, preserving its text. -}
bufText : Buffer -> List (List Char)
bufText
(sz <[
cz <[ <> ]> cs
]> ss)
= sz <>> ((cz <>> cs) :> ss)
{- Here's an example of a proof of a fact about fish and chips. -}
firstFishFact : {X : Set} -> (xz : Bwd X)(xs : List X) ->
(xz <>< xs) <>> [] == xz <>> xs
firstFishFact xz [] = refl
firstFishFact xz (x :> xs) = firstFishFact (xz <: x) xs
{- You will need more such facts. -}
{- EXERCISE 5.1 -}
{- When we start the editor with the command
./Edit foo.txt
the contents of foo.txt will be turned into a list of lines.
Your (not so tricky) mission is to turn the file contents into a buffer which
contains the same text.
(1 mark)
-}
initBuf : List (List Char) -> Buffer
initBuf ss =
[] <[
[] <[ <> ]> []
]> []
{- As you can see, the current version will run, but it always gives the empty
buffer, which is not what we want unless the input is empty. -}
{- Next comes the heart of the editor. You get a keystroke and the current buffer,
and you have to say what is the new buffer. You also have to say what is the
extent of the change.
The tricky part is this: you have to be honest enough about your change
report, so that we don't underestimate the amount of updating the screen needs.
-}
Honest : Buffer -> Change /*/ Buffer -> Set
Honest b (allQuiet , b') = b == b'
Honest b (cursorMove , b') = bufText b == bufText b'
Honest (sz <[ _ ]> ss) (lineEdit , (sz' <[ _ ]> ss')) = (sz == sz') /*/ (ss == ss')
Honest _ (bigChange , _) = One
record UpdateFrom (b : Buffer) : Set where -- b is the starting buffer
constructor _///_
field
update : Change /*/ Buffer -- change and new buffer
honest : Honest b update
open UpdateFrom
infix 2 _///_
{- EXERCISE 5.2 -}
{- Implement the appropriate behaviour for as many keystrokes as you can.
I have done a couple for you, but I don't promise to have done them
correctly. -}
keystroke : Key -> (b : Buffer) -> UpdateFrom b
keystroke (char c)
(sz <[
cz <[ <> ]> cs
]> ss)
= lineEdit ,
(sz <[
cz <[ <> ]> c :> cs
]> ss)
/// refl , refl -- see? same above and below
keystroke (arrow normal right)
(sz <: s <[
[] <[ <> ]> cs
]> ss)
= cursorMove ,
(sz <[ ([] <>< s) <[ <> ]> [] ]> cs :> ss)
/// within (\ x -> sz <>> (x :> cs :> ss)) turn s into ([] <>< s) <>> []
because symmetry (firstFishFact [] s)
keystroke k b = allQuiet , b /// refl
{- Please expect to need to invent extra functions, e.g., to measure where you
are, so that up and down arrow work properly. -}
{- Remember also that you can always overestimate the change by saying bigChange,
which needs only a trivial proof. But you may find that the display will flicker
badly if you do. -}
{- (char c) 1 mark
enter 2 marks
backspace delete 2 marks for the pair
left right 2 marks for the pair (with cursorMove change)
up down 2 marks for the pair (with cursorMove change)
-}
{- EXERCISE 5.3 -}
{- You will need to improve substantially on my implementation of the next component,
whose purpose is to update the window. Mine displays only one line! -}
render :
Nat /*/ Nat -> -- height and width of window -- CORRECTION! width and height
Nat /*/ Nat -> -- first visible row, first visible column
Change /*/ Buffer -> -- what just happened
List Action /*/ -- how to update screen
(Nat /*/ Nat) -- new first visible row, first visible column
render _ tl (allQuiet , _) = ([] , tl)
render _ tl (_ , (_ <[ cz <[ <> ]> cs ]> _))
= (goRowCol 0 0 :> sendText (cz <>> cs) :> []) , tl
{- The editor window gives you a resizable rectangular viewport onto the editor buffer.
You get told
the current size of the viewport
which row and col of the buffer are at the top left of the viewport
(so you can handle documents which are taller or wider than the window)
the most recent change report and buffer
You need to figure out whether you need to move the viewport
(by finding out if the cursor is still within the viewport)
and if so, where to.
You need to figure out what to redisplay. If the change report says
lineEdit and the viewport has not moved, you need only repaint the
current line. If the viewport has moved or the change report says
bigChange, you need to repaint the whole buffer.
You will need to be able to grab a rectangular region of text from the
buffer, but you do know how big and where from.
Remember to put the cursor in the right place, relative to where in
the buffer the viewport is supposed to be. The goRowCol action takes
*viewport* coordinates, not *buffer* coordinates! You will need to
invent subtraction!
-}
{- Your code does not need to worry about resizing the window. My code does
that. On detecting a size change, my code just calls your code with a
bigChange report and the same buffer, so if you are doing a proper repaint,
the right thing will happen. -}
{- 2 marks for ensuring that a buffer smaller than the viewport displays
correctly, with the cursor in the right place, if nobody changes
the viewport size
2 marks for ensuring that the cursor remains within the viewport even if
the viewport needs to move
1 mark for ensuring that lineEdit changes need only affect one line of
the display (provided the cursor stays in the viewport)
-}
{- FOR MASOCHISTS ONLY, you have a chance to be even more creative. You have
spare detectable keys that you could invent meanings for. You also have the
freedom to change the definition of Buffer, as my code does not care what
a Buffer is: it only needs to know how to initialize, update and render,
and these are defined by you.
Additional structural cursor moves (beginning and end of line, etc) are quite
easy. Going left or right word-by-word would be more fun: you can match
against a pattern such as ' '.
Selection and cut/copy/paste are more challenging. For these, you need to
modify the Buffer structure to remember the clipboard contents (if any),
and to manage the extent of any selected region.
If you feel the need to vary the foreground or background colour of the displayed
text (e.g. to show a selection), please let me know.
(SUBTEXT: this exercise is a cut-down version of last year's post-Easter
task. Feel free to ignore the cutting-down.)
-}
{- Your code then hooks into mine to produce a top level executable! -}
main : IO One
main = mainLoop initBuf (\ k b -> update (keystroke k b)) render
{- To build the editor, just do
make
in a shell window (with Ex5 the current directory).
To run the editor, once compiled, do
./Edit
in the shell window, which should become the editor window.
To quit the editor, do
ctrl-C
like an old-fashioned soul.
-}
{- There is no one right way to do this exercise, and there is some scope for
extension. It's important that you get in touch if you need help, either in
achieving the basic deliverable, or in finding ways to explore beyond it.
-}
```
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex4Sol where
{- Mark Scheme
as indicated, below, totalling 15
-}
open import Ex1Prelude
open import IxCon
{-# BUILTIN BOOL Two #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #-}
{-# BUILTIN CONS _:>_ #-}
postulate -- this means that we just suppose the following things exist...
Char : Set
String : Set
{-# BUILTIN CHAR Char #-}
{-# BUILTIN STRING String #-}
primitive -- these are baked in; they even work!
primCharEquality : Char -> Char -> Two
primStringAppend : String -> String -> String
primStringToList : String -> List Char
primStringFromList : List Char -> String
---------------------------------------------------------------------------
-- WRITING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- If you possess the ability to open a file for writing, you might
have the following interface. -}
-- States
data WriteState : Set where
opened closed : WriteState -- do you currently have a file open or not?
-- Commands
data WriteC : WriteState -> Set where
openWrite : (fileName : String) -> WriteC closed
writeChar : Char -> WriteC opened
closeWrite : WriteC opened
-- Responses
WriteR : (j : WriteState)(c : WriteC j) -> Set
WriteR .closed (openWrite fileName) = WriteState
WriteR .opened (writeChar x) = One
WriteR .opened closeWrite = One
{- 4.1 Implement the following operation which determines the next
state. You should ensure that you can write characters only to
a successfully opened file, and that you can write as many as
you want. It should also be possible to insist that a process
closes its file. (1 mark) -}
{-
writeNext : (j : WriteState)(c : WriteC j) -> WriteR j c -> WriteState
writeNext j c r = {!!}
-}
writeNext : (j : WriteState)(c : WriteC j) -> WriteR j c -> WriteState
writeNext ._ (openWrite fileName) j = j
writeNext .opened (writeChar x) r = opened
writeNext .opened closeWrite r = closed
-- the file writing interface, assembled as an indexed container
WRITE : WriteState => WriteState
WRITE = WriteC <! WriteR / writeNext
---------------------------------------------------------------------------
-- READING FILES, AN INTERFACE
---------------------------------------------------------------------------
{- To read from a file, it should be open, and you shouldn't be at the
end of it. -}
-- States
data ReadState : Set where
opened : (eof : Two) -> ReadState -- eof is tt if we're at end of file
closed : ReadState
{- 4.2 Finish the READ implementation, in accordance with the description.
(3 marks, for commands, responses and next) -}
{-
-- Commands
data ReadC : ReadState -> Set where
openRead : {- your stuff -} ReadC {!!} -- needs a filename; might not open successfully;
-- might open an empty file
readChar : {- your stuff -} ReadC {!!} -- makes sense only if we're not at end of file
-- and might take us to end of file
closeRead : {- your stuff -} ReadC {!!} -- makes sense only if the file is open
-- but you should not be forced to read the whole file
-- Responses
ReadR : (j : ReadState)(c : ReadC j) -> Set
ReadR j c = {!!}
-- next State; you need to make sure the response gives enough info
readNext : (j : ReadState)(c : ReadC j) -> ReadR j c -> ReadState
readNext j c r = {!!}
-}
-- Commands
data ReadC : ReadState -> Set where
openRead : String -> ReadC closed -- needs a filename; might not open successfully;
-- might open an empty file
readChar : ReadC (opened ff) -- makes sense only if we're not at end of file
-- and might take us to end of file
closeRead : {b : Two} -> ReadC (opened b) -- makes sense only if the file is open
-- Responses
ReadR : (j : ReadState)(c : ReadC j) -> Set
ReadR .closed (openRead x) = ReadState
ReadR .(opened ff) readChar = Char /*/ Two
ReadR ._ closeRead = One
-- next State; you need to make sure the resonse gives enough info
readNext : (j : ReadState)(c : ReadC j) -> ReadR j c -> ReadState
readNext .closed (openRead x) s = s
readNext .(opened ff) readChar (c , b) = opened b
readNext ._ closeRead r = closed
-- the file reading interface, assembled as an indexed container
READ : ReadState => ReadState
READ = ReadC <! ReadR / readNext
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SHARED STATE
---------------------------------------------------------------------------
{- 4.3 Let's suppose we have two command-response interfaces which offer
different functionality for the same system. Correspondingly, we'll
have two indexed containers for the same index set. Show that you
can combine them into one indexed container which lets you choose a
command from either menu and evolves the state as specified by
whichever interface offered the chosen command.
(2 marks, one for commands, one for the rest)
-}
_=+=_ : {I : Set} -> I => I -> I => I -> I => I
(C0 <! R0 / n0) =+= (C1 <! R1 / n1)
= (\ i -> C0 i /+/ C1 i)
<! (\ { i (inl c0) -> R0 i c0 ; i (inr c1) -> R1 i c1 })
/ (\ { i (inl c0) r0 -> n0 i c0 r0 ; i (inr c1) r1 -> n1 i c1 r1 })
---------------------------------------------------------------------------
-- WHEN IGNORANCE IS BLISS, BIS
---------------------------------------------------------------------------
{- 4.4 If we have a command-response interface with index I representing
states of the system, show that we can index basically the same
commands and responses over a state, I /*/ J, where the J is just
useless information which never changes. (This operation isn't
super-useful on its own, but it's handy in combination with other
things. (2 marks; half each for C, R, n, half for deploying
symmetry) -}
GrowR : {I J : Set} -> I => I -> (I /*/ J) => (I /*/ J)
GrowR (C <! R / n)
= (\ { (i , j) -> C i })
<! (\ { (i , j) c -> R i c })
/ (\ { (i , j) c r -> n i c r , j })
-- do the same for "growing the index on the left"
GrowL : {I J : Set} -> I => I -> (J /*/ I) => (J /*/ I)
GrowL (C <! R / n)
= (\ { (j , i) -> C i })
<! (\ { (j , i) c -> R i c })
/ (\ { (j , i) c r -> j , n i c r })
---------------------------------------------------------------------------
-- COMBINING TWO INTERFACES WITH SEPARATE STATE
---------------------------------------------------------------------------
{- 4.5 Making use of 4.4 and 4.5, show how to combine two interfaces which
operate independently on separate state: commands from one should
not affect the state of the other. (1 mark)
-}
{-
_<+>_ : {I0 I1 : Set} -> I0 => I0 -> I1 => I1 -> (I0 /*/ I1) => (I0 /*/ I1)
C0 <+> C1 = {!!}
-}
_<+>_ : {I0 I1 : Set} -> I0 => I0 -> I1 => I1 -> (I0 /*/ I1) => (I0 /*/ I1)
C0 <+> C1 = GrowR C0 =+= GrowL C1
---------------------------------------------------------------------------
-- ERROR REPORTING, AN INTERFACE
---------------------------------------------------------------------------
{- I'm building the next bit for you.
When things go wrong, we need to trigger an error condition and abort
mission. However, if we have other stuff going on (open files, etc),
it may not always be ok to drop everything and run away. There will
be some states in which it is safe to escape (and deliver a suitable
error message, perhaps) and other states in which escape should be
impossible.
If it is safe to issue an error message, we should be able to do so
without fear of any response from the environment that would oblige
us to carry on.
-}
data ErrorC {I : Set}(SafeMessage : I -> Set)(i : I) : Set where
error : SafeMessage i -> ErrorC SafeMessage i
-- the SafeMessage parameter tells us what is an acceptable
-- error message in any given state; in states where this gives
-- Zero, it will be impossible to trigger an error!
ErrorR : {I : Set}{SafeMessage : I -> Set}(i : I)(c : ErrorC SafeMessage i) -> Set
ErrorR _ _ = Zero -- there's no comeback
errorNext : {I : Set}{SafeMessage : I -> Set}
(i : I)(c : ErrorC SafeMessage i) -> ErrorR i c -> I
errorNext i c () -- so we don't have to say how the state will evolve
ERROR : {I : Set}(SafeMessage : I -> Set) -> I => I
ERROR SafeMessage = ErrorC SafeMessage <! ErrorR / errorNext
---------------------------------------------------------------------------
-- COPY A FILE
---------------------------------------------------------------------------
{- 4.6 Implement a process which, given access to suitable interfaces, will
give the process for copying a named source file to a named target
file. You should:
(1) construct the appropriate combination of interfaces
(2) ensure that errors are appropriately signalled, including the
text of any relevant filenames
(3) ensure that all files are guaranteed by typechecking to be closed,
whether or not there is an error
(4) buffer as little data in memory as possible (so write early,
write often)
-}
IndexCP : Set
IndexCP = (ReadState /*/ WriteState)
BothClosed : IndexCP -> Set
BothClosed (closed , closed) = String
BothClosed _ = Zero
InterfaceCP : IndexCP => IndexCP -- (1 mark)
InterfaceCP = ERROR BothClosed =+= (READ <+> WRITE)
SuccessCP : IndexCP -> Set
SuccessCP (closed , closed) = One
SuccessCP _ = Zero
initialCP : IndexCP
initialCP = (closed , closed)
concat : List String -> String
concat [] = ""
concat (s :> ss) = primStringAppend s (concat ss)
{-# NO_TERMINATION_CHECK #-}
copyOpen : (b : Two) -> Game InterfaceCP SuccessCP (opened b , opened)
copyOpen tt = < inr (inl closeRead) , ( \ _ -> < inr (inr closeWrite) , ( \ _ -> win <> ) > ) >
copyOpen ff = < inr (inl readChar) , ( \ { (c , b) -> < inr (inr (writeChar c)) , (\ _ -> copyOpen b) > } ) >
-- (3 marks for beginning, middle, end)
cp : (sourceFile targetFile : String) -> Game InterfaceCP SuccessCP initialCP
cp sourceFile targetFile
= < inr (inl (openRead sourceFile)) , (\
{ (opened b) ->
< inr (inr (openWrite targetFile)) , ((\
{ opened -> copyOpen b
; closed -> < inr (inl closeRead) , (\ _ ->
< inl (error (concat ("Could not open " :> targetFile :> []))) , (\ ()) > ) >
})) >
; closed -> < inl (error (concat ("Could not open " :> sourceFile :> []))) , (\ ()) >
}) >
-- (1 mark)
SCRIPT : {I : Set} -> I => I -> I => I
SCRIPT {I} CRn = Game CRn (\ I -> One) <! Rs / ns where
Rs : (i : I) -> Game CRn (\ I -> One) i -> Set
Rs i (win x) = One
Rs i < c , k > = Sigma (Response CRn i c) \ r -> Rs (next CRn i c r) (k r)
ns : (i : I)(cs : Game CRn (\ I -> One) i) -> Rs i cs -> I
ns i (win x) rs = i
ns i < c , k > (r , rs) = ns (next CRn i c r) (k r) rs
-- (1 mark)
unScript : {I : Set}(CRn : I => I){X : I -> Set}{i : I} ->
Game (SCRIPT CRn) X i -> Game CRn X i
runScript : {I : Set}(CRn : I => I){X : I -> Set}{i : I} ->
(cs : Command (SCRIPT CRn) i)
(k : (rs : Response (SCRIPT CRn) i cs) ->
Game CRn X (next (SCRIPT CRn) i cs rs))
-> Game CRn X i
unScript CRn (win x) = win x
unScript CRn {X}{i} < cs , k > = runScript CRn cs \ rs -> unScript CRn (k rs)
runScript CRn (win x) k = k <>
runScript CRn < c , f > k = < c , (\ r -> runScript CRn (f r) \ rs -> k (r , rs)) >
-- the rest was for fun
data Maybe (X : Set) : Set where
yes : X -> Maybe X
no : Maybe X
data IOMode : Set where
readMode writeMode appendMode readWriteMode : IOMode
postulate Handle : Set
data HaskellIOCommand (_ : One) : Set where
hOpen : String -> IOMode -> HaskellIOCommand <>
hClose hIsEOF hGetChar : Handle -> HaskellIOCommand <>
hPutChar : Handle -> Char -> HaskellIOCommand <>
hError : String -> HaskellIOCommand <>
HaskellIOResponse : (i : One) -> HaskellIOCommand i -> Set
HaskellIOResponse i (hOpen f m) = Maybe Handle
HaskellIOResponse i (hClose h) = One
HaskellIOResponse i (hIsEOF h) = Two
HaskellIOResponse i (hGetChar h) = Char
HaskellIOResponse i (hPutChar h c) = One
HaskellIOResponse i (hError e) = Zero
HASKELLIO : One => One
HASKELLIO = HaskellIOCommand <! HaskellIOResponse / _
record Driver {I J : Set}(Sync : I -> J -> Set)
(Hi : I => I)(Lo : J => J) : Set where
field
hiClo : (i : I)(j : J) -> Sync i j ->
Command Hi i -> Command Lo j
loRhi : (i : I)(j : J)(s : Sync i j)(c : Command Hi i) ->
Response Lo j (hiClo i j s c) -> Response Hi i c
nSync : (i : I)(j : J)(s : Sync i j)(c : Command Hi i)
(r : Response Lo j (hiClo i j s c)) ->
Sync (next Hi i c (loRhi i j s c r)) (next Lo j (hiClo i j s c) r)
open Driver public
RH : ReadState -> Set
RH (opened eof) = Handle
RH closed = One
WH : WriteState -> Set
WH opened = Handle
WH closed = One
hC : (i : IndexCP) (j : One) ->
RH (outl i) /*/ WH (outr i) ->
Command InterfaceCP i -> Command (SCRIPT HASKELLIO) j
hC (.closed , w) j (rh , wh) (inr (inl (openRead x)))
= < hOpen x readMode , (\ { no -> win <> ;
(yes h) -> < hIsEOF h , (\ b -> win <>) > }) >
hC (.(opened ff) , w) j (rh , wh) (inr (inl readChar))
= < hGetChar rh , (\ c -> < hIsEOF rh , (\ b -> win <>) >) >
hC (._ , w) j (rh , wh) (inr (inl closeRead))
= < hClose rh , (\ _ -> win <>) >
hC (r , .closed) j (rh , wh) (inr (inr (openWrite fileName)))
= < hOpen fileName writeMode , (\ _ -> win <>) >
hC (r , .opened) j (rh , wh) (inr (inr (writeChar x)))
= < hPutChar wh x , (\ _ -> win <>) >
hC (r , .opened) j (rh , wh) (inr (inr closeWrite))
= < hClose wh , (\ _ -> win <>) >
hC (opened eof , opened) j (rh , wh) (inl (error ()))
hC (opened eof , closed) j (rh , wh) (inl (error ()))
hC (closed , opened) j (rh , wh) (inl (error ()))
hC (closed , closed) j (rh , wh) (inl (error e)) = < hError e , (\ ()) >
hR : (i : IndexCP) (j : One) (s : RH (outl i) /*/ WH (outr i))
(c : Command InterfaceCP i) ->
Response (SCRIPT HASKELLIO) j (hC i j s c) ->
Response InterfaceCP i c
hR (.closed , w) j (<> , wh) (inr (inl (openRead x))) (yes rh , b , <>)
= opened b
hR (.closed , w) j (<> , wh) (inr (inl (openRead x))) (no , <>)
= closed
hR (.(opened ff) , w) j (rh , wh) (inr (inl readChar)) (c , b , <>) = c , b
hR (._ , w) j (rh , wh) (inr (inl closeRead)) rs = <>
hR (r , .closed) j (rh , <>) (inr (inr (openWrite fileName))) (yes wh , <>)
= opened
hR (r , .closed) j (rh , <>) (inr (inr (openWrite fileName))) (no , <>)
= closed
hR (r , .opened) j (rh , wh) (inr (inr (writeChar x))) rs = <>
hR (r , .opened) j (rh , wh) (inr (inr closeWrite)) rs = <>
hR (opened eof , opened) j (rh , wh) (inl (error ())) rs
hR (opened eof , closed) j (rh , wh) (inl (error ())) rs
hR (closed , opened) j (rh , wh) (inl (error ())) rs
hR (closed , closed) j (rh , wh) (inl (error x)) (() , snd)
hnS : (i : IndexCP) (j : One) (s : RH (outl i) /*/ WH (outr i))
(c : Command InterfaceCP i)
(r : Response (SCRIPT HASKELLIO) j (hC i j s c)) ->
RH (outl (next InterfaceCP i c (hR i j s c r))) /*/
WH (outr (next InterfaceCP i c (hR i j s c r)))
hnS (.closed , w) j (<> , wh) (inr (inl (openRead x))) (yes rh , snd) = rh , wh
hnS (.closed , w) j (<> , wh) (inr (inl (openRead x))) (no , snd) = <> , wh
hnS (.(opened ff) , w) j (rh , wh) (inr (inl readChar)) rs = rh , wh
hnS (._ , w) j (rh , wh) (inr (inl closeRead)) rs = <> , wh
hnS (r , .closed) j (rh , <>) (inr (inr (openWrite fileName))) (yes wh , snd)
= rh , wh
hnS (r , .closed) j (rh , <>) (inr (inr (openWrite fileName))) (no , snd) = rh , <>
hnS (r , .opened) j (rh , wh) (inr (inr (writeChar x))) rs = rh , wh
hnS (r , .opened) j (rh , wh) (inr (inr closeWrite)) rs = rh , <>
hnS (opened eof , opened) j (rh , wh) (inl (error ())) rs
hnS (opened eof , closed) j (rh , wh) (inl (error ())) rs
hnS (closed , opened) j (rh , wh) (inl (error ())) rs
hnS (closed , closed) j (rh , wh) (inl (error x)) (() , snd)
safe2unsafe : Driver {IndexCP}{One} (\ { (r , w) j -> RH r /*/ WH w })
InterfaceCP (SCRIPT HASKELLIO)
safe2unsafe = record
{ hiClo = hC
; loRhi = hR
; nSync = hnS
}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module ANSIEscapes
(upLine,
downLine,
up,
down,
forward,
backward,
killLine,
restoreCursor,
saveCursor,
clearScreen,
yellow,
brown,
red,
blue,
purple,
green,
orange,
white,
yellowOnGrey,
brownOnGrey,
redOnGrey,
blueOnGrey,
purpleOnGrey,
greenOnGrey,
whiteOnGrey,
onBlack,
onGrey,
onGreyEsc,
onWhiteEsc,
resetCursor,
initTermSize) where
data Dir = UpDir | DownDir | RightDir | LeftDir
instance Show Dir where
show UpDir = "A"
show DownDir = "B"
show RightDir = "C"
show LeftDir = "D"
upLine = putStr "\ESC[1A"
downLine = putStr "\ESC[1B"
up = moveCursor UpDir
down = moveCursor DownDir
backward = moveCursor LeftDir
forward = moveCursor RightDir
moveCursor :: Dir -> Int -> IO ()
moveCursor dir 0 = return ()
moveCursor dir n = putStr $ "\ESC[" ++ show n ++ show dir
killLine = escape "K"
restoreCursor = escape "u"
saveCursor = escape "s"
clearScreen = escape "2J"
initTermSize = (escape "[=3h")
resetCursor = escape "0;0H"
escape e = putStr $ "\ESC[" ++ e
yellow str = "\ESC[1;33m" ++ str ++ "\ESC[0m"
brown str = "\ESC[0;33m" ++ str ++ "\ESC[0m"
blue str = "\ESC[1;34m" ++ str ++ "\ESC[0m"
red str = "\ESC[1;31m" ++ str ++ "\ESC[0m"
green str = "\ESC[1;32m" ++ str ++ "\ESC[0m"
purple str = "\ESC[1;35m" ++ str ++ "\ESC[0m"
white str = "\ESC[37m" ++ str ++ "\ESC[0m"
--Be careful, these assume someone else will reset the background colour
yellowOnGrey str = "\ESC[1;33m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
brownOnGrey str = "\ESC[0;33m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
blueOnGrey str = "\ESC[1;34m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
redOnGrey str = "\ESC[1;31m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
greenOnGrey str = "\ESC[1;32m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
purpleOnGrey str = "\ESC[1;35m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
whiteOnGrey str = "\ESC[37m" ++ str ++ "\ESC[0m"
onBlack str = "\ESC[40m" ++ str ++ "\ESC[0m"
onGrey str = onGreyEsc ++ str ++ onWhiteEsc
onGreyEsc = "\ESC[47m"
onWhiteEsc = "\ESC[0m"
orange str = str | {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module AgdaSetup where
{- This file contains all the basic types you need for the editor. You should
read and understand the Agda in this file, but not bother too much about
the funny compiler directives. -}
data Nat : Set where
zero : Nat
suc : Nat -> Nat
{-# BUILTIN NATURAL Nat #-}
{-# COMPILED_DATA Nat HaskellSetup.Nat HaskellSetup.Zero HaskellSetup.Suc #-}
_+_ : Nat -> Nat -> Nat
zero + n = n
suc m + n = suc (m + n)
infixr 5 _+_
data Zero : Set where
magic : {X : Set} ->
Zero -> X
magic ()
{- In order to compile them, I have to define One and /*/ as data types
rather than records. -}
data One : Set where
<> : One
{-# COMPILED_DATA One () () #-}
data _/*/_ (S T : Set) : Set where
_,_ : S -> T -> S /*/ T
{-# COMPILED_DATA _/*/_ (,) (,) #-}
data Two : Set where
tt ff : Two
{-# BUILTIN BOOL Two #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
{-# COMPILED_DATA Two Bool True False #-}
_<=_ : Nat -> Nat -> Two
zero <= y = tt
suc x <= zero = ff
suc x <= suc y = x <= y
if_then_else_ : {X : Set} -> Two -> X -> X -> X
if tt then t else f = t
if ff then t else f = f
data List (X : Set) : Set where
[] : List X
_:>_ : X -> List X -> List X
infixr 5 _:>_
_++_ : {A : Set} -> List A -> List A -> List A
[] ++ ys = ys
(x :> xs) ++ ys = x :> (xs ++ ys)
{-# COMPILED_DATA List [] [] (:) #-}
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #-}
{-# BUILTIN CONS _:>_ #-}
{- Here are backward lists, which are useful when the closest element is
conceptually at the right end. They aren't really crucial as you could use
ordinary lists but think of the data as being reversed, but I prefer to
keep my thinking straight and use data which look like what I have in mind. -}
data Bwd (X : Set) : Set where
[] : Bwd X
_<:_ : Bwd X -> X -> Bwd X
infixl 5 _<:_
{- You will need access to characters, imported from Haskell. You can write
character literals like 'c'. You also get strings, with String literals like
"fred" -}
postulate -- this means that we just suppose the following things exist...
Char : Set
String : Set
{-# BUILTIN CHAR Char #-}
{-# COMPILED_TYPE Char Char #-} -- ...and by the time we reach Haskell...
{-# BUILTIN STRING String #-}
{-# COMPILED_TYPE String String #-} -- ...they *do* exist!
primitive -- these are baked in; they even work!
primCharEquality : Char -> Char -> Two
primStringAppend : String -> String -> String
primStringToList : String -> List Char
primStringFromList : List Char -> String
postulate -- Haskell has a monad for doing IO, which we use at the top level
IO : Set -> Set
return : {A : Set} -> A -> IO A
_>>=_ : {A B : Set} -> IO A -> (A -> IO B) -> IO B
infixl 1 _>>=_
{-# BUILTIN IO IO #-}
{-# COMPILED_TYPE IO IO #-}
{-# COMPILED return (\ _ -> return) #-}
{-# COMPILED _>>=_ (\ _ _ -> (>>=)) #-}
{- Here's the characterization of keys I give you -}
data Direction : Set where up down left right : Direction
data Modifier : Set where normal shift control : Modifier
data Key : Set where
char : Char -> Key
arrow : Modifier -> Direction -> Key
enter : Key
backspace : Key
delete : Key
escape : Key
{- This type classifies the difference between two editor states. -}
data Change : Set where
allQuiet : Change -- the buffer should be exactly the same
cursorMove : Change -- the cursor has moved but the text is the same
lineEdit : Change -- only the text on the current line has changed
bigChange : Change -- goodness knows!
{- This type collects the things you're allowed to do with the text window. -}
data Action : Set where
goRowCol : Nat -> Nat -> Action -- send the cursor somewhere
sendText : List Char -> Action -- send some text
{- I wire all of that stuff up to its Haskell counterpart. -}
{-# IMPORT HaskellSetup #-}
{-# COMPILED_DATA Direction
HaskellSetup.Direction
HaskellSetup.DU HaskellSetup.DD HaskellSetup.DL HaskellSetup.DR #-}
{-# COMPILED_DATA Modifier
HaskellSetup.Modifier
HaskellSetup.Normal HaskellSetup.Shift HaskellSetup.Control #-}
{-# COMPILED_DATA Key
HaskellSetup.Key
HaskellSetup.Char HaskellSetup.Arrow HaskellSetup.Enter
HaskellSetup.Backspace HaskellSetup.Delete HaskellSetup.Escape #-}
{-# COMPILED_DATA Change
HaskellSetup.Change
HaskellSetup.AllQuiet HaskellSetup.CursorMove HaskellSetup.LineEdit
HaskellSetup.BigChange #-}
{-# COMPILED_DATA Action
HaskellSetup.Action
HaskellSetup.GoRowCol HaskellSetup.SendText #-}
{- This is the bit of code I wrote to animate your code. -}
postulate
mainLoop : {B : Set} -> -- buffer type
-- INITIALIZER
(List (List Char) -> B) -> -- make a buffer from some lines of text
-- KEYSTROKE HANDLER
(Key -> B -> -- keystroke and buffer in
Change /*/ B) -> -- change report and buffer out
-- RENDERER
((Nat /*/ Nat) -> -- height and width of screen
(Nat /*/ Nat) -> -- top line number, left column number
(Change /*/ B) -> -- change report and buffer to render
(List Action /*/ -- how to update the display
(Nat /*/ Nat))) -> -- new top line number, left column number
-- PUT 'EM TOGETHER AND YOU'VE GOT AN EDITOR!
IO One
{-# COMPILED mainLoop (\ _ -> HaskellSetup.mainLoop) #-}
{- You can use this to put noisy debug messages in Agda code. So
trace "fred" tt
evaluates to tt, but prints "fred" in the process. -}
postulate
trace : {A : Set} -> String -> A -> A
{-# IMPORT Debug.Trace #-}
{-# COMPILED trace (\ _ -> Debug.Trace.trace) #-}
{- You can use this to print an error message when you don't know what else to do.
It's very useful for filling in unfinished holes to persuade the compiler to
compile your code even though it isn't finished: you get an error if you try
to run a missing bit. -}
postulate
error : {A : Set} -> String -> A
{-# COMPILED error (\ _ -> error) #-}
{- Equality -}
{- x == y is a type whenever x and y are values in the same type -}
{-
data _==_ {X : Set}(x : X) : X -> Set where
refl : x == x -- and x == y has a constructor only when y actually is x!
infixl 1 _==_
-- {-# BUILTIN EQUALITY _==_ #-}
-- {-# BUILTIN REFL refl #-}
{-# COMPILED_DATA _==_ HaskellSetup.EQ HaskellSetup.Refl #-}
within_turn_into_because_ :
{X Y : Set}(f : X -> Y)(x x' : X) ->
x == x' -> f x == f x'
within f turn x into .x because refl = refl
-- the dot tells Agda that *only* x can go there
symmetry : {X : Set}{x x' : X} -> x == x' -> x' == x
symmetry refl = refl
transitivity : {X : Set}{x0 x1 x2 : X} -> x0 == x1 -> x1 == x2 -> x0 == x2
transitivity refl refl = refl
-}
postulate
_==_ : {X : Set} -> X -> X -> Set -- the evidence that two X-values are equal
refl : {X : Set}{x : X} -> x == x
symmetry : {X : Set}{x x' : X} -> x == x' -> x' == x
transitivity : {X : Set}{x0 x1 x2 : X} -> x0 == x1 -> x1 == x2 -> x0 == x2
within_turn_into_because_ :
{X Y : Set}(f : X -> Y)(x x' : X) ->
x == x' -> f x == f x'
infix 1 _==_
{-# COMPILED_TYPE _==_ HaskellSetup.EQ #-}
{- Here's an example. -}
additionAssociative : (x y z : Nat) -> (x + y) + z == x + (y + z)
additionAssociative zero y z = refl
additionAssociative (suc x) y z
= within suc turn ((x + y) + z) into (x + (y + z))
because additionAssociative x y z
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
default: Edit
Edit: Edit.agda ANSIEscapes.hs HaskellSetup.hs AgdaSetup.agda
agda --compile --ghc-flag "-lncurses" Edit.agda
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Edit where
{- This is the file where you should work. -}
open import AgdaSetup
{- The key editor data structure is the cursor. A Cursor M X represents
being somewhere in the middle of a sequence of X values, holding an M. -}
record Cursor (M X : Set) : Set where
constructor _<[_]>_
field
beforeMe : Bwd X
atMe : M
afterMe : List X
infix 4 _<[_]>_
{- An editor buffer is a nested cursor: we're in the middle of a bunch of
*lines*, holding a cursor for the current line, which puts us in the
middle of a bunch of characters, holding the element of One. -}
Buffer : Set
Buffer = Cursor (Cursor One Char) (List Char)
{- This operator, called "chips", shuffles the elements from a backward list
on to the start of a forward list, keeping them in the same order. -}
_<>>_ : {X : Set} -> Bwd X -> List X -> List X
[] <>> xs = xs
(xz <: x) <>> xs = xz <>> (x :> xs)
{- The "fish" operator goes the other way. -}
_<><_ : {X : Set} -> Bwd X -> List X -> Bwd X
xz <>< [] = xz
xz <>< (x :> xs) = (xz <: x) <>< xs
{- You can turn a buffer into a list of lines, preserving its text. -}
bufText : Buffer -> List (List Char)
bufText
(sz <[
cz <[ <> ]> cs
]> ss)
= sz <>> ((cz <>> cs) :> ss)
{- Here's an example of a proof of a fact about fish and chips. -}
firstFishFact : {X : Set} -> (xz : Bwd X)(xs : List X) ->
(xz <>< xs) <>> [] == xz <>> xs
firstFishFact xz [] = refl
firstFishFact xz (x :> xs) = firstFishFact (xz <: x) xs
{- You will need more such facts. -}
{- EXERCISE 5.1 -}
{- When we start the editor with the command
./Edit foo.txt
the contents of foo.txt will be turned into a list of lines.
Your (not so tricky) mission is to turn the file contents into a buffer which
contains the same text.
(1 mark)
-}
initBuf : List (List Char) -> Buffer
initBuf ss =
[] <[
[] <[ <> ]> []
]> []
{- As you can see, the current version will run, but it always gives the empty
buffer, which is not what we want unless the input is empty. -}
{- Next comes the heart of the editor. You get a keystroke and the current buffer,
and you have to say what is the new buffer. You also have to say what is the
extent of the change.
The tricky part is this: you have to be honest enough about your change
report, so that we don't underestimate the amount of updating the screen needs.
-}
Honest : Buffer -> Change /*/ Buffer -> Set
Honest b (allQuiet , b') = b == b'
Honest b (cursorMove , b') = bufText b == bufText b'
Honest (sz <[ _ ]> ss) (lineEdit , (sz' <[ _ ]> ss')) = (sz == sz') /*/ (ss == ss')
Honest _ (bigChange , _) = One
record UpdateFrom (b : Buffer) : Set where -- b is the starting buffer
constructor _///_
field
update : Change /*/ Buffer -- change and new buffer
honest : Honest b update
open UpdateFrom
infix 2 _///_
{- EXERCISE 5.2 -}
{- Implement the appropriate behaviour for as many keystrokes as you can.
I have done a couple for you, but I don't promise to have done them
correctly. -}
keystroke : Key -> (b : Buffer) -> UpdateFrom b
keystroke (char c)
(sz <[
cz <[ <> ]> cs
]> ss)
= lineEdit ,
(sz <[
cz <[ <> ]> c :> cs
]> ss)
/// refl , refl -- see? same above and below
keystroke (arrow normal right)
(sz <: s <[
[] <[ <> ]> cs
]> ss)
= cursorMove ,
(sz <[ ([] <>< s) <[ <> ]> [] ]> cs :> ss)
/// within (\ x -> sz <>> (x :> cs :> ss)) turn s into ([] <>< s) <>> []
because symmetry (firstFishFact [] s)
keystroke k b = allQuiet , b /// refl
{- Please expect to need to invent extra functions, e.g., to measure where you
are, so that up and down arrow work properly. -}
{- Remember also that you can always overestimate the change by saying bigChange,
which needs only a trivial proof. But you may find that the display will flicker
badly if you do. -}
{- (char c) 1 mark
enter 2 marks
backspace delete 2 marks for the pair
left right 2 marks for the pair (with cursorMove change)
up down 2 marks for the pair (with cursorMove change)
-}
{- EXERCISE 5.3 -}
{- You will need to improve substantially on my implementation of the next component,
whose purpose is to update the window. Mine displays only one line! -}
render :
Nat /*/ Nat -> -- height and width of window -- CORRECTION! width and height
Nat /*/ Nat -> -- first visible row, first visible column
Change /*/ Buffer -> -- what just happened
List Action /*/ -- how to update screen
(Nat /*/ Nat) -- new first visible row, first visible column
render _ tl (allQuiet , _) = ([] , tl)
render _ tl (_ , (_ <[ cz <[ <> ]> cs ]> _))
= (goRowCol 0 0 :> sendText (cz <>> cs) :> []) , tl
{- The editor window gives you a resizable rectangular viewport onto the editor buffer.
You get told
the current size of the viewport
which row and col of the buffer are at the top left of the viewport
(so you can handle documents which are taller or wider than the window)
the most recent change report and buffer
You need to figure out whether you need to move the viewport
(by finding out if the cursor is still within the viewport)
and if so, where to.
You need to figure out what to redisplay. If the change report says
lineEdit and the viewport has not moved, you need only repaint the
current line. If the viewport has moved or the change report says
bigChange, you need to repaint the whole buffer.
You will need to be able to grab a rectangular region of text from the
buffer, but you do know how big and where from.
Remember to put the cursor in the right place, relative to where in
the buffer the viewport is supposed to be. The goRowCol action takes
*viewport* coordinates, not *buffer* coordinates! You will need to
invent subtraction!
-}
{- Your code does not need to worry about resizing the window. My code does
that. On detecting a size change, my code just calls your code with a
bigChange report and the same buffer, so if you are doing a proper repaint,
the right thing will happen. -}
{- 2 marks for ensuring that a buffer smaller than the viewport displays
correctly, with the cursor in the right place, if nobody changes
the viewport size
2 marks for ensuring that the cursor remains within the viewport even if
the viewport needs to move
1 mark for ensuring that lineEdit changes need only affect one line of
the display (provided the cursor stays in the viewport)
-}
{- FOR MASOCHISTS ONLY, you have a chance to be even more creative. You have
spare detectable keys that you could invent meanings for. You also have the
freedom to change the definition of Buffer, as my code does not care what
a Buffer is: it only needs to know how to initialize, update and render,
and these are defined by you.
Additional structural cursor moves (beginning and end of line, etc) are quite
easy. Going left or right word-by-word would be more fun: you can match
against a pattern such as ' '.
Selection and cut/copy/paste are more challenging. For these, you need to
modify the Buffer structure to remember the clipboard contents (if any),
and to manage the extent of any selected region.
If you feel the need to vary the foreground or background colour of the displayed
text (e.g. to show a selection), please let me know.
(SUBTEXT: this exercise is a cut-down version of last year's post-Easter
task. Feel free to ignore the cutting-down.)
-}
{- Your code then hooks into mine to produce a top level executable! -}
main : IO One
main = mainLoop initBuf (\ k b -> update (keystroke k b)) render
{- To build the editor, just do
make
in a shell window (with Ex5 the current directory).
To run the editor, once compiled, do
./Edit
in the shell window, which should become the editor window.
To quit the editor, do
ctrl-C
like an old-fashioned soul.
-}
{- There is no one right way to do this exercise, and there is some scope for
extension. It's important that you get in touch if you need help, either in
achieving the basic deliverable, or in finding ways to explore beyond it.
-}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module HaskellSetup where
{- This is the low-level stuff that hooks into the ncurses library, together
with the Haskell versions of the Agda types. You should not need to bother
reading or modifying this file. -}
import Debug.Trace
import Foreign
import Foreign.C (CInt(..))
import ANSIEscapes
import System.IO
import System.Environment
import Control.Applicative
import Control.Concurrent
foreign import ccall
initscr :: IO ()
foreign import ccall "endwin"
endwin :: IO CInt
foreign import ccall "refresh"
refresh :: IO CInt
foreign import ccall "&LINES"
linesPtr :: Ptr CInt
foreign import ccall "&COLS"
colsPtr :: Ptr CInt
scrSize :: IO (Int, Int)
scrSize = do
lnes <- peek linesPtr
cols <- peek colsPtr
return (fromIntegral cols, fromIntegral lnes)
data Direction = DU | DD | DL | DR deriving Show
data Modifier = Normal | Shift | Control deriving Show
data Key = Char Char | Arrow Modifier Direction | Enter | Backspace | Delete | Escape deriving Show
data Nat = Zero | Suc Nat
toNat :: Int -> Nat
toNat 0 = Zero
toNat n = Suc (toNat (n - 1))
fromNat :: Nat -> Int
fromNat Zero = 0
fromNat (Suc n) = 1 + fromNat n
data EQ a b c = Refl
data Change = AllQuiet | CursorMove | LineEdit | BigChange
data Action = GoRowCol Nat Nat | SendText [Char]
act :: Action -> IO ()
act (GoRowCol y x) = do
resetCursor
forward (fromNat x)
down (fromNat y)
act (SendText s) = putStr s
getEscapeKey :: [(String, Key)] -> IO (Maybe Key)
getEscapeKey [] = return Nothing
getEscapeKey sks = case lookup "" sks of
Just k -> return (Just k)
_ -> do
c <- getChar
getEscapeKey [(cs, k) | (d : cs, k) <- sks, d == c]
directions :: [(Char, Direction)]
directions = [('A', DU), ('B', DD),
('C', DR), ('D', DL)]
escapeKeys :: [(String, Key)]
escapeKeys =
[([c], Arrow Normal d) | (c, d) <- directions] ++
[("1;2" ++ [c], Arrow Shift d) | (c, d) <- directions] ++
[("1;5" ++ [c], Arrow Control d) | (c, d) <- directions] ++
[("3~", Delete)]
keyReady :: IO (Maybe Key)
keyReady = do
b <- hReady stdin
if not b then return Nothing else do
c <- getChar
case c of
'\n' -> return $ Just Enter
'\r' -> return $ Just Enter
'\b' -> return $ Just Backspace
'\DEL' -> return $ Just Backspace
_ | c >= ' ' -> return $ Just (Char c)
'\ESC' -> do
b <- hReady stdin
if not b then return $ Just Escape else do
c <- getChar
case c of
'[' -> getEscapeKey escapeKeys
_ -> return $ Just Escape
_ -> return $ Nothing
pni :: (Int, Int) -> (Nat, Nat)
pni (y, x) = (toNat y, toNat x)
mainLoop ::
([[Char]] -> b) ->
(Key -> b -> (Change, b)) ->
((Nat, Nat) -> (Nat, Nat) -> (Change, b) -> ([Action], (Nat, Nat))) ->
IO ()
mainLoop initBuf keystroke render = do
hSetBuffering stdout NoBuffering
hSetBuffering stdin NoBuffering
xs <- getArgs
buf <- case xs of
[] -> return (initBuf [])
(x : _) -> (initBuf . lines) <$> readFile x
initscr
innerLoop (0, 0) (Zero, Zero) (BigChange, buf)
endwin
return ()
where
innerLoop oldSize topLeft (c, b) = do
refresh
size <- scrSize
(acts, topLeft) <- return $
if size /= oldSize
then render (pni size) topLeft (BigChange, b)
else render (pni size) topLeft (c, b)
mapM_ act acts
mc <- keyReady
case mc of
Nothing -> threadDelay 100 >> innerLoop size topLeft (AllQuiet, b)
Just k -> innerLoop size topLeft (keystroke k b)
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-1-Vec where
open import Ex6-Setup
---------------------------------------------------------------------------
-- VECTORS (5 marks) --
---------------------------------------------------------------------------
-- We've touched on them before, when we needed to manage the height of a
-- stack, but here are the "vectors", or "lists of known length.
data Vec (X : Set) : Nat -> Set where
[] : Vec X zero
_::_ : {n : Nat} -> X -> Vec X n -> Vec X (suc n)
infixr 6 _::_
-- This chunk of exercise 6 is about building the basic equipment to work
-- with vectors. We'll need this equipment later.
---------------------------------------------------------------------------
-- CONCATENATION AND ITS INVERSE --
---------------------------------------------------------------------------
infixr 6 _++_
-- Implement concatenation for any two vectors.
-- You will need to say how long the result will be.
-- (1 mark)
_++_ : {X : Set}{m n : Nat} -> Vec X m -> Vec X n -> Vec X {!!}
xs ++ ys = {!!}
-- Now, we could write "take" and "drop", but it's more useful to
-- prove that every long vector can be given by concatenating two
-- short vectors.
data Chop {X : Set}(m : Nat){n : Nat} : Vec X {!!} -> Set where
is++ : (xs : Vec X m)(ys : Vec X n) -> Chop m (xs ++ ys)
-- A "Chop" for a given vector consists of the evidence that it can
-- be made by concatenation. You will need to fill in the Chop length,
-- above, the same way you filled in the length for _++_.
-- Show that you can compute a Chop for any vector.
-- Hint: you will need to use "with" at some point.
-- (1 mark)
chop : {X : Set}(m : Nat){n : Nat}(xs : Vec X {!!}) -> Chop m xs
chop m xs = {!!}
-- Where take and drop give you vectors which you *hope* are the prefix
-- and suffix of the input. Chop gives you the pieces which are seen to
-- be the prefix and suffix of the input. Once you have chop, it's easy
-- to write take and drop in terms of it, and you can see they're right.
-- Try uncommenting and finishing the following (for fun).
{-
take : {X : Set}(m : Nat){n : Nat}(xs : Vec X {!!}) -> Vec X m
take m xs with chop m xs
take m .(xs ++ ys) | is++ xs ys = xs
-}
-- EXTRA! For no marks, but some utility in future, check that you can
-- use chop to define the function which just gives you the pair of the
-- prefix and the suffix.
vchop : {X : Set}(m : Nat){n : Nat} ->
Vec X {!!} -> Vec X m /*/ Vec X n
vchop x xs = {!!}
---------------------------------------------------------------------------
-- APPLICATIVE STRUCTURE --
---------------------------------------------------------------------------
-- Implement the function which makes a vector from a single element by
-- copying it the relevant number of times. Implement the "vectorized
-- application" operator which takes n functions and n arguments and gives
-- you the n results: the jth result should be given by applying the jth
-- function to the jth argument.
-- (1 mark)
vec : {n : Nat}{X : Set}(x : X) -> Vec X n
vec x = {!!}
_<*>_ : {n : Nat}{S T : Set} -> Vec (S -> T) n -> Vec S n -> Vec T n
fs <*> ss = {!!}
infixl 2 _<*>_
-- The applicative structure is very useful for working with vectors in
-- bulk. For example, I can take the successor of every number in a vector
-- by applying a vector of successor-functions to the vector of numbers.
mySucs : Vec Nat 5
mySucs = vec suc <*> (0 :: 1 :: 2 :: 3 :: 4 :: [])
-- should evaluate to 1 :: 2 :: 3 :: 4 :: 5 :: []
-- Now, using vec and <*> rather than explicit case analysis and recursion,
-- implement vector zipping as a one-liner, turning a pair of vectors into a
-- vector of pairs.
-- (1 mark)
zip : {n : Nat}{X Y : Set} -> Vec X n -> Vec Y n -> Vec (X /*/ Y) n
zip xs ys = {!!}
-- Play the same game as we did for concatenation, take and drop. Show
-- that every vector of pairs can be made by zipping two vectors.
-- (1 mark)
data Unzip {n : Nat}{X Y : Set} : Vec (X /*/ Y) n -> Set where
-- what goes here?
unzip : {n : Nat}{X Y : Set}(xys : Vec (X /*/ Y) n) -> Unzip xys
unzip xys = {!!}
-- EXTRA! For no marks, but some utility in future, check that you can
-- use unzip to define the function which just gives you the pair of the
-- two vectors.
vunzip : {X Y : Set}{n : Nat} -> Vec (X /*/ Y) n -> Vec X n /*/ Vec Y n
vunzip xys = {!!}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-3-Cut-Sol where
open import Ex6-Setup
open import Ex6-1-Vec-Sol
open import Ex6-2-Box-Sol
---------------------------------------------------------------------------
-- CUTTING UP BOXES (5 marks) --
---------------------------------------------------------------------------
-- Previously...
-- ... we established what it is to be a CutKit, and we built CutKits
-- for some sorts of basic tile. Now we need to build the CutKit for
-- Box. Let's think about what that involves for a moment. We're going
-- to need a CutKit for basic tiles to stand a chance. But how do we
-- cut compound tiles?
--
-- Suppose we're writing cutLR, and we have some
-- cq : cwl + cwr == w -- the "cut widths" equation
-- telling us where we want to make the cut in something of width w.
--
-- v
-- +--------:------+
-- | : |
-- | : |
-- +--cwl---:-cwr--+
-- : ^ :
-- :.......w.......:
--
-- The tricky part is when the box we're cutting here is built with
-- leri bwl bl bwr br bq
-- where
-- bq : bwl + bwr == w -- the "box widths" equation
--
-- There are three possible situations, all of which you must detect
-- and handle.
--
-- (i) you hit the sweet spot...
--
-- v
-- +--bwl---+-bwr--+
-- | | |
-- | | |
-- +--cwl---+-cwr--+
-- : ^ :
-- :.......w.......:
--
-- ...where the box is already divided in the place where the cut
-- has to go. Happy days.
--
-- (ii) you're cutting to the left of the join...
--
-- v
-- +--bwl-----+bwr-+
-- | : | |
-- | : | |
-- +--cwl---:-cwr--+
-- : ^ :
-- :.......w.......:
--
-- ...so you'll need to cut the left box in the correct place. You
-- will need some evidence about widths to do that. And then you'll
-- the have three pieces you can see in my diagram, so to complete
-- the cut, you will need to put two of those pieces together, which
-- will take more evidence.
--
-- (iii) you're cutting to the right of the join...
--
-- v
-- +--bwl-+--bwr---+
-- | | : |
-- | | : |
-- +--cwl---:-cwr--+
-- : ^ :
-- :.......w.......:
--
-- ...so you'll need to cut the right box in the correct place, and
-- reassemble the bits.
--
-- HINT: THE FIRST THREE MARKS IN THIS EPISODE COME FROM ONE PROBLEM.
-- TREAT THEM AS A WHOLE.
---------------------------------------------------------------------------
-- COMPARING THE CUT POSITION --
---------------------------------------------------------------------------
data CutCompare (x x' y y' n : Nat) : Set where
cutLt : (d : Nat) -> x + suc d == y -> suc d + y' == x' ->
CutCompare x x' y y' n
cutEq : x == y -> x' == y' ->
CutCompare x x' y y' n
cutGt : (d : Nat) -> y + suc d == x -> suc d + x' == y' ->
CutCompare x x' y y' n
-- Give three constructors for this type which characterize the three
-- possibilities described above whenever
-- x + x' == n and y + y' == n
-- (E.g., take n to be w, x and x' to be cwl and cwr, y and y' to be
-- bwl and bwr. But later, you'll need to do use the same tool for
-- heights.)
--
-- You will need to investigate what evidence must be packaged in each
-- situation. On the one hand, you need to be able to *generate* the
-- evidence, with cutCompare, below. On the other hand, the evidence
-- must be *useful* when you come to write boxCutKit, further below.
-- Don't expect to know what to put here from the get-go. Figure it
-- out by discovering what you *need*.
--
-- (1 mark)
-- Show that whenever you have two ways to express the same n as a sum,
-- you can always deliver the CutCompare evidence. (1 mark)
cutCompare : (x x' y y' n : Nat) -> x + x' == n -> y + y' == n ->
CutCompare x x' y y' n
cutCompare zero .n zero .n n refl refl
= cutEq refl refl
cutCompare zero .(suc (y + y')) (suc y) y' .(suc (y + y')) refl refl
= cutLt y refl refl
cutCompare (suc x) x' zero .(suc (x + x')) .(suc (x + x')) refl refl
= cutGt x refl refl
cutCompare (suc x) x' (suc y) y' zero () ()
cutCompare (suc x) x' (suc y) y' (suc n) xq yq
with cutCompare x x' y y' n (sucInj xq) (sucInj yq)
cutCompare (suc x) x' (suc y) y' (suc n) xq yq
| cutLt d aq bq = cutLt d (sucResp aq) bq
cutCompare (suc x) x' (suc y) y' (suc n) xq yq
| cutEq aq bq = cutEq (sucResp aq) bq
cutCompare (suc x) x' (suc y) y' (suc n) xq yq
| cutGt d aq bq = cutGt d (sucResp aq) bq
-- cutCompare x x' y y' n xq yq = {!!}
---------------------------------------------------------------------------
-- A CUTKIT FOR BOXES --
---------------------------------------------------------------------------
-- Now, show that you can construct a CutKit for Box X, given a CutKit
-- for X. There will be key points where you get stuck for want of crucial
-- information. The purpose of CutCompare is to *describe* that
-- information. The purpose of cutCompare is to *compute* that information.
-- Note that cutLR and cutTB will work out very similarly, just exchanging
-- the roles of width and height.
-- (1 mark)
boxCutKit : {X : Nat -> Nat -> Set} -> CutKit X -> CutKit (Box X)
boxCutKit {X} ck = record { cutLR = clr ; cutTB = ctb } where
open CutKit ck
clr : (w h wl wr : Nat) ->
wl + wr == w -> Box X w h -> Box X wl h /*/ Box X wr h
clr w h wl wr wq [ x ] with cutLR w h wl wr wq x
clr w h wl wr wq [ x ] | xl , xr = [ xl ] , [ xr ]
clr w h wl wr wq (leri wl' bl wr' br wq')
with cutCompare wl wr wl' wr' w wq wq'
clr w h wl wr wq (leri wl' bl wr' br wq')
| cutLt d lq rq with clr wl' h wl (suc d) lq bl
clr w h wl wr wq (leri wl' bl wr' br wq')
| cutLt d lq rq | bll , blr = bll , leri (suc d) blr wr' br rq
clr w h wl wr wq (leri .wl bl .wr br wq')
| cutEq refl refl = bl , br
clr w h wl wr wq (leri wl' bl wr' br wq')
| cutGt d lq rq with clr wr' h (suc d) wr rq br
clr w h wl wr wq (leri wl' bl wr' br wq')
| cutGt d lq rq | brl , brr = leri wl' bl (suc d) brl lq , brr
clr w h wl wr wq (tobo ht bt hb bb x)
with clr w ht wl wr wq bt | clr w hb wl wr wq bb
clr w h wl wr wq (tobo ht bt hb bb x)
| tl , tr | bl , br = tobo ht tl hb bl x , tobo ht tr hb br x
-- clr w h wl wr wq b = {!!}
ctb : (w h ht hb : Nat) ->
ht + hb == h -> Box X w h -> Box X w ht /*/ Box X w hb
ctb w h ht hb hq [ x ] with cutTB w h ht hb hq x
ctb w h ht hb hq [ x ] | xt , xb = [ xt ] , [ xb ]
ctb w h ht hb hq (leri wl bl wr br x)
with ctb wl h ht hb hq bl | ctb wr h ht hb hq br
ctb w h ht hb hq (leri wl bl wr br x)
| lt , lb | rt , rb = leri wl lt wr rt x , leri wl lb wr rb x
ctb w h ht hb hq (tobo ht' bt hb' bb hq')
with cutCompare ht hb ht' hb' h hq hq'
ctb w h ht hb hq (tobo ht' bt hb' bb hq')
| cutLt d tq bq with ctb w ht' ht (suc d) tq bt
ctb w h ht hb hq (tobo ht' bt hb' bb hq')
| cutLt d tq bq | btt , btb = btt , tobo (suc d) btb hb' bb bq
ctb w h ht hb hq (tobo .ht bt .hb bb hq')
| cutEq refl refl = bt , bb
ctb w h ht hb hq (tobo ht' bt hb' bb hq')
| cutGt d tq bq with ctb w hb' (suc d) hb bq bb
ctb w h ht hb hq (tobo ht' bt hb' bb hq')
| cutGt d tq bq | bbt , bbb = tobo ht' bt (suc d) bbt tq , bbb
-- ctb w h ht hb hq b = {!!}
---------------------------------------------------------------------------
-- CROP --
---------------------------------------------------------------------------
-- Show that, given a CutKit, you can implement the "crop" operation which
-- trims a small rectangle out of an enclosing rectangle.
-- (1 mark)
crop : {X : Nat -> Nat -> Set} -> CutKit X ->
(wl wc wr ht hc hb : Nat) ->
X (wl + wc + wr) (ht + hc + hb) -> X wc hc
crop ck wl wc wr ht hc hb x
= fst (cutLR _ _ _ wr refl (snd (cutLR _ _ wl _ refl
(fst (cutTB _ _ _ hb refl (snd (cutTB _ _ ht _ refl x))))
))) where
open CutKit ck
-- crop ck wl wc wr ht hc hb x = {!!}
-- For fun, practice, and the chance to test your work, try building
-- a nontrivially tiled...
testBigBox : Box (HoleOr _*C*_) 20 15
testBigBox = -- {!!}
leri
3 [ Hole ]
17 (leri
10 (tobo
6 [ Hole ]
9 (tobo
3 [ [ [- "marmalades" -] :: [- "cantilever" -] :: [- "balderdash" -]
:: [] ] ]
6 [ [ vec (vec '*') ] ]
refl) refl)
7 [ Hole ] refl) refl
-- ...so that you can see this stuff in action:
textDisplayCutKit : CutKit (Box (HoleOr _*C*_))
textDisplayCutKit = boxCutKit (holeCutKit matrixCutKit)
testWeeBox : Box (HoleOr _*C*_) 10 5
testWeeBox = crop textDisplayCutKit 5 10 5 5 5 5 testBigBox
---------------------------------------------------------------------------
-- OVERLAY --
---------------------------------------------------------------------------
-- If we use HoleOr X as the basic tile, we can think of Hole as meaning
-- a bit of a box we can see through. Correspondingly, if we have two
-- boxes (the "front" one and the "back" one), both the same size, we
-- should be able to see through the holes in the front box to whatever
-- stuff is in the back box in the corresponding place.
--
-- Your task here is to show that you can combine front and back layers
-- into a single box, corresponding to what you would actually see. That
-- is, you will need to fill the front holes in with stuff cut from the
-- back. Which is why you need a CutKit for boxes.
--
-- Hint: you may be tempted to use crop, but try without crop first.
--
-- (1 mark)
overlay : {X : Nat -> Nat -> Set} -> CutKit X ->
{w h : Nat} ->
{- front -} Box (HoleOr X) w h ->
{- back -} Box (HoleOr X) w h ->
{- combined -} Box (HoleOr X) w h
overlay {X} ck = go where
open CutKit (boxCutKit (holeCutKit ck))
go : {w h : Nat} ->
Box (HoleOr X) w h -> Box (HoleOr X) w h -> Box (HoleOr X) w h
go [ Hole ] b = b
go [ [ x ] ] b = [ [ x ] ]
go (leri wl al wr ar wq) b with cutLR _ _ wl wr wq b
go (leri wl al wr ar wq) b | bl , br
= leri wl (go al bl) wr (go ar br) wq
go (tobo ht at hb ab hq) b with cutTB _ _ ht hb hq b
go (tobo ht at hb ab hq) b | bt , bb
= tobo ht (go at bt) hb (go ab bb) hq
-- go front back = {!!}
-- You should ensure (but I won't ask you to prove) that you have thus
-- equipped Box (HoleOr X) w h with the structure of a *monoid* with
-- the neutral value (nil-like thing) being [ Hole ] and the
-- associative operation (append-like thing) being (overlay ck), where
-- ck is your CutKit X. That is, there is such a thing as a totally
-- transparent layer, and you can overlay *any* number of layers by
-- combining any two neighbouring layers at a time.
-- For fun, and the shape of things to come, build two box tilings.
-- Make sure each has a rectangle of text in the middle and Hole all
-- around. Make sure that the rectangles overlap each other, but not
-- completely. See what happens when you overlay them, either way
-- around.
rectangleA : Box (HoleOr _*C*_) 20 15
rectangleA = -- {!!}
leri 3 [ Hole ] 17 (leri 10
(tobo 3 [ Hole ] 12 (tobo 6
[ [ [- "+--------+" -] ::
[- "|Let joy |" -] ::
[- "|be uncon|" -] ::
[- "|fined! |" -] ::
[- "|(thanks)|" -] ::
[- "+--------+" -] :: [] ] ] 6 [ Hole ] refl) refl)
7 [ Hole ] refl) refl
rectangleB : Box (HoleOr _*C*_) 20 15
rectangleB = -- {!!}
leri 7 [ Hole ] 13 (leri 10
(tobo 6 [ Hole ] 9 (tobo 6
[ [ [- "+--------+" -] ::
[- "|My heart|" -] ::
[- "|has gone|" -] ::
[- "|but I |" -] ::
[- "|live on.|" -] ::
[- "+--------+" -] :: [] ] ] 3 [ Hole ] refl) refl)
3 [ Hole ] refl) refl
frontA_backB : 20 *C* 15
frontA_backB = renderHoleOrText (overlay matrixCutKit rectangleA rectangleB)
frontB_backA : 20 *C* 15
frontB_backA = renderHoleOrText (overlay matrixCutKit rectangleB rectangleA)
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-4-Dis where
open import Ex6-Setup
open import Ex6-1-Vec-Sol
open import Ex6-2-Box-Sol
open import Ex6-3-Cut-Sol
---------------------------------------------------------------------------
-- CURSES DISPLAY FOR APPLICATIONS (5 marks) --
---------------------------------------------------------------------------
-- You may need to look at the Ex6-Setup file to find some of the relevant
-- kit for this episode, and it's worth looking there for goodies, anyway.
-- We start from the idea of a main loop.
{- This is the bit of code I wrote in Haskell to animate your code. -}
postulate
mainLoop : {S : Set} -> -- program state
-- INITIALIZER
S -> -- initial state
-- EVENT HANDLER
(Event -> S -> -- event and state in
S /**/ List Action) -> -- new state and screen actions out
-- PUT 'EM TOGETHER AND YOU'VE GOT AN APPLICATION!
IO Thud
{-# COMPILED mainLoop (\ _ -> HaskellSetup.mainLoop) #-}
-- The type S /**/ T is a type of pairs that the compiler can share with
-- Haskell. Its constructor is _,_ just as for S /*/ T. Meanwhile Thud
-- does the same job for One, but you won't need to bother with it.
-- To make a thing you can run, you need to
-- (i) choose a type to represent the program's internal state S
-- (ii) give the initial state
-- (iii) explain how, given an event and the current state, to
-- produce a new state and a list of actions to update the
-- display.
-- Let me show you the example I gave in class...
---------------------------------------------------------------------------
-- My silly wee demo --
---------------------------------------------------------------------------
-- the program state...
SillyState : Set
SillyState = Char /*/ Nat /*/ Nat
-- ...knows the character to put round the edge of the window, and the
-- size of the window
-- To paint a window whose dimensions are both at least 2, we...
sillyPaint : SillyState -> List Action
sillyPaint (c , suc (suc w), suc (suc h))
= goRowCol 0 0 -- send the cursor home
:: bgText black :: fgText green -- adopt our colour scheme
:: sendText (concat ( -- send ...
list (suc (suc w)) c :: -- ... top
concat (list h (c :: list w ' ' +-+ c :: [])) :: -- middle
list (suc (suc w)) c :: [])) :: -- and bottom
[]
sillyPaint _ = []
-- There are two kinds of event we must consider: keystroke and resize.
sillyHandler : Event -> SillyState -> SillyState /**/ List Action
sillyHandler (key (char c)) (_ , w , h) = s , sillyPaint s where
-- if we get an ordinary character key,
-- update the character and repaint
s : SillyState
s = (c , w , h)
sillyHandler (resize w h) (c , _ , _) = s , sillyPaint s where
-- if we get a resizing event,
-- update the size and repaint
s : SillyState
s = (c , w , h)
sillyHandler _ s = s , [] -- otherwise, relax
-- To finish the job, we write a "main" function, plugging in the initial
-- state. The initial size of 0 by 0 will provoke an immediate resize event,
-- giving the correct size!
{- -}
main : IO Thud
main = mainLoop ('*' , 0 , 0) sillyHandler
{- -}
-- To run this program, start a terminal, change to your Ex6 directory, then
--
-- make go4
--
-- You should be able to press keys and resize the thing and see sensible
-- stuff happen. Ctrl-C quits.
-- When you're bored of green rectangles, comment out the above main
-- function, so you can move on to the actual work. There are other
-- main functions further down the file which you can comment in as you
-- need them. Of course, you can have at most one main at a time.
---------------------------------------------------------------------------
-- PAINTINGS --
---------------------------------------------------------------------------
-- Now that we're in colour, one cell of display will be a ColourChar ...
data ColourChar : Set where
_-_/_ : (fg : Colour)(c : Char)(bg : Colour) -> ColourChar
-- ... e.g. green - '*' / black for what we had, above.
-- a painting is a Box structure whose basic tiles are either transparent
-- holes or opaque rectangles of coloured text.
Painting : Nat -> Nat -> Set
Painting = Box (HoleOr (Matrix ColourChar))
-- Now your turn. Making use of the equipment you developed in epsiode 2,
-- get us from a Painting to a List Action in two hops. Note that you will
-- have to decide how to render a Hole: some bland background stuff, please.
-- (1 mark)
paintMatrix : Painting []> Matrix ColourChar
paintMatrix p = {!!}
paintAction : {w h : Nat} -> Matrix ColourChar w h -> List Action
paintAction = {!!}
---------------------------------------------------------------------------
-- APPLICATIONS --
---------------------------------------------------------------------------
-- Here's a general idea of what it means to be an "application".
-- You need to choose some sort of size-dependent state, then provide these
-- bits and pieces. We need to know how the state is updated according to
-- events, with resizing potentially affecting the state's type. We must
-- be able to paint the state. The state should propose a cursor position.
-- (Keen students may modify this definition to ensure the cursor must be
-- within the bounds of the application.)
record Application (S : Nat -> Nat -> Set) : Set where
field
handleKey : Key -> S []> S
handleResize : {w h : Nat}(w' h' : Nat) -> S w h -> S w' h'
paintMe : S []> Painting
cursorMe : {w h : Nat} -> S w h -> Nat /*/ Nat -- x,y coords
open Application
-- Now your turn. Build the appropriate handler to connect these
-- applications with mainLoop. Again, work in two stages, first
-- figuring out how to do the right actions, then managing the
-- state properly. (1 mark)
AppState : (S : Nat -> Nat -> Set) -> Set
AppState S = Sg Nat \ w -> Sg Nat \ h -> S w h
appPaint : {S : Nat -> Nat -> Set}{w h : Nat} ->
Application S -> S w h -> List Action
appPaint app s = {!!}
where
p = paintMe app s -- a wee reminder of how to use record stuff
xy = cursorMe app s
appHandler : {S : Nat -> Nat -> Set} ->
Application S ->
Event -> AppState S -> AppState S /**/ List Action
appHandler app e whs = {!!}
-- Your code turns into a main function, as follows.
appMain : {S : Nat -> Nat -> Set} -> Application S -> S 0 0 -> IO Thud
appMain app s = mainLoop (0 , 0 , s) (appHandler app)
---------------------------------------------------------------------------
-- THE DEMO, MADE INTO AN APPLICATION --
---------------------------------------------------------------------------
sillyChar : Char -> {w h : Nat} -> Painting w h
sillyChar c = [ [ vec (vec (green - c / black)) ] ]
sillyApp : Application \ _ _ -> Char
sillyApp = record
{ handleKey = \ { (char c) _ -> c ; _ c -> c }
; handleResize = \ _ _ c -> c
; paintMe = \
{ {suc (suc w)} {suc (suc h)} c ->
tobo 1 (sillyChar c)
(suc h) (tobo h
(leri 1 (sillyChar c) (suc w)
(leri w (sillyChar ' ') 1 (sillyChar c) (plusCommFact 1 w))
refl)
1 (sillyChar c) (plusCommFact 1 h) )
refl
; c -> sillyChar c
}
; cursorMe = \ _ -> 0 , 0
}
{- -
main : IO Thud
main = appMain sillyApp '*'
- -}
---------------------------------------------------------------------------
-- COMPARING TWO NUMBERS --
---------------------------------------------------------------------------
-- You've done the tricky part in episode 3, comparing two splittings of
-- the same number. Here's an easy way to reuse that code just to compare
-- two numbers. It may help in what is to come.
Compare : Nat -> Nat -> Set
Compare x y = CutCompare x y y x (x + y)
compare : (x y : Nat) -> Compare x y
compare x y = cutCompare x y y x (x + y) refl (plusCommFact x y)
-- To make sure you've got the message, try writing these things
-- "with compare" to resize paintings. If you need to make a painting
-- bigger, pad its right or bottom with a hole. If you need to make it
-- smaller, trim off the right or bottom excess. You have all the gadgets
-- you need! I'm not giving marks for these, but they'll be useful in
-- the next bit.
cropPadLR : (w h w' : Nat) -> Painting w h -> Painting w' h
cropPadLR w h w' p = {!!}
cropPadTB : (w h h' : Nat) -> Painting w h -> Painting w h'
cropPadTB w h h' p = {!!}
---------------------------------------------------------------------------
-- THE MOVING RECTANGLE --
---------------------------------------------------------------------------
-- This is the crux of the episode. Please build me an application which
-- displays a movable resizeable rectangle drawn with ascii art as follows
--
-- +--------------+
-- | |
-- | |
-- +--------------+
--
-- The "size" of the application is the terminal size: the rectangle should
-- be freely resizable *within* the terminal, so you should pad out the
-- rectangle to the size of the screen using Hole.
-- That is, only the rectangle is opaque; the rest is transparent.
-- The background colour of the rectangle should be given as an argument.
-- The foreground colour of the rectangle should be white.
-- The rectangle should have an interior consisting of opaque space with
-- the given background colour.
--
-- The arrow keys should move the rectangle around inside the terminal
-- window, preserving its size (like when you drag a window around).
-- Shifted arrow keys should resize the rectangle by moving its bottom
-- right corner (again, like you might do with a mouse).
-- You do not need to ensure that the rectangle fits inside the terminal.
-- The cursor should sit at the bottom right corner of the rectangle.
--
-- Mac users: the Terminal application which ships with OS X does NOT
-- give the correct treatment to shift-up and shift-down. You can get a
-- suitable alternative from http://iterm2.com/ (Thank @sigfpe for the tip!)
--
-- (2 marks, one for key handling, one for painting)
rectApp : Colour -> Application \ w h -> {!!}
rectApp c = record
{ handleKey = {!!}
; handleResize = {!!}
; paintMe = {!!}
; cursorMe = {!!}
}
{- -
main : IO Thud
main = appMain (rectApp blue) (rect 10 40 3 15)
- -}
---------------------------------------------------------------------------
-- TWO BECOME ONE --
---------------------------------------------------------------------------
-- Write a function which turns two sub-applications into one main
-- application by layering them.
--
-- For some S and T, you get an Application S and an Application T
-- You should choose a suitable state representation so that you know
-- (i) which of the two applications is at the front, and which behind
-- (ii) the states of both.
--
-- The Tab key should swap which sub-application is at the front, as if you had
-- clicked on the one at the back. All other keys should be handled by
-- whichever action is in front at the time. Also, the cursor position
-- should be chosen by the sub-application at the front.
--
-- The overall application size will be used as the size for both
-- sub-application sizes, which means you should be able to compute the
-- layered Painting, using equipment from episode 3. Crucially, we should be
-- able to see through the holes in the front sub-application to stuff from
-- the back sub-application.
--
-- (1 mark)
frontBack : {S T : Nat -> Nat -> Set} ->
Application S ->
Application T ->
Application \ w h -> {!!}
frontBack appS appT = record
{ handleKey = {!!}
; handleResize = {!!}
; paintMe = {!!}
; cursorMe = {!!}
}
-- By way of example, let's have a blue rectangle and a red rectangle.
{- -
main : IO Thud
main = appMain (frontBack (rectApp blue) (rectApp red))
(inl (rect 10 40 3 15 , rect 20 40 8 15))
- -}
---------------------------------------------------------------------------
-- NEXT TIME ... --
---------------------------------------------------------------------------
-- You get to figure out how to reduce flicker.
-- You get to think up some fun stuff to put in the rectangles.
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-1-Vec-Dummy where
open import Ex6-Setup
---------------------------------------------------------------------------
-- This is the dummy version of episode 1, which you can use to access --
-- episode 2 early, if you must, just by importing this instead. --
---------------------------------------------------------------------------
postulate SHUT_IT : {X : Set} -> X
---------------------------------------------------------------------------
-- VECTORS (5 marks) --
---------------------------------------------------------------------------
-- We've touched on them before, when we needed to manage the height of a
-- stack, but here are the "vectors", or "lists of known length.
data Vec (X : Set) : Nat -> Set where
[] : Vec X zero
_::_ : {n : Nat} -> X -> Vec X n -> Vec X (suc n)
infixr 6 _::_
-- This chunk of exercise 6 is about building the basic equipment to work
-- with vectors. We'll need this equipment later.
---------------------------------------------------------------------------
-- CONCATENATION AND ITS INVERSE --
---------------------------------------------------------------------------
infixr 6 _++_
-- Implement concatenation for any two vectors.
-- You will need to say how long the result will be.
-- (1 mark)
_++_ : {X : Set}{m n : Nat} -> Vec X m -> Vec X n -> Vec X SHUT_IT
xs ++ ys = SHUT_IT
-- Now, we could write "take" and "drop", but it's more useful to
-- prove that every long vector can be given by concatenating two
-- short vectors.
data Chop {X : Set}(m : Nat){n : Nat} : Vec X SHUT_IT -> Set where
is++ : (xs : Vec X m)(ys : Vec X n) -> Chop m (xs ++ ys)
-- A "Chop" for a given vector consists of the evidence that it can
-- be made by concatenation. You will need to fill in the Chop length,
-- above, the same way you filled in the length for _++_.
-- Show that you can compute a Chop for any vector.
-- Hint: you will need to use "with" at some point.
-- (1 mark)
chop : {X : Set}(m : Nat){n : Nat}(xs : Vec X SHUT_IT) -> Chop m {SHUT_IT} xs
chop m xs = SHUT_IT
-- Where take and drop give you vectors which you *hope* are the prefix
-- and suffix of the input. Chop gives you the pieces which are seen to
-- be the prefix and suffix of the input. Once you have chop, it's easy
-- to write take and drop in terms of it, and you can see they're right.
-- Try uncommenting and finishing the following (for fun).
{-
take : {X : Set}(m : Nat){n : Nat}(xs : Vec X {!!}) -> Vec X m
take m xs with chop m xs
take m .(xs ++ ys) | is++ xs ys = xs
-}
-- EXTRA! For no marks, but some utility in future, check that you can
-- use chop to define the function which just gives you the pair of the
-- prefix and the suffix.
vchop : {X : Set}(m : Nat){n : Nat} ->
Vec X SHUT_IT -> Vec X m /*/ Vec X n
vchop x xs = SHUT_IT
---------------------------------------------------------------------------
-- APPLICATIVE STRUCTURE --
---------------------------------------------------------------------------
-- Implement the function which makes a vector from a single element by
-- copying it the relevant number of times. Implement the "vectorized
-- application" operator which takes n functions and n arguments and gives
-- you the n results: the jth result should be given by applying the jth
-- function to the jth argument.
-- (1 mark)
vec : {n : Nat}{X : Set}(x : X) -> Vec X n
vec x = SHUT_IT
_<*>_ : {n : Nat}{S T : Set} -> Vec (S -> T) n -> Vec S n -> Vec T n
fs <*> ss = SHUT_IT
infixl 2 _<*>_
-- The applicative structure is very useful for working with vectors in
-- bulk. For example, I can take the successor of every number in a vector
-- by applying a vector of successor-functions to the vector of numbers.
mySucs : Vec Nat 5
mySucs = vec suc <*> (0 :: 1 :: 2 :: 3 :: 4 :: [])
-- should evaluate to 1 :: 2 :: 3 :: 4 :: 5 :: []
-- Now, using vec and <*> rather than explicit case analysis and recursion,
-- implement vector zipping as a one-liner, turning a pair of vectors into a
-- vector of pairs.
-- (1 mark)
zip : {n : Nat}{X Y : Set} -> Vec X n -> Vec Y n -> Vec (X /*/ Y) n
zip xs ys = SHUT_IT
-- Play the same game as we did for concatenation, take and drop. Show
-- that every vector of pairs can be made by zipping two vectors.
-- (1 mark)
data Unzip {n : Nat}{X Y : Set} : Vec (X /*/ Y) n -> Set where
-- what goes here?
unzip : {n : Nat}{X Y : Set}(xys : Vec (X /*/ Y) n) -> Unzip xys
unzip xys = SHUT_IT
-- EXTRA! For no marks, but some utility in future, check that you can
-- use unzip to define the function which just gives you the pair of the
-- two vectors.
vunzip : {X Y : Set}{n : Nat} -> Vec (X /*/ Y) n -> Vec X n /*/ Vec Y n
vunzip xys = SHUT_IT
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module ViewDemo where
open import Ex6-Setup
-- This file gives an example of the "view" method, which allows us to write
-- testing operations which actually generate evidence about the things being
-- tested, and in a very visual way. You get to develop more powerful ways of
-- seeing.
-- I recommend commenting out the example code, then redeveloping it
-- interactively, which will give you a much more animated experience of
-- what is going on.
map : {S T : Set} -> (S -> T) -> List S -> List T
map f [] = []
map f (s :: ss) = f s :: map f ss
-- Note, +-+ is concatenation for lists, here, to leave ++ for vectors.
-- trying to find out whether a list of choices all chooses inr
allRight : {S T : Set} -> List (S /+/ T) -> One /+/ List T
allRight [] = inr [] -- trivially all right
allRight (inl s :: xs) = inl <> -- busted!
-- Now the interesting case:
{-
allRight (inr t :: xs) = {!!}
-}
-- We need to know the situation about xs, so here's what to do
-- before the = sign, do a bit of typing to get
{-
allRight (inr t :: xs) with allRight xs
... | r = ?
-}
-- What does that mean? It means we want to be able to see everything
-- we had before on the left-hand side, but also the result of the
-- recursive call. The next line looks like
-- <pattern for main call> | <pattern for extra stuff> = ?
-- but we're allowed to write "..." when, left of |, nothing has changed
-- from the line containing "with". The "r" is just a freshly named
-- pattern variable. Now reload the file, and it's
{-
allRight (inr t :: xs) with allRight xs
... | r = {!!}
-}
-- Next, do case analysis on r! The "..." expands and you see the whole
-- picture.
allRight (inr t :: xs) with allRight xs
allRight (inr t :: xs) | inl <> = inl <>
allRight (inr t :: xs) | inr ts = inr (t :: ts)
-- Here's a more informative way to write the same test. Instead of
-- returning some bits and pieces which we *hope* tell us something
-- about the input, we *demand* to know what the input looks like
-- We introduce a list-dependent type which describes the possible things
-- that list can be. There is one constructor for each possibility.
-- Think of (AllRightable xs) as the type of "knowing whether xs is all
-- right". We know if we can tell these two cases apart.
-- This technique is known as declaring a "view" of some data.
data AllRightable {S T : Set} : List (S /+/ T) -> Set where
-- is it made from a bunch of ts, all wrapped with inr?
isAllRight : (ts : List T) -> AllRightable (map inr ts)
-- or does it have some ts, then a first s, then some more stuff?
hasFirstLeft : (ts : List T)(s : S)(xs : List (S /+/ T)) ->
AllRightable (map inr ts +-+ inl s :: xs)
-- Next, show that we can always know. That is, we establish that we can
-- see the data according to the declared "view".
-- You write the program with exactly the same case analysis and "with"
-- steps as the above, but when you come to fill in the return values,
-- just use C-c C-a. There is no choice: the type is an exact specification
-- of the analysis, so you can't lie and say you found an s that wasn't
-- there. But there's something else.
allRightable : {S T : Set}(xs : List (S /+/ T)) -> AllRightable xs
allRightable [] = isAllRight []
allRightable (inl s :: xs) = hasFirstLeft [] s xs
allRightable (inr t :: xs) with allRightable xs
-- As before we start from this after "with"
{-
... | r = {!!}
-}
-- but when we do a case split on r, something wonderful happens!
-- In each case, we see the list for what it really is.
allRightable (inr t :: .(map inr ts)) | isAllRight ts
= isAllRight (t :: ts)
-- In your face, it's all on the right.
allRightable (inr t :: .(map inr ts +-+ inl s :: xs)) | hasFirstLeft ts s xs
= hasFirstLeft (t :: ts) s xs
-- In your face, it has a leftmost inl s.
-- Patterns which start with . are a new thing. Normally, when you write a
-- pattern, you are *asking* what is present. When you write (or rather,
-- when you get Agda to write) a .-pattern, you are *telling* what is present.
-- Operationally, a .-pattern means "don't bother looking at that because we
-- already know what it is". They exist for code comprehension purposes,
-- to show you exactly what you've got in your hand.
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module ANSIEscapes where
data Direction = DU | DD | DL | DR
instance Show Direction where
show DU = "A"
show DD = "B"
show DR = "C"
show DL = "D"
upLine = putStr "\ESC[1A"
downLine = putStr "\ESC[1B"
up = moveCursor DU
down = moveCursor DD
backward = moveCursor DL
forward = moveCursor DR
moveCursor :: Direction -> Int -> IO ()
moveCursor dir 0 = return ()
moveCursor dir n = putStr $ "\ESC[" ++ show n ++ show dir
killLine = escape "K"
restoreCursor = escape "u"
saveCursor = escape "s"
clearScreen = escape "2J"
initTermSize = (escape "[=3h")
resetCursor = escape "0;0H"
escape e = putStr $ "\ESC[" ++ e
yellow str = "\ESC[1;33m" ++ str ++ "\ESC[0m"
brown str = "\ESC[0;33m" ++ str ++ "\ESC[0m"
blue str = "\ESC[1;34m" ++ str ++ "\ESC[0m"
red str = "\ESC[1;31m" ++ str ++ "\ESC[0m"
green str = "\ESC[1;32m" ++ str ++ "\ESC[0m"
purple str = "\ESC[1;35m" ++ str ++ "\ESC[0m"
white str = "\ESC[37m" ++ str ++ "\ESC[0m"
--Be careful, these assume someone else will reset the background colour
yellowOnGrey str = "\ESC[1;33m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
brownOnGrey str = "\ESC[0;33m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
blueOnGrey str = "\ESC[1;34m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
redOnGrey str = "\ESC[1;31m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
greenOnGrey str = "\ESC[1;32m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
purpleOnGrey str = "\ESC[1;35m\ESC[47m" ++ str ++ "\ESC[0m\ESC[47m"
whiteOnGrey str = "\ESC[37m" ++ str ++ "\ESC[0m"
onBlack str = "\ESC[40m" ++ str ++ "\ESC[0m"
onGrey str = onGreyEsc ++ str ++ onWhiteEsc
onGreyEsc = "\ESC[47m"
onWhiteEsc = "\ESC[0m"
orange str = str | {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-2-Box-Sol where
open import Ex6-Setup
open import Ex6-1-Vec-Sol
---------------------------------------------------------------------------
-- BOXES (5 marks) --
---------------------------------------------------------------------------
-- Boxes are sized rectangular tilings which fit together precisely.
-- They allow us to talk about the use of 2D space, e.g., on a screen.
data Box (X : Nat -> Nat -> Set)(w h : Nat) : Set where
-- ^basic-tile width^ ^height
[_] : X w h -> Box X w h
-- a basic tile is a tiling
leri : (wl : Nat) (bl : Box X wl h)
(wr : Nat) (br : Box X wr h)
-> wl + wr == w -> Box X w h
-- combine "left" and "right" tilings the same height
-- to make a tiling with their total width
tobo : (ht : Nat) (bt : Box X w ht)
(hb : Nat) (bb : Box X w hb)
-> ht + hb == h -> Box X w h
-- combine "top" and "bottom" tilings the same width
-- to make a tiling with their total height
---------------------------------------------------------------------------
-- MONADIC STRUCTURE --
---------------------------------------------------------------------------
-- If X and Y are both kinds of "sized stuff", we can say what it is to be
-- a "size-preserving function" between them.
_[]>_ : (X Y : Nat -> Nat -> Set) -> Set
X []> Y = {w h : Nat} -> X w h -> Y w h
-- A size preserving function turns an X of some size
-- into a Y the same size.
-- Think of X as "sized placeholders". If we have a way to turn each
-- placeholder into a tiling which fits into the place, we should be
-- able to deploy it across a whole tiling of placeholders. Check
-- that you can achieve that.
_=<<_ : forall {X Y} -> X []> Box Y -> Box X []> Box Y
f =<< [ x ] = f x
f =<< leri wl bl wr br x = leri wl (f =<< bl) wr (f =<< br) x
f =<< tobo ht bt hb bb x = tobo ht (f =<< bt) hb (f =<< bb) x
-- Using _=<<_, rather than more recursion, define...
mapBox : forall {X Y} -> X []> Y -> Box X []> Box Y
mapBox f b = ([_] o f) =<< b
-- roll out a size-preserving function on basic tiles to a whole tiling
joinBox : forall {X} -> Box (Box X) []> Box X
joinBox b = id =<< b
-- turn a tiling-of-tilings into a simple tiling
-- (1 mark) for the lot
---------------------------------------------------------------------------
-- PASTE KITS AND MATRICES --
---------------------------------------------------------------------------
-- A "paste kit" for sized stuff is whatever you need to combine stuff
-- left-to-right and top-to-bottom
record PasteKit (X : Nat -> Nat -> Set) : Set where
field
leriPaste : (wl wr : Nat){h : Nat} -> X wl h -> X wr h -> X (wl + wr) h
toboPaste : {w : Nat}(ht hb : Nat) -> X w ht -> X w hb -> X w (ht + hb)
-- Show that a PasteKit is just what you need to turn a tiling of
-- stuff into some stuff. (1 mark)
pasteBox : {X : Nat -> Nat -> Set} -> PasteKit X -> Box X []> X
pasteBox {X} pk = go where
open PasteKit pk -- brings leriPaste and toboPaste into scope
go : Box X []> X
go [ x ] = x
go (leri wl lb wr rb refl) = leriPaste wl wr (go lb) (go rb)
go (tobo ht tb hb bb refl) = toboPaste ht hb (go tb) (go bb)
-- If you were wondering what any of this had to do with part 1, here we
-- go...
Matrix : Set -> Nat -> Nat -> Set
Matrix C w h = Vec (Vec C w) h
-- matrices are "sized stuff", represented as a vector the right height
-- of rows which are vectors the right width of some sort of unit "cell".
-- Using the equipment you built in part 1, give matrices their PasteKit.
-- (1 mark)
matrixPasteKit : {C : Set} -> PasteKit (Matrix C)
matrixPasteKit = record {
leriPaste = \ _ _ ls rs -> vec _++_ <*> ls <*> rs ;
toboPaste = \ _ _ -> _++_ }
---------------------------------------------------------------------------
-- INTERLUDE: TESTING WITH TEXT --
---------------------------------------------------------------------------
-- Turn a list into a vector, either by truncating or padding with
-- a given dummy element.
paddy : {X : Set} -> X -> List X -> {n : Nat} -> Vec X n
paddy _ _ {zero} = []
paddy x [] {suc n} = x :: paddy x [] {n}
paddy x (y :: ys) {suc n} = y :: paddy x ys {n}
-- Use that to make vectors of characters from strings, padding with space.
[-_-] : String -> {n : Nat} -> Vec Char n
[- s -] = paddy ' ' (primStringToList s)
-- Now we can have character matrices of a given size
_*C*_ : Nat -> Nat -> Set
w *C* h = Matrix Char w h
-- Here are some.
mat43-1 : 4 *C* 3
mat43-1 = [- "post" -] :: [- "cake" -] :: [- "flop" -] :: []
mat43-2 : 4 *C* 3
mat43-2 = [- "horn" -] :: [- "walk" -] :: [- "ping" -] :: []
mat22 : 2 *C* 2
mat22 = [- "go" -] :: [- "do" -] :: []
mat62 : 6 *C* 2
mat62 = [- "getter" -] :: [- "gooder" -] :: []
-- Put them together as a tiling.
myTiling : Box _*C*_ 8 5
myTiling = tobo 3 (leri 4 [ mat43-1 ] 4 [ mat43-2 ] refl)
2 (leri 2 [ mat22 ] 6 [ mat62 ] refl) refl
-- Paste all the pieces and see what you get!
myText : 8 *C* 5
myText = pasteBox matrixPasteKit myTiling
---------------------------------------------------------------------------
-- CUT KITS, MATRICES --
---------------------------------------------------------------------------
-- A "cut kit" for sized stuff is whatever you need to cut stuff into
-- smaller pieces: left-and-right pieces, or top-and-bottom pieces.
record CutKit (X : Nat -> Nat -> Set) : Set where
field
cutLR : (w h wl wr : Nat) -> wl + wr == w ->
X w h -> X wl h /*/ X wr h
cutTB : (w h ht hb : Nat) -> ht + hb == h ->
X w h -> X w ht /*/ X w hb
-- Equip matrices with their CutKit. (1 mark)
matrixCutKit : {C : Set} -> CutKit (Matrix C)
matrixCutKit {C} = record {
cutLR = \ {.(wl + wr) h wl wr refl css ->
vunzip (vec (vchop wl) <*> css)} ;
cutTB = \ {w .(ht + hb) ht hb refl -> vchop ht } }
---------------------------------------------------------------------------
-- HOLES --
---------------------------------------------------------------------------
-- We might want to make sure that, whatever other basic tiles are in play,
-- we can have tiles which are "missing", as if we had cut rectangular
-- holes in a piece of paper.
data HoleOr (X : Nat -> Nat -> Set)(w h : Nat) : Set where
Hole : HoleOr X w h
[_] : X w h -> HoleOr X w h
-- A HoleOr X is (you guessed it) either a hole or an X.
-- Show that if X has a CutKit, so has HoleOr X. What do you get when you
-- cut up a hole? (1 mark)
holeCutKit : {X : Nat -> Nat -> Set} -> CutKit X -> CutKit (HoleOr X)
holeCutKit {X} ck = record { cutLR = clr ; cutTB = ctb } where
open CutKit ck
clr : (w h wl wr : Nat) ->
wl + wr == w -> HoleOr X w h -> HoleOr X wl h /*/ HoleOr X wr h
clr w h wl wr wq Hole = Hole , Hole
clr w h wl wr wq [ x ] with cutLR w h wl wr wq x
clr w h wl wr wq [ x ] | xl , xr = [ xl ] , [ xr ]
ctb : (w h ht hb : Nat) ->
ht + hb == h -> HoleOr X w h -> HoleOr X w ht /*/ HoleOr X w hb
ctb w h ht hb hq Hole = Hole , Hole
ctb w h ht hb hq [ x ] with cutTB w h ht hb hq x
ctb w h ht hb hq [ x ] | xt , xb = [ xt ] , [ xb ]
---------------------------------------------------------------------------
-- A BIT OF FUN --
---------------------------------------------------------------------------
-- Show that you can turn holes into spaces.
holeSpace : HoleOr _*C*_ []> _*C*_
holeSpace Hole = vec (vec ' ')
holeSpace [ x ] = x
-- Show how to render a tiling made of text or holes as text.
renderHoleOrText : Box (HoleOr _*C*_) []> _*C*_
renderHoleOrText = pasteBox matrixPasteKit o mapBox holeSpace
-- Make a test example and see!
myTest : 8 *C* 6
myTest = renderHoleOrText
(leri 3 (tobo 4 [ [ vec (vec '*') ] ] 2 [ Hole ] refl)
5 (tobo 2 [ Hole ] 4 [ [ vec (vec '=') ] ] refl) refl)
---------------------------------------------------------------------------
-- NEXT TIME... --
---------------------------------------------------------------------------
-- Have a wee think about what you might need to equip Box X with a CutKit.
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-4-Dis-Sol where
open import Ex6-Setup
open import Ex6-1-Vec-Sol
open import Ex6-2-Box-Sol
open import Ex6-3-Cut-Sol
---------------------------------------------------------------------------
-- CURSES DISPLAY FOR APPLICATIONS (5 marks) --
---------------------------------------------------------------------------
-- You may need to look at the Ex6-Setup file to find some of the relevant
-- kit for this episode, and it's worth looking there for goodies, anyway.
-- We start from the idea of a main loop.
{- This is the bit of code I wrote in Haskell to animate your code. -}
postulate
mainLoop : {S : Set} -> -- program state
-- INITIALIZER
S -> -- initial state
-- EVENT HANDLER
(Event -> S -> -- event and state in
S /**/ List Action) -> -- new state and screen actions out
-- PUT 'EM TOGETHER AND YOU'VE GOT AN APPLICATION!
IO Thud
{-# COMPILED mainLoop (\ _ -> HaskellSetup.mainLoop) #-}
-- The type S /**/ T is a type of pairs that the compiler can share with
-- Haskell. Its constructor is _,_ just as for S /*/ T. Meanwhile Thud
-- does the same job for One, but you won't need to bother with it.
-- To make a thing you can run, you need to
-- (i) choose a type to represent the program's internal state S
-- (ii) give the initial state
-- (iii) explain how, given an event and the current state, to
-- produce a new state and a list of actions to update the
-- display.
-- Let me show you the example I gave in class...
---------------------------------------------------------------------------
-- My silly wee demo --
---------------------------------------------------------------------------
-- the program state...
SillyState : Set
SillyState = Char /*/ Nat /*/ Nat
-- ...knows the character to put round the edge of the window, and the
-- size of the window
-- To paint a window whose dimensions are both at least 2, we...
sillyPaint : SillyState -> List Action
sillyPaint (c , suc (suc w), suc (suc h))
= goRowCol 0 0 -- send the cursor home
:: bgText black :: fgText green -- adopt our colour scheme
:: sendText (concat ( -- send ...
list (suc (suc w)) c :: -- ... top
concat (list h (c :: list w ' ' +-+ c :: [])) :: -- middle
list (suc (suc w)) c :: [])) :: -- and bottom
[]
sillyPaint _ = []
-- There are two kinds of event we must consider: keystroke and resize.
sillyHandler : Event -> SillyState -> SillyState /**/ List Action
sillyHandler (key (char c)) (_ , w , h) = s , sillyPaint s where
-- if we get an ordinary character key,
-- update the character and repaint
s : SillyState
s = (c , w , h)
sillyHandler (resize w h) (c , _ , _) = s , sillyPaint s where
-- if we get a resizing event,
-- update the size and repaint
s : SillyState
s = (c , w , h)
sillyHandler _ s = s , [] -- otherwise, relax
-- To finish the job, we write a "main" function, plugging in the initial
-- state. The initial size of 0 by 0 will provoke an immediate resize event,
-- giving the correct size!
{- -
main : IO Thud
main = mainLoop ('*' , 0 , 0) sillyHandler
- -}
-- To run this program, start a terminal, change to your Ex6 directory, then
--
-- make go4
--
-- You should be able to press keys and resize the thing and see sensible
-- stuff happen. Ctrl-C quits.
-- When you're bored of green rectangles, comment out the above main
-- function, so you can move on to the actual work. There are other
-- main functions further down the file which you can comment in as you
-- need them. Of course, you can have at most one main at a time.
---------------------------------------------------------------------------
-- PAINTINGS --
---------------------------------------------------------------------------
-- Now that we're in colour, one cell of display will be a ColourChar ...
data ColourChar : Set where
_-_/_ : (fg : Colour)(c : Char)(bg : Colour) -> ColourChar
-- ... e.g. green - '*' / black for what we had, above.
-- a painting is a Box structure whose basic tiles are either transparent
-- holes or opaque rectangles of coloured text.
Painting : Nat -> Nat -> Set
Painting = Box (HoleOr (Matrix ColourChar))
-- Now your turn. Making use of the equipment you developed in epsiode 2,
-- get us from a Painting to a List Action in two hops. Note that you will
-- have to decide how to render a Hole: some bland background stuff, please.
-- (1 mark)
paintMatrix : Painting []> Matrix ColourChar
paintMatrix p = pasteBox matrixPasteKit (mapBox fill p) where
fill : HoleOr (Matrix ColourChar) []> Matrix ColourChar
fill Hole = vec (vec (black - ' ' / white))
fill [ m ] = m
vecFoldR : {X Y : Set} -> (X -> Y -> Y) -> Y -> {n : Nat} -> Vec X n -> Y
vecFoldR c n [] = n
vecFoldR c n (x :: xs) = c x (vecFoldR c n xs)
paintAction : {w h : Nat} -> Matrix ColourChar w h -> List Action
paintAction = vecFoldR (vecFoldR (\ {(f - c / b) k -> \ as ->
fgText f :: bgText b :: sendText (c :: []) :: k as}) id) []
---------------------------------------------------------------------------
-- APPLICATIONS --
---------------------------------------------------------------------------
-- Here's a general idea of what it means to be an "application".
-- You need to choose some sort of size-dependent state, then provide these
-- bits and pieces. We need to know how the state is updated according to
-- events, with resizing potentially affecting the state's type. We must
-- be able to paint the state. The state should propose a cursor position.
-- (Keen students may modify this definition to ensure the cursor must be
-- within the bounds of the application.)
record Application (S : Nat -> Nat -> Set) : Set where
field
handleKey : Key -> S []> S
handleResize : {w h : Nat}(w' h' : Nat) -> S w h -> S w' h'
paintMe : S []> Painting
cursorMe : {w h : Nat} -> S w h -> Nat /*/ Nat -- x,y coords
open Application public
-- Now your turn. Build the appropriate handler to connect these
-- applications with mainLoop. Again, work in two stages, first
-- figuring out how to do the right actions, then managing the
-- state properly. (1 mark)
AppState : (S : Nat -> Nat -> Set) -> Set
AppState S = Sg Nat \ w -> Sg Nat \ h -> S w h
appPaint : {S : Nat -> Nat -> Set}{w h : Nat} ->
Application S -> S w h -> List Action
appPaint app s =
goRowCol 0 0 :: paintAction (paintMatrix p)
+-+ (goRowCol (snd xy) (fst xy) :: [])
where
p = paintMe app s
xy = cursorMe app s
appHandler : {S : Nat -> Nat -> Set} ->
Application S ->
Event -> AppState S -> AppState S /**/ List Action
appHandler app (key k) (w , h , s) = (w , h , s') , appPaint app s'
where s' = handleKey app k s
appHandler app (resize w' h') (w , h , s) = (w' , h' , s') , appPaint app s'
where s' = handleResize app w' h' s
-- Your code turns into a main function, as follows.
appMain : {S : Nat -> Nat -> Set} -> Application S -> S 0 0 -> IO Thud
appMain app s = mainLoop (0 , 0 , s) (appHandler app)
---------------------------------------------------------------------------
-- THE DEMO, MADE INTO AN APPLICATION --
---------------------------------------------------------------------------
sillyChar : Char -> {w h : Nat} -> Painting w h
sillyChar c = [ [ vec (vec (green - c / black)) ] ]
sillyApp : Application \ _ _ -> Char
sillyApp = record
{ handleKey = \ { (char c) _ -> c ; _ c -> c }
; handleResize = \ _ _ c -> c
; paintMe = \
{ {suc (suc w)} {suc (suc h)} c ->
tobo 1 (sillyChar c)
(suc h) (tobo h
(leri 1 (sillyChar c) (suc w)
(leri w (sillyChar ' ') 1 (sillyChar c) (plusCommFact 1 w))
refl)
1 (sillyChar c) (plusCommFact 1 h) )
refl
; c -> sillyChar c
}
; cursorMe = \ _ -> 0 , 0
}
{- -
main : IO Thud
main = appMain sillyApp '*'
- -}
---------------------------------------------------------------------------
-- COMPARING TWO NUMBERS --
---------------------------------------------------------------------------
-- You've done the tricky part in episode 3, comparing two splittings of
-- the same number. Here's an easy way to reuse that code just to compare
-- two numbers. It may help in what is to come.
Compare : Nat -> Nat -> Set
Compare x y = CutCompare x y y x (x + y)
compare : (x y : Nat) -> Compare x y
compare x y = cutCompare x y y x (x + y) refl (plusCommFact x y)
-- To make sure you've got the message, try writing these things
-- "with compare" to resize paintings. If you need to make a painting
-- bigger, pad its right or bottom with a hole. If you need to make it
-- smaller, trim off the right or bottom excess. You have all the gadgets
-- you need! I'm not giving marks for these, but they'll be useful in
-- the next bit.
cropPadLR : (w h w' : Nat) -> Painting w h -> Painting w' h
cropPadLR w h w' p with compare w w'
cropPadLR w h w' p | cutLt d q _ = leri w p (suc d) [ Hole ] q
cropPadLR w h .w p | cutEq refl _ = p
cropPadLR w h w' p | cutGt d q _
= fst (CutKit.cutLR (boxCutKit (holeCutKit matrixCutKit))
w h w' (suc d) q p)
cropPadTB : (w h h' : Nat) -> Painting w h -> Painting w h'
cropPadTB w h h' p with compare h h'
cropPadTB w h h' p | cutLt d q _ = tobo h p (suc d) [ Hole ] q
cropPadTB w h .h p | cutEq refl _ = p
cropPadTB w h h' p | cutGt d q _
= fst (CutKit.cutTB (boxCutKit (holeCutKit matrixCutKit))
w h h' (suc d) q p)
---------------------------------------------------------------------------
-- THE MOVING RECTANGLE --
---------------------------------------------------------------------------
-- This is the crux of the episode. Please build me an application which
-- displays a movable resizeable rectangle drawn with ascii art as follows
--
-- +--------------+
-- | |
-- | |
-- +--------------+
--
-- The "size" of the application is the terminal size: the rectangle should
-- be freely resizable *within* the terminal, so you should pad out the
-- rectangle to the size of the screen using Hole.
-- That is, only the rectangle is opaque; the rest is transparent.
-- The background colour of the rectangle should be given as an argument.
-- The foreground colour of the rectangle should be white.
-- The rectangle should have an interior consisting of opaque space with
-- the given background colour.
--
-- The arrow keys should move the rectangle around inside the terminal
-- window, preserving its size (like when you drag a window around).
-- Shifted arrow keys should resize the rectangle by moving its bottom
-- right corner (again, like you might do with a mouse).
-- You do not need to ensure that the rectangle fits inside the terminal.
-- The cursor should sit at the bottom right corner of the rectangle.
--
-- Mac users: the Terminal application which ships with OS X does NOT
-- give the correct treatment to shift-up and shift-down. You can get a
-- suitable alternative from http://iterm2.com/ (Thank @sigfpe for the tip!)
--
-- (2 marks, one for key handling, one for painting)
record RectState : Set where
constructor rect
field
gapL rectW : Nat
gapT rectH : Nat
rectKey : Key -> RectState -> RectState
rectKey (arrow normal up) (rect gapL rectW (suc gapT) rectH)
= rect gapL rectW gapT rectH
rectKey (arrow normal down) (rect gapL rectW gapT rectH)
= rect gapL rectW (suc gapT) rectH
rectKey (arrow normal left) (rect (suc gapL) rectW gapT rectH)
= rect gapL rectW gapT rectH
rectKey (arrow normal right) (rect gapL rectW gapT rectH)
= rect (suc gapL) rectW gapT rectH
rectKey (arrow shift up) (rect gapL rectW gapT (suc rectH))
= rect gapL rectW gapT rectH
rectKey (arrow shift down) (rect gapL rectW gapT rectH)
= rect gapL rectW gapT (suc rectH)
rectKey (arrow shift left) (rect gapL (suc rectW) gapT rectH)
= rect gapL rectW gapT rectH
rectKey (arrow shift right) (rect gapL rectW gapT rectH)
= rect gapL (suc rectW) gapT rectH
rectKey _ s = s
rectApp : Colour -> Application \ _ _ -> RectState
rectApp c = record
{ handleKey = \ k -> rectKey k
; handleResize = \ _ _ -> id
; paintMe = \ { (rect gapL rectW gapT rectH) ->
cropPadTB _ _ _ (cropPadLR _ _ _
(tobo gapT [ Hole ] (suc (rectH + 1))
(leri gapL [ Hole ] (suc (rectW + 1))
(tobo 1 (horiz rectW) _
(tobo rectH
(leri 1 (vert rectH) _
(leri rectW (interior rectW rectH)
1 (vert rectH) refl) refl)
1 (horiz rectW) refl) refl)
refl) refl)) }
; cursorMe = \ { (rect gapL rectW gapT rectH) ->
(1 + gapL + rectW) , (1 + gapT + rectH)
}
} where
horiz : (w : Nat) -> Painting (suc (w + 1)) 1
horiz w = leri 1 [ [ (white - '+' / c :: []) :: [] ] ] _
(leri w [ [ vec (white - '-' / c) :: [] ] ] 1
[ [ (white - '+' / c :: []) :: [] ] ] refl) refl
vert : (h : Nat) -> Painting 1 h
vert h = [ [ vec (vec (white - '|' / c)) ] ]
interior : (w h : Nat) -> Painting w h
interior w h = [ [ vec (vec (white - ' ' / c)) ] ]
{- -
main : IO Thud
main = appMain (rectApp blue) (rect 10 40 3 15)
- -}
---------------------------------------------------------------------------
-- TWO BECOME ONE --
---------------------------------------------------------------------------
-- Write a function which turns two sub-applications into one main
-- application by layering them.
--
-- For some S and T, you get an Application S and an Application T
-- You should choose a suitable state representation so that you know
-- (i) which of the two applications is at the front, and which behind
-- (ii) the states of both.
--
-- The Tab key should swap which sub-application is at the front, as if you had
-- clicked on the one at the back. All other keys should be handled by
-- whichever action is in front at the time. Also, the cursor position
-- should be chosen by the sub-application at the front.
--
-- The overall application size will be used as the size for both
-- sub-application sizes, which means you should be able to compute the
-- layered Painting, using equipment from episode 3. Crucially, we should be
-- able to see through the holes in the front sub-application to stuff from
-- the back sub-application.
--
-- (1 mark)
frontBack : {S T : Nat -> Nat -> Set} ->
Application S ->
Application T ->
Application \ w h -> (S w h /*/ T w h) /+/ (T w h /*/ S w h)
frontBack appS appT = record
{ handleKey = \
{ tab (inl (s , t)) -> inr (t , s)
; tab (inr (t , s)) -> inl (s , t)
; k (inl (s , t)) -> inl (handleKey appS k s , t)
; k (inr (t , s)) -> inr (handleKey appT k t , s)
}
; handleResize = \
{ w h (inl (s , t)) -> inl ( handleResize appS w h s
, handleResize appT w h t )
; w h (inr (t , s)) -> inr ( handleResize appT w h t
, handleResize appS w h s )
}
; paintMe = \
{ (inl (s , t)) -> overlay matrixCutKit (paintMe appS s) (paintMe appT t)
; (inr (t , s)) -> overlay matrixCutKit (paintMe appT t) (paintMe appS s)
}
; cursorMe = \
{ (inl (s , t)) -> cursorMe appS s
; (inr (t , s)) -> cursorMe appT t
}
}
-- By way of example, let's have a blue rectangle and a red rectangle.
{- -
main : IO Thud
main = appMain (frontBack (rectApp blue) (rectApp red))
(inl (rect 10 40 3 15 , rect 20 40 8 15))
- -}
---------------------------------------------------------------------------
-- NEXT TIME ... --
---------------------------------------------------------------------------
-- You get to figure out how to reduce flicker.
-- You get to think up some fun stuff to put in the rectangles.
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-Setup where
---------------------------------------------------------------------------
-- NATURAL NUMBERS --
---------------------------------------------------------------------------
data Nat : Set where
zero : Nat
suc : Nat -> Nat
{-# BUILTIN NATURAL Nat #-}
{-# COMPILED_DATA Nat HaskellSetup.Nat HaskellSetup.Zero HaskellSetup.Suc #-}
_+_ : Nat -> Nat -> Nat
zero + y = y
suc x + y = suc (x + y)
infixr 5 _+_
---------------------------------------------------------------------------
-- ONE, SIGMA TYPES AND BINARY PRODUCT --
---------------------------------------------------------------------------
record One : Set where constructor <>
record Sg (S : Set)(T : S -> Set) : Set where
constructor _,_
field
fst : S
snd : T fst
open Sg public
_/*/_ : Set -> Set -> Set
S /*/ T = Sg S \ _ -> T
infixr 3 _/*/_
infixr 3 _,_
---------------------------------------------------------------------------
-- EQUALITY, AND SOME FACTS ABOUT SUC AND ADDITION --
---------------------------------------------------------------------------
data _==_ {X : Set}(x : X) : X -> Set where
refl : x == x
infixr 4 _==_
transitivity : {X : Set}{x y z : X} -> x == y -> y == z -> x == z
transitivity refl q = q
sucInj : {x y : Nat} -> suc x == suc y -> x == y
sucInj refl = refl
sucResp : {x y : Nat} -> x == y -> suc x == suc y
sucResp refl = refl
plusZeroFact : (x : Nat) -> x + zero == x
plusZeroFact zero = refl
plusZeroFact (suc x) = sucResp (plusZeroFact x)
plusSucFact : (x y : Nat) -> x + suc y == suc (x + y)
plusSucFact zero y = refl
plusSucFact (suc x) y = sucResp (plusSucFact x y)
plusCommFact : (x y : Nat) -> y + x == x + y
plusCommFact zero y = plusZeroFact y
plusCommFact (suc x) y
= transitivity (plusSucFact y x) (sucResp (plusCommFact x y))
---------------------------------------------------------------------------
-- IDENTITY AND COMPOSITION FUNCTIONS --
---------------------------------------------------------------------------
id : {X : Set} -> X -> X
id x = x
_o_ : {X : Set}{Y : X -> Set}{Z : (x : X) -> Y x -> Set}
(f : {x : X}(y : Y x) -> Z x y)(g : (x : X) -> Y x) ->
(x : X) -> Z x (g x)
(f o g) x = f (g x)
---------------------------------------------------------------------------
-- ORDINARY LISTS --
---------------------------------------------------------------------------
data List (X : Set) : Set where
[] : List X
_::_ : X -> List X -> List X
infixr 6 _::_
{-# COMPILED_DATA List [] [] (:) #-}
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #-}
{-# BUILTIN CONS _::_ #-}
_+-+_ : {X : Set} -> List X -> List X -> List X
[] +-+ ys = ys
(x :: xs) +-+ ys = x :: (xs +-+ ys)
infixr 6 _+-+_
concat : {X : Set} -> List (List X) -> List X
concat [] = []
concat (xs :: xss) = xs +-+ concat xss
list : {X : Set} -> Nat -> X -> List X
list zero x = []
list (suc n) x = x :: list n x
---------------------------------------------------------------------------
-- ORDINARY BOOLEANS --
---------------------------------------------------------------------------
data Two : Set where
tt ff : Two
{-# BUILTIN BOOL Two #-}
{-# BUILTIN TRUE tt #-}
{-# BUILTIN FALSE ff #-}
{-# COMPILED_DATA Two Bool True False #-}
---------------------------------------------------------------------------
-- ORDINARY SUMS --
---------------------------------------------------------------------------
data _/+/_ (S T : Set) : Set where
inl : S -> S /+/ T
inr : T -> S /+/ T
infixr 2 _/+/_
{-# COMPILED_DATA _/+/_ Either Left Right #-}
---------------------------------------------------------------------------
-- CHARACTERS AND STRINGS --
---------------------------------------------------------------------------
postulate -- we just suppose the following things exist...
Char : Set
String : Set
{-# BUILTIN CHAR Char #-}
{-# COMPILED_TYPE Char Char #-} -- ...and by the time we reach Haskell...
{-# BUILTIN STRING String #-}
{-# COMPILED_TYPE String String #-} -- ...they *do* exist!
primitive -- these are baked in; they even work!
primCharEquality : Char -> Char -> Two
primStringAppend : String -> String -> String
primStringToList : String -> List Char
primStringFromList : List Char -> String
---------------------------------------------------------------------------
-- IO IN HASKELL --
---------------------------------------------------------------------------
postulate -- Haskell has a monad for doing IO, which is our route out
IO : Set -> Set
return : {A : Set} -> A -> IO A
_>>=_ : {A B : Set} -> IO A -> (A -> IO B) -> IO B
infixl 1 _>>=_
{-# BUILTIN IO IO #-}
{-# COMPILED_TYPE IO IO #-}
{-# COMPILED return (\ _ -> return) #-}
{-# COMPILED _>>=_ (\ _ _ -> (>>=)) #-}
---------------------------------------------------------------------------
-- KEYS --
---------------------------------------------------------------------------
{- Here's the characterization of keys I give you -}
data Direction : Set where up down left right : Direction
data Modifier : Set where normal shift control : Modifier
data Key : Set where
char : Char -> Key
arrow : Modifier -> Direction -> Key
enter : Key
backspace : Key
delete : Key
escape : Key
tab : Key
data Event : Set where
key : (k : Key) -> Event
resize : (w h : Nat) -> Event
{-# IMPORT ANSIEscapes #-}
{-# IMPORT HaskellSetup #-}
{-# COMPILED_DATA Direction
ANSIEscapes.Direction
ANSIEscapes.DU ANSIEscapes.DD ANSIEscapes.DL ANSIEscapes.DR #-}
{-# COMPILED_DATA Modifier
HaskellSetup.Modifier
HaskellSetup.Normal HaskellSetup.Shift HaskellSetup.Control #-}
{-# COMPILED_DATA Key
HaskellSetup.Key
HaskellSetup.Char HaskellSetup.Arrow HaskellSetup.Enter
HaskellSetup.Backspace HaskellSetup.Delete HaskellSetup.Escape
HaskellSetup.Tab #-}
{-# COMPILED_DATA Event
HaskellSetup.Event
HaskellSetup.Key HaskellSetup.Resize #-}
---------------------------------------------------------------------------
-- COLOURS --
---------------------------------------------------------------------------
data Colour : Set where
black red green yellow blue magenta cyan white : Colour
{-# COMPILED_DATA Colour HaskellSetup.Colour
HaskellSetup.Black HaskellSetup.Red HaskellSetup.Green
HaskellSetup.Yellow HaskellSetup.Blue HaskellSetup.Magenta
HaskellSetup.Cyan HaskellSetup.White #-}
---------------------------------------------------------------------------
-- ACTIONS --
---------------------------------------------------------------------------
data Action : Set where
goRowCol : Nat -> Nat -> Action -- top left is zero zero
sendText : List Char -> Action
move : Direction -> Nat -> Action -- which way and how much
fgText : Colour -> Action
bgText : Colour -> Action
{-# COMPILED_DATA Action HaskellSetup.Action
HaskellSetup.GoRowCol HaskellSetup.SendText HaskellSetup.Move
HaskellSetup.FgText HaskellSetup.BgText #-}
---------------------------------------------------------------------------
-- HASKELL TUPLES --
---------------------------------------------------------------------------
data _/**/_ (S T : Set) : Set where
_,_ : S -> T -> S /**/ T
{-# COMPILED_DATA _/**/_ (,) (,) #-}
data Thud : Set where <> : Thud
{-# COMPILED_DATA Thud () () #-}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-5-App where
open import Ex6-Setup
open import Ex6-1-Vec-Sol
open import Ex6-2-Box-Sol
open import Ex6-3-Cut-Sol
open import Ex6-4-Dis-Sol
---------------------------------------------------------------------------
-- SMOOTHER AND MORE INTERESTING APPLICATIONS (5 marks) --
---------------------------------------------------------------------------
-- As these are the 5 marks which get you from "awesome first" to
-- "perfection", I'm leaving this task more open. There are two
-- parts to it.
-- Part 1. MINIMIZE FLICKER. The episode 4 setup repaints the whole
-- screenful every time. With a little bit of redesign, it's possible
-- to ensure that you repaint only what changes. Re-engineer the
-- functionality of exercise 4 to reduce flicker.
-- (2 marks)
-- Part 2. PUT SOMETHING INTERESTING IN THE RECTANGLES. It's one thing
-- being able to shove rectangles around the screen, but it would be
-- good if there was some actual content to them. You're free to design
-- whatever you like (and to raid Ex5 for spare parts, of course), but
-- I have some marking guidelines.
-- any nontrivial static content in the rectangles scores 1 mark,
-- provided you can still move and resize them;
-- treating the rectangle as a viewport into some content larger than
-- the rectangle scores 1 mark, provided you can move the viewport
-- all around the content
-- significant keyboard interaction with the rectangle at the front,
-- beyond what is needed for moving it, resizing it and refocusing
-- it, is worth 1 mark
-- (3 marks)
-- If you can think of other interesting things you might want to do that
-- don't quite fit the mark scheme for part 2, by all means pitch them to
-- me and I'll tell you how much I'd be willing to "pay" for them.
-- The rest of the file consists of some bits and pieces I came up with
-- while I was experimenting. You are free to adopt, adapt or reject these
-- components.
---------------------------------------------------------------------------
-- GENERALIZING OVERLAY TO MASKING --
---------------------------------------------------------------------------
-- Here's what I should have asked you to build in episode 3.
mask : {X Y Z : Nat -> Nat -> Set} -> CutKit Y ->
({w h : Nat} -> X w h -> Box Y w h -> Box Z w h) ->
{w h : Nat} ->
{- front -} Box X w h ->
{- back -} Box Y w h ->
{- combined -} Box Z w h
mask {X}{Y}{Z} ck m = go where
open CutKit (boxCutKit ck)
go : {w h : Nat} -> Box X w h -> Box Y w h -> Box Z w h
go xb yb = {!!}
-- The idea, as with "overlay", is that the box of X stuff is in front
-- and the box of Y stuff is behind. You need to combine them to make
-- a box of Z stuff. Fortunately, once you've cut your way through the
-- structure to reach each basic X tile, the parameter m is just what
-- you need to know to combine that tile with the Y box to make a Z box.
-- You should find that the implementation is almost the same as "overlay"
-- but the extra generality is quite useful. You might find the following
-- concepts helpful.
Update : Nat -> Nat -> Set
Update w h
= Two -- does it demand repainting?
/*/ HoleOr (Matrix ColourChar) w h -- transparent or opaque stuff?
-- A Box Update is more informative than a Painting, in that every primitive
-- tile tells you whether it is "new" or not; now you can build the logic
-- to combine the changes which happen in each layer. In particular, you can
-- model the idea that moving or resizing in the front can reveal stuff which
-- used to be hidden at the back: that's a "new hole", and even if what's
-- behind it hasn't changed, you'll need to update the display.
Selection : Nat -> Nat -> Set
Selection = Box \ _ _ -> Two
-- A selection is a tiling of the rectangle with tt or ff. You can lift all
-- the usual logical operations to selections using mask and mapBox. For
-- example, XOR-ing selections gives you everything in one but not the other,
-- which might help you spot what has changed.
---------------------------------------------------------------------------
-- RUN-LENGTH ENCODING INACTIVITY --
---------------------------------------------------------------------------
-- An idea which might be useful in helping you to manage more selective
-- redrawing is to build the idea of "doing nothing for a bit" into the
-- lists of actions that you build up. Think about updating one line of
-- the display: it might sometimes help to be able to say "keep the next
-- n cells as they were", which you could interpret as a cursor move, rather
-- than a text output.
-- Correspondingly, you might benefit from a data structure like this:
data Skippy (X : Set) : Set where
[] : Skippy X -- stop
_::_ : X -> Skippy X -> Skippy X -- give one X then keep going
_>_ : Nat -> Skippy X -> Skippy X -- skip n places, then keep going
-- Now, when you work with these structures, you should enforce that
-- (i) you never have zero > xs (if there's nothing to skip, don't)
-- (ii) you never have m > n > xs (don't skip twice, skip further)
-- It's possible to refine the type Skippy to enforce those properties by
-- the power of type checking. Or you could just make sure you never cheat
-- by the more traditional method of defining a "smart constructor"
_>>_ : {X : Set} -> Nat -> Skippy X -> Skippy X
-- special cases go here
n >> xs = n > xs
-- The definition I've given you isn't very smart: >> is the same as >.
-- But the idea is that you add some special cases before that last line
-- which catch the possibilities that should never happen and do something
-- else instead. Now you can define operations like concatenation, using
-- the smart constructor in place of the regular one.
_+>+_ : {X : Set} -> Skippy X -> Skippy X -> Skippy X
[] +>+ ys = ys
(x :: xs) +>+ ys = x :: (xs +>+ ys)
(m > xs) +>+ ys = m >> (xs +>+ ys)
-- ^^ see?
-- That way, you know that if the lists you're concatenating satisfy the
-- above rules, so will the result.
---------------------------------------------------------------------------
-- ANOTHER SMART CONSTRUCTOR --
---------------------------------------------------------------------------
-- You might consider playing the same game with the List Action type that
-- we use for displaying things. Here's part of mine.
_:a:_ : Action -> List Action -> List Action
goRowCol _ _ :a: (goRowCol r c :: as) = goRowCol r c :: as
sendText x :a: (sendText y :: as) = sendText (x +-+ y) :: as
a :a: as = a :: as
-- That's to say
-- (i) there's no point in positioning the cursor twice in a row, when
-- the second just overrides the first;
-- (ii) don't send two small texts when you can send one big text.
---------------------------------------------------------------------------
-- CROP-AND-PAD --
---------------------------------------------------------------------------
-- As with overlay, the types of cropPadLR and cropPadTB from episode 4
-- are more specific than is necessarily helpful. How about this instead?
cropPadXLR : {X : Nat -> Nat -> Set} -- some stuff
(ck : CutKit X) -> -- how to cut stuff
(px : {w h : Nat} -> X w h) -> -- how to make "blank" stuff
(w h w' : Nat) -> Box X w h -> Box X w' h
cropPadXLR ck px w h w' b = {!!}
-- and its TB friend, of course. Now you can crop things other than
-- Paintings.
---------------------------------------------------------------------------
-- FROM APPLICATIONS TO UPPLICATIONS --
---------------------------------------------------------------------------
-- The notion of "Application" from episode 4 required you to define a
-- paintMe function which just gives the full display. You may need to
-- rethink this concept to get an *updating* application, or "Upplication"
-- in which at least some of the event handlers tell you just what has
-- changed. You will certainly need *more* information, but you should
-- also consider whether it would be better if the existing information
-- took a different form.
---------------------------------------------------------------------------
-- PUTTING UPPLICATIONS TOGETHER --
---------------------------------------------------------------------------
-- In episode 4, you had to define the frontBack operator, which combined
-- two applications into one by *layering* them. How does that work for
-- upplications? What other spatial combinations of upplications make sense?
-- Here are three possibilities worth considering:
-- (i) putting two applications side-by-side,
-- (ii) putting one application above another,
-- (iii) viewing an application through a rectangular viewport.
-- Of course, there are many more possibilities.
--
-- Toggling with the tab key is all very well when there are only two
-- components, but you might need to think a little harder about how to
-- navigate when there are more. Normally, you'd use your finger for that,
-- or a mouse. Sadly, I don't know how to organise mouse interaction with
-- terminal windows. But you could make a pretend mouse: a top layer which
-- displays a "mouse cursor" that you can move around with arrow keys when
-- you're in "mouse mode". Clicking could be a keystroke which activates
-- the frontmost opaque thing behind the mouse and exits mouse mode.
---------------------------------------------------------------------------
-- MAIN --
---------------------------------------------------------------------------
-- I've added
-- make go5
-- to the Makefile
-- I've set the main application to be the silly one from episode 4, but
-- you can swap in your own thing.
main : IO Thud
main = mainLoop ('*' , 0 , 0) sillyHandler
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-3-Cut where
open import Ex6-Setup
open import Ex6-1-Vec
open import Ex6-2-Box
---------------------------------------------------------------------------
-- CUTTING UP BOXES (5 marks) --
---------------------------------------------------------------------------
-- Previously...
-- ... we established what it is to be a CutKit, and we built CutKits
-- for some sorts of basic tile. Now we need to build the CutKit for
-- Box. Let's think about what that involves for a moment. We're going
-- to need a CutKit for basic tiles to stand a chance. But how do we
-- cut compound tiles?
--
-- Suppose we're writing cutLR, and we have some
-- cq : cwl + cwr == w -- the "cut widths" equation
-- telling us where we want to make the cut in something of width w.
--
-- v
-- +--------:------+
-- | : |
-- | : |
-- +--cwl---:-cwr--+
-- : ^ :
-- :.......w.......:
--
-- The tricky part is when the box we're cutting here is built with
-- leri bwl bl bwr br bq
-- where
-- bq : bwl + bwr == w -- the "box widths" equation
--
-- There are three possible situations, all of which you must detect
-- and handle.
--
-- (i) you hit the sweet spot...
--
-- v
-- +--bwl---+-bwr--+
-- | | |
-- | | |
-- +--cwl---+-cwr--+
-- : ^ :
-- :.......w.......:
--
-- ...where the box is already divided in the place where the cut
-- has to go. Happy days.
--
-- (ii) you're cutting to the left of the join...
--
-- v
-- +--bwl-----+bwr-+
-- | : | |
-- | : | |
-- +--cwl---:-cwr--+
-- : ^ :
-- :.......w.......:
--
-- ...so you'll need to cut the left box in the correct place. You
-- will need some evidence about widths to do that. And then you'll
-- the have three pieces you can see in my diagram, so to complete
-- the cut, you will need to put two of those pieces together, which
-- will take more evidence.
--
-- (iii) you're cutting to the right of the join...
--
-- v
-- +--bwl-+--bwr---+
-- | | : |
-- | | : |
-- +--cwl---:-cwr--+
-- : ^ :
-- :.......w.......:
--
-- ...so you'll need to cut the right box in the correct place, and
-- reassemble the bits.
--
-- HINT: THE FIRST THREE MARKS IN THIS EPISODE COME FROM ONE PROBLEM.
-- TREAT THEM AS A WHOLE.
---------------------------------------------------------------------------
-- COMPARING THE CUT POSITION --
---------------------------------------------------------------------------
data CutCompare (x x' y y' n : Nat) : Set where
-- Give three constructors for this type which characterize the three
-- possibilities described above whenever
-- x + x' == n and y + y' == n
-- (E.g., take n to be w, x and x' to be cwl and cwr, y and y' to be
-- bwl and bwr. But later, you'll need to do use the same tool for
-- heights.)
--
-- You will need to investigate what evidence must be packaged in each
-- situation. On the one hand, you need to be able to *generate* the
-- evidence, with cutCompare, below. On the other hand, the evidence
-- must be *useful* when you come to write boxCutKit, further below.
-- Don't expect to know what to put here from the get-go. Figure it
-- out by discovering what you *need*.
--
-- (1 mark)
-- Show that whenever you have two ways to express the same n as a sum,
-- you can always deliver the CutCompare evidence. (1 mark)
cutCompare : (x x' y y' n : Nat) -> x + x' == n -> y + y' == n ->
CutCompare x x' y y' n
cutCompare x x' y y' n xq yq = {!!}
---------------------------------------------------------------------------
-- A CUTKIT FOR BOXES --
---------------------------------------------------------------------------
-- Now, show that you can construct a CutKit for Box X, given a CutKit
-- for X. There will be key points where you get stuck for want of crucial
-- information. The purpose of CutCompare is to *describe* that
-- information. The purpose of cutCompare is to *compute* that information.
-- Note that cutLR and cutTB will work out very similarly, just exchanging
-- the roles of width and height.
-- (1 mark)
boxCutKit : {X : Nat -> Nat -> Set} -> CutKit X -> CutKit (Box X)
boxCutKit {X} ck = record { cutLR = clr ; cutTB = ctb } where
open CutKit ck
clr : (w h wl wr : Nat) ->
wl + wr == w -> Box X w h -> Box X wl h /*/ Box X wr h
clr w h wl wr wq b = {!!}
ctb : (w h ht hb : Nat) ->
ht + hb == h -> Box X w h -> Box X w ht /*/ Box X w hb
ctb w h ht hb hq b = {!!}
---------------------------------------------------------------------------
-- CROP --
---------------------------------------------------------------------------
-- Show that, given a CutKit, you can implement the "crop" operation which
-- trims a small rectangle out of an enclosing rectangle.
-- (1 mark)
crop : {X : Nat -> Nat -> Set} -> CutKit X ->
(wl wc wr ht hc hb : Nat) ->
X (wl + wc + wr) (ht + hc + hb) -> X wc hc
crop ck wl wc wr ht hc hb x = {!!}
-- For fun, practice, and the chance to test your work, try building
-- a nontrivially tiled...
testBigBox : Box (HoleOr _*C*_) 20 15
testBigBox = {!!}
-- ...so that you can see this stuff in action:
textDisplayCutKit : CutKit (Box (HoleOr _*C*_))
textDisplayCutKit = boxCutKit (holeCutKit matrixCutKit)
testWeeBox : Box (HoleOr _*C*_) 10 5
testWeeBox = crop textDisplayCutKit 5 10 5 5 5 5 testBigBox
---------------------------------------------------------------------------
-- OVERLAY --
---------------------------------------------------------------------------
-- If we use HoleOr X as the basic tile, we can think of Hole as meaning
-- a bit of a box we can see through. Correspondingly, if we have two
-- boxes (the "front" one and the "back" one), both the same size, we
-- should be able to see through the holes in the front box to whatever
-- stuff is in the back box in the corresponding place.
--
-- Your task here is to show that you can combine front and back layers
-- into a single box, corresponding to what you would actually see. That
-- is, you will need to fill the front holes in with stuff cut from the
-- back. Which is why you need a CutKit for boxes.
--
-- Hint: you may be tempted to use crop, but try without crop first.
--
-- (1 mark)
overlay : {X : Nat -> Nat -> Set} -> CutKit X ->
{w h : Nat} ->
{- front -} Box (HoleOr X) w h ->
{- back -} Box (HoleOr X) w h ->
{- combined -} Box (HoleOr X) w h
overlay {X} ck = go where
open CutKit (boxCutKit (holeCutKit ck))
go : {w h : Nat} ->
Box (HoleOr X) w h -> Box (HoleOr X) w h -> Box (HoleOr X) w h
go front back = {!!}
-- You should ensure (but I won't ask you to prove) that you have thus
-- equipped Box (HoleOr X) w h with the structure of a *monoid* with
-- the neutral value (nil-like thing) being [ Hole ] and the
-- associative operation (append-like thing) being (overlay ck), where
-- ck is your CutKit X. That is, there is such a thing as a totally
-- transparent layer, and you can overlay *any* number of layers by
-- combining any two neighbouring layers at a time.
-- For fun, and the shape of things to come, build two box tilings.
-- Make sure each has a rectangle of text in the middle and Hole all
-- around. Make sure that the rectangles overlap each other, but not
-- completely. See what happens when you overlay them, either way
-- around.
rectangleA : Box (HoleOr _*C*_) 20 15
rectangleA = {!!}
rectangleB : Box (HoleOr _*C*_) 20 15
rectangleB = {!!}
frontA_backB : 20 *C* 15
frontA_backB = renderHoleOrText (overlay matrixCutKit rectangleA rectangleB)
frontB_backA : 20 *C* 15
frontB_backA = renderHoleOrText (overlay matrixCutKit rectangleB rectangleA)
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
Ex6-4-Dis: Ex6-4-Dis.agda ANSIEscapes.hs HaskellSetup.hs Ex6-Setup.agda Ex6-1-Vec.agda Ex6-2-Box.agda Ex6-3-Cut.agda
agda --compile --ghc-flag "-lncurses" Ex6-4-Dis.agda
go4: Ex6-4-Dis
./Ex6-4-Dis
Ex6-4-Dis-Sol: Ex6-4-Dis-Sol.agda ANSIEscapes.hs HaskellSetup.hs Ex6-Setup.agda Ex6-1-Vec-Sol.agda Ex6-2-Box-Sol.agda Ex6-3-Cut-Sol.agda
agda --compile --ghc-flag "-lncurses" Ex6-4-Dis-Sol.agda
go4sol: Ex6-4-Dis-Sol
./Ex6-4-Dis-Sol
Ex6-5-App-Sol: Ex6-5-App-Sol.agda Ex6-4-Dis-Sol.agda ANSIEscapes.hs HaskellSetup.hs Ex6-Setup.agda Ex6-1-Vec-Sol.agda Ex6-2-Box-Sol.agda Ex6-3-Cut-Sol.agda Ex6-4-Dis-Sol.agda
agda --compile --ghc-flag "-lncurses" Ex6-5-App-Sol.agda
go5sol: Ex6-5-App-Sol
./Ex6-5-App-Sol
Ex6-5-App: Ex6-5-App.agda Ex6-4-Dis.agda ANSIEscapes.hs HaskellSetup.hs Ex6-Setup.agda Ex6-1-Vec.agda Ex6-2-Box.agda Ex6-3-Cut.agda Ex6-4-Dis.agda
agda --compile --ghc-flag "-lncurses" Ex6-5-App.agda
go5: Ex6-5-App
./Ex6-5-App
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-5-App-Sol where
open import Ex6-Setup
open import Ex6-1-Vec-Sol
open import Ex6-2-Box-Sol
open import Ex6-3-Cut-Sol
open import Ex6-4-Dis-Sol
mask : {X Y Z : Nat -> Nat -> Set} -> CutKit Y ->
({w h : Nat} -> X w h -> Box Y w h -> Box Z w h) ->
{w h : Nat} ->
{- front -} Box X w h ->
{- back -} Box Y w h ->
{- combined -} Box Z w h
mask {X}{Y}{Z} ck m = go where
open CutKit (boxCutKit ck)
go : {w h : Nat} -> Box X w h -> Box Y w h -> Box Z w h
go [ x ] yb = m x yb
go (leri wl xlb wr xrb wq) yb with cutLR _ _ wl wr wq yb
go (leri wl xlb wr xrb wq) yb | ylb , yrb
= leri wl (go xlb ylb) wr (go xrb yrb) wq
go (tobo ht xtb hb xbb hq) yb with cutTB _ _ ht hb hq yb
go (tobo ht xtb hb xbb hq) yb | ytb , ybb
= tobo ht (go xtb ytb) hb (go xbb ybb) hq
Update : Nat -> Nat -> Set
Update w h
= Two -- does it demand repainting?
/*/ HoleOr (Matrix ColourChar) w h -- transparent or opaque stuff?
upCutKit : CutKit Update
upCutKit = record
{ cutLR = \ { w h wl wr wq (b , x) ->
let y = cutLR w h wl wr wq x in (b , fst y) , (b , snd y) }
; cutTB = \ { w h ht hb hq (b , x) ->
let y = cutTB w h ht hb hq x in (b , fst y) , (b , snd y) }
} where open CutKit (holeCutKit matrixCutKit)
upPaint : {w h : Nat} -> Update w h -> Update w h
upPaint (_ , x) = tt , x
upMask : {w h : Nat} -> Update w h -> Box Update w h -> Box Update w h
upMask (b , [ x ]) ub = [ b , [ x ] ] -- opaque always wins
upMask (ff , Hole) ub = ub
upMask (tt , Hole) ub = mapBox upPaint ub
upLayer : {w h : Nat} -> Box Update w h -> Box Update w h -> Box Update w h
upLayer = mask upCutKit upMask
Selection : Nat -> Nat -> Set
Selection = Box \ _ _ -> Two
select : {w h : Nat} -> Selection w h -> Painting w h -> Box Update w h
select s p = mask (holeCutKit matrixCutKit) (\ b -> mapBox (_,_ b)) s p
data Skippy (X : Set) : Set where
[] : Skippy X
_::_ : X -> Skippy X -> Skippy X
_>_ : Nat -> Skippy X -> Skippy X
_>>_ : {X : Set} -> Nat -> Skippy X -> Skippy X
zero >> xs = xs
m >> (n > xs) = (m + n) > xs
m >> xs = m > xs
_+>+_ : {X : Set} -> Skippy X -> Skippy X -> Skippy X
[] +>+ ys = ys
(x :: xs) +>+ ys = x :: (xs +>+ ys)
(m > xs) +>+ ys = m >> (xs +>+ ys)
Curses : Set
Curses = Skippy (Skippy Action)
skippy : {X : Set} -> Nat -> X -> Skippy X
skippy zero x = []
skippy (suc n) x = x :: skippy n x
skjoin : {X : Set} -> Skippy (Skippy X) -> Skippy X
skjoin [] = []
skjoin (xs :: xss) = xs +>+ skjoin xss
skjoin (_ > xss) = skjoin xss
cursing : {w h : Nat} -> Update w h -> Curses
cursing {w}{h} (tt , Hole)
= skippy h (fgText black :: bgText white :: skippy w (sendText (' ' :: [])) )
cursing (tt , [ css ]) =
vecFoldR (\ cs ss ->
vecFoldR (\ { (f - c / b) s ->
fgText f :: bgText b :: sendText (c :: []) :: s })
[] cs :: ss)
[] css
cursing {w}{h} (ff , _) = h > []
{-# NO_TERMINATION_CHECK #-}
jux : Nat -> Nat -> Curses -> Curses -> Curses
jux l r [] ys = []
jux l r xs [] = []
jux l r (zero > xs) ys = jux l r xs ys
jux l r xs (zero > ys) = jux l r xs ys
jux l r (x :: xs) (y :: ys) = (x +>+ y) :: jux l r xs ys
jux l r (x :: xs) (suc n > ys) = (x +>+ (r >> [])) :: jux l r xs (n >> ys)
jux l r (suc m > xs) (y :: ys) = ((l >> []) +>+ y) :: jux l r (m >> xs) ys
jux l r (suc m > xs) (suc n > ys) with compare m n
jux l r (suc m > xs) (suc .(m + suc d) > ys) | cutLt d refl x
= suc m >> jux l r xs (suc d >> ys)
jux l r (suc m > xs) (suc .m > ys) | cutEq refl x
= suc m >> jux l r xs ys
jux l r (suc .(n + suc d) > xs) (suc n > ys) | cutGt d refl x
= suc n >> jux l r (suc d >> xs) ys
pasteCurses : PasteKit \ _ _ -> Curses
pasteCurses = record
{ leriPaste = \ wl wr -> jux wl wr
; toboPaste = \ _ _ -> _+>+_
}
_:a:_ : Action -> List Action -> List Action
goRowCol _ _ :a: (goRowCol r c :: as) = goRowCol r c :: as
goRowCol r c :a: (move down n :: as) = goRowCol (r + n) c :: as
goRowCol r c :a: (move right n :: as) = goRowCol r (c + n) :: as
move down m :a: (move down n :: as) = move down (m + n) :: as
move right m :a: (move right n :: as) = move right (m + n) :: as
sendText x :a: (sendText y :: as) = sendText (x +-+ y) :: as
a :a: as = a :: as
lineAction : Skippy Action -> List Action
lineAction [] = []
lineAction (a :: as) = a :a: lineAction as
lineAction (n > as) = move right n :a: lineAction as
curseAction : Nat -> Curses -> List Action
curseAction row [] = []
curseAction row (c :: cs) =
(goRowCol row zero :a: lineAction c) +-+
curseAction (suc row) cs
curseAction row (n > cs) = curseAction (row + n) cs
uppPaint : {w h : Nat} -> Selection w h -> Painting w h -> List Action
uppPaint s p = curseAction zero
(pasteBox pasteCurses (mapBox cursing (select s p)))
Upplication : (Nat -> Nat -> Set) -> Set
Upplication S = Application S /*/ (Key -> S []> Selection)
uppHandler : {S : Nat -> Nat -> Set} ->
Upplication S ->
Event -> AppState S -> AppState S /**/ List Action
uppHandler (app , sel) (key k) (w , h , s) = (w , h , s') ,
uppPaint (sel k s) (paintMe app s') +-+ (goRowCol (snd xy) (fst xy) :: [])
where s' = handleKey app k s ; xy = cursorMe app s'
uppHandler (app , _) (resize w' h') (w , h , s) = (w' , h' , s') , appPaint app s'
where s' = handleResize app w' h' s
-- Your code turns into a main function, as follows.
uppMain : {S : Nat -> Nat -> Set} -> Upplication S -> S 0 0 -> IO Thud
uppMain upp s = mainLoop (0 , 0 , s) (uppHandler upp)
selCutKit : CutKit \ _ _ -> Two
selCutKit = record
{ cutLR = \ _ _ _ _ _ b -> b , b
; cutTB = \ _ _ _ _ _ b -> b , b
}
cropPadSLR : (w h w' : Nat) -> Selection w h -> Selection w' h
cropPadSLR w h w' p with compare w w'
cropPadSLR w h w' p | cutLt d q _ = leri w p (suc d) [ ff ] q
cropPadSLR w h .w p | cutEq refl _ = p
cropPadSLR w h w' p | cutGt d q _
= fst (CutKit.cutLR (boxCutKit selCutKit)
w h w' (suc d) q p)
cropPadSTB : (w h h' : Nat) -> Selection w h -> Selection w h'
cropPadSTB w h h' p with compare h h'
cropPadSTB w h h' p | cutLt d q _ = tobo h p (suc d) [ ff ] q
cropPadSTB w h .h p | cutEq refl _ = p
cropPadSTB w h h' p | cutGt d q _
= fst (CutKit.cutTB (boxCutKit selCutKit)
w h h' (suc d) q p)
rectKeySel : Key -> RectState -> Sg Nat \ w -> Sg Nat \ h -> Selection w h
rectKeySel (arrow normal up) (rect gapL rectW (suc gapT) rectH)
= (gapL + 2 + rectW) , (gapT + 3 + rectH) ,
tobo gapT [ ff ] (3 + rectH) (leri gapL [ ff ] (2 + rectW) [ tt ] refl) refl
rectKeySel (arrow normal down) (rect gapL rectW gapT rectH)
= (gapL + 2 + rectW) , (gapT + 3 + rectH) ,
tobo gapT [ ff ] (3 + rectH) (leri gapL [ ff ] (2 + rectW) [ tt ] refl) refl
rectKeySel (arrow normal left) (rect (suc gapL) rectW gapT rectH)
= (gapL + 3 + rectW) , (gapT + 2 + rectH) ,
tobo gapT [ ff ] (2 + rectH) (leri gapL [ ff ] (3 + rectW) [ tt ] refl) refl
rectKeySel (arrow normal right) (rect gapL rectW gapT rectH)
= (gapL + 3 + rectW) , (gapT + 2 + rectH) ,
tobo gapT [ ff ] (2 + rectH) (leri gapL [ ff ] (3 + rectW) [ tt ] refl) refl
rectKeySel (arrow shift up) (rect gapL rectW gapT (suc rectH))
= (gapL + 2 + rectW) , ((gapT + suc rectH) + 2) ,
tobo (gapT + suc rectH) [ ff ] 2 (leri gapL [ ff ] (2 + rectW) [ tt ] refl) refl
rectKeySel (arrow shift down) (rect gapL rectW gapT rectH)
= (gapL + 2 + rectW) , ((gapT + suc rectH) + 2) ,
tobo (gapT + suc rectH) [ ff ] 2 (leri gapL [ ff ] (2 + rectW) [ tt ] refl) refl
rectKeySel (arrow shift left) (rect gapL (suc rectW) gapT rectH)
= ((gapL + suc rectW) + 2) , (gapT + 2 + rectH) ,
tobo gapT [ ff ] (2 + rectH) (leri (gapL + suc rectW) [ ff ] 2 [ tt ] refl) refl
rectKeySel (arrow shift right) (rect gapL rectW gapT rectH)
= ((gapL + suc rectW) + 2) , (gapT + 2 + rectH) ,
tobo gapT [ ff ] (2 + rectH) (leri (gapL + suc rectW) [ ff ] 2 [ tt ] refl) refl
rectKeySel _ s = 0 , 0 , [ ff ]
rectUpp : Colour -> Upplication \ _ _ -> RectState
rectUpp c = rectApp c , \ k s ->
cropPadSTB _ _ _ (cropPadSLR _ _ _ (snd (snd (rectKeySel k s))))
frontBackUpp : {S T : Nat -> Nat -> Set} ->
Upplication S ->
Upplication T ->
Upplication \ w h -> (S w h /*/ T w h) /+/ (T w h /*/ S w h)
frontBackUpp (appS , selS) (appT , selT) = frontBack appS appT ,
(\ { tab (inl (s , t)) ->
mask (holeCutKit matrixCutKit) see (paintMe appS s) (paintMe appT t)
; tab (inr (t , s)) ->
mask (holeCutKit matrixCutKit) see (paintMe appT t) (paintMe appS s)
; k (inl (s , t)) -> selS k s
; k (inr (t , s)) -> selT k t
})
where
see : {w h : Nat} -> HoleOr (Matrix ColourChar) w h ->
Painting w h -> Selection w h
see Hole y = [ ff ]
see [ x ] y = mapBox (\ { Hole -> ff ; [ _ ] -> tt }) y
try : Selection 80 25
try = cropPadSTB _ _ _ (cropPadSLR _ _ _ (snd (snd (rectKeySel (arrow normal up) (rect 10 40 3 15)))))
blah : Painting 80 25
blah = paintMe (rectApp blue) (handleKey (rectApp blue) (arrow normal up) {80}{25} ((rect 10 40 3 15)))
foo : Box (\ _ _ -> Curses) 80 25
foo = mapBox cursing (select try blah)
{- -}
main : IO Thud
main = uppMain (frontBackUpp (rectUpp blue) (rectUpp red))
(inl (rect 10 40 3 15 , rect 20 40 8 15))
{- -}
{-
data SkipVec (X : Set) : Two -> Nat -> Set where
[] : {b : Two} -> SkipVec X b zero
_::_ : {b : Two}{n : Nat} -> X -> SkipVec X tt n -> SkipVec X b (suc n)
_$>_ : (k : Nat){n : Nat} -> (xs : SkipVec X ff n) -> SkipVec X tt (suc (k + n))
plusAssoc : (a b c : Nat) -> (a + (b + c)) == ((a + b) + c)
plusAssoc zero b c = refl
plusAssoc (suc x) b c = sucResp (plusAssoc x b c)
_$$>_ : {X : Set}(k : Nat){n : Nat} -> SkipVec X tt n -> SkipVec X tt (suc (k + n))
k $$> [] = k $> []
k $$> (x :: xs) = k $> (x :: xs)
k $$> (_$>_ l {n} xs) with k + suc l + n | plusAssoc k (suc l) n
k $$> (l $> xs) | ._ | refl = (k + suc l) $> xs
_+$+_ : {X : Set}{b : Two}{m n : Nat} ->
SkipVec X b m -> SkipVec X tt n -> SkipVec X tt (m + n)
[] +$+ ys = ys
(x :: xs) +$+ ys = x :: (xs +$+ ys)
_+$+_ {n = n} (_$>_ k {m} xs) ys with ((k + m) + n) | plusAssoc k m n
(k $> xs) +$+ ys | ._ | refl = k $$> (xs +$+ ys)
skip : {X : Set}{n : Nat} -> SkipVec X tt n
skip {X}{zero} = []
skip {X}{suc n} with n + 0 | _$>_ {X} n [] | plusZeroFact n
skip {X} {suc .n} | n | r | refl = r
jux : {X : Set}{b b' : Two}{h h' m n : Nat} -> h == h' ->
SkipVec (SkipVec X tt m) b h ->
SkipVec (SkipVec X tt n) b' h' ->
SkipVec (SkipVec X tt (m + n)) tt h
jux hq [] [] = []
jux () [] (y :: ys)
jux () [] (k $> ys)
jux () (x :: xs) []
jux refl (x :: xs) (y :: ys) = (x +$+ y) :: jux refl xs ys
jux refl (x :: xs) (zero $> ys) = (x +$+ skip) :: jux refl xs ys
jux refl (x :: xs) (suc k $> ys) = (x +$+ skip) :: jux refl xs (k $> ys)
jux () (k $> xs) []
jux {m = m} refl (zero $> xs) (y :: ys)
= (skip {n = m} +$+ y) :: jux refl xs ys
jux {m = m} refl (suc k $> xs) (y :: ys)
= (skip {n = m} +$+ y) :: jux refl (k $> xs) ys
jux hq (k $> xs) (l $> ys) with compare k l
jux hq (k $> xs) (l $> ys) | cutLt d x x₁ = {!!}
jux hq (k $> xs) (.k $> ys) | cutEq refl _ = {!!}
jux hq (k $> xs) (l $> ys) | cutGt d x x₁ = {!!}
-}
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-1-Vec-Sol where
open import Ex6-Setup
---------------------------------------------------------------------------
-- VECTORS (5 marks) --
---------------------------------------------------------------------------
-- We've touched on them before, when we needed to manage the height of a
-- stack, but here are the "vectors", or "lists of known length.
data Vec (X : Set) : Nat -> Set where
[] : Vec X zero
_::_ : {n : Nat} -> X -> Vec X n -> Vec X (suc n)
infixr 6 _::_
-- This chunk of exercise 6 is about building the basic equipment to work
-- with vectors. We'll need this equipment later.
---------------------------------------------------------------------------
-- CONCATENATION AND ITS INVERSE --
---------------------------------------------------------------------------
infixr 6 _++_
-- Implement concatenation for any two vectors.
-- You will need to say how long the result will be.
-- (1 mark)
_++_ : {X : Set}{m n : Nat} -> Vec X m -> Vec X n -> Vec X (m + n)
[] ++ ys = ys
(x :: xs) ++ ys = x :: xs ++ ys
-- Now, we could write "take" and "drop", but it's more useful to
-- prove that every long vector can be given by concatenating two
-- short vectors.
data Chop {X : Set}(m : Nat){n : Nat} : Vec X (m + n) -> Set where
is++ : (xs : Vec X m)(ys : Vec X n) -> Chop m (xs ++ ys)
-- A "Chop" for a given vector consists of the evidence that it can
-- be made by concatenation. You will need to fill in the Chop length,
-- above, the same way you filled in the length for _++_.
-- Show that you can compute a Chop for any vector.
-- Hint: you will need to use "with" at some point.
-- (1 mark)
chop : {X : Set}(m : Nat){n : Nat}(xs : Vec X (m + n)) -> Chop m xs
chop zero xs = is++ [] xs
chop (suc m) (x :: xs) with chop m xs
chop (suc m) (x :: .(xs ++ ys)) | is++ xs ys = is++ (x :: xs) ys
-- Where take and drop give you vectors which you *hope* are the prefix
-- and suffix of the input. Chop gives you the pieces which are seen to
-- be the prefix and suffix of the input. Once you have chop, it's easy
-- to write take and drop in terms of it, and you can see they're right.
-- Try uncommenting and finishing the following (for fun).
take : {X : Set}(m : Nat){n : Nat}(xs : Vec X (m + n)) -> Vec X m
take m xs with chop m xs
take m .(xs ++ ys) | is++ xs ys = xs
-- EXTRA! For no marks, but some utility in future, check that you can
-- use chop to define the function which just gives you the pair of the
-- prefix and the suffix.
vchop : {X : Set}(m : Nat){n : Nat} ->
Vec X (m + n) -> Vec X m /*/ Vec X n
vchop m xs with chop m xs
vchop m .(xs ++ ys) | is++ xs ys = xs , ys
---------------------------------------------------------------------------
-- APPLICATIVE STRUCTURE --
---------------------------------------------------------------------------
-- Implement the function which makes a vector from a single element by
-- copying it the relevant number of times. Implement the "vectorized
-- application" operator which takes n functions and n arguments and gives
-- you the n results: the jth result should be given by applying the jth
-- function to the jth argument.
-- (1 mark)
vec : {n : Nat}{X : Set}(x : X) -> Vec X n
vec {zero} x = []
vec {suc n} x = x :: vec x
_<*>_ : {n : Nat}{S T : Set} -> Vec (S -> T) n -> Vec S n -> Vec T n
[] <*> [] = []
f :: fs <*> s :: ss = f s :: (fs <*> ss)
infixl 2 _<*>_
-- The applicative structure is very useful for working with vectors in
-- bulk. For example, I can take the successor of every number in a vector
-- by applying a vector of successor-functions to the vector of numbers.
mySucs : Vec Nat 5
mySucs = vec suc <*> (0 :: 1 :: 2 :: 3 :: 4 :: [])
-- should evaluate to 1 :: 2 :: 3 :: 4 :: 5 :: []
-- Now, using vec and <*> rather than explicit case analysis and recursion,
-- implement vector zipping as a one-liner, turning a pair of vectors into a
-- vector of pairs.
-- (1 mark)
zip : {n : Nat}{X Y : Set} -> Vec X n -> Vec Y n -> Vec (X /*/ Y) n
zip xs ys = vec _,_ <*> xs <*> ys
-- Play the same game as we did for concatenation, take and drop. Show
-- that every vector of pairs can be made by zipping two vectors.
-- (1 mark)
data Unzip {n : Nat}{X Y : Set} : Vec (X /*/ Y) n -> Set where
isZip : (xs : Vec X n)(ys : Vec Y n) -> Unzip (zip xs ys)
unzip : {n : Nat}{X Y : Set}(xys : Vec (X /*/ Y) n) -> Unzip xys
unzip [] = isZip [] []
unzip ((x , y) :: xys) with unzip xys
unzip ((x , y) :: .(zip xs ys)) | isZip xs ys = isZip (x :: xs) (y :: ys)
-- EXTRA! For no marks, but some utility in future, check that you can
-- use unzip to define the function which just gives you the pair of the
-- two vectors.
vunzip : {X Y : Set}{n : Nat} -> Vec (X /*/ Y) n -> Vec X n /*/ Vec Y n
vunzip xys with unzip xys
vunzip .(vec _,_ <*> xs <*> ys) | isZip xs ys = xs , ys
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module Ex6-2-Box where
open import Ex6-Setup
open import Ex6-1-Vec
---------------------------------------------------------------------------
-- BOXES (5 marks) --
---------------------------------------------------------------------------
-- Boxes are sized rectangular tilings which fit together precisely.
-- They allow us to talk about the use of 2D space, e.g., on a screen.
data Box (X : Nat -> Nat -> Set)(w h : Nat) : Set where
-- ^basic-tile width^ ^height
[_] : X w h -> Box X w h
-- a basic tile is a tiling
leri : (wl : Nat) (bl : Box X wl h)
(wr : Nat) (br : Box X wr h)
-> wl + wr == w -> Box X w h
-- combine "left" and "right" tilings the same height
-- to make a tiling with their total width
tobo : (ht : Nat) (bt : Box X w ht)
(hb : Nat) (bb : Box X w hb)
-> ht + hb == h -> Box X w h
-- combine "top" and "bottom" tilings the same width
-- to make a tiling with their total height
---------------------------------------------------------------------------
-- MONADIC STRUCTURE --
---------------------------------------------------------------------------
-- If X and Y are both kinds of "sized stuff", we can say what it is to be
-- a "size-preserving function" between them.
_[]>_ : (X Y : Nat -> Nat -> Set) -> Set
X []> Y = {w h : Nat} -> X w h -> Y w h
-- A size preserving function turns an X of some size
-- into a Y the same size.
-- Think of X as "sized placeholders". If we have a way to turn each
-- placeholder into a tiling which fits into the place, we should be
-- able to deploy it across a whole tiling of placeholders. Check
-- that you can achieve that.
_=<<_ : forall {X Y} -> X []> Box Y -> Box X []> Box Y
f =<< b = {!!}
-- Using _=<<_, rather than more recursion, define...
mapBox : forall {X Y} -> X []> Y -> Box X []> Box Y
mapBox = {!!}
-- roll out a size-preserving function on basic tiles to a whole tiling
joinBox : forall {X} -> Box (Box X) []> Box X
joinBox = {!!}
-- turn a tiling-of-tilings into a simple tiling
-- (1 mark) for the lot
---------------------------------------------------------------------------
-- PASTE KITS AND MATRICES --
---------------------------------------------------------------------------
-- A "paste kit" for sized stuff is whatever you need to combine stuff
-- left-to-right and top-to-bottom
record PasteKit (X : Nat -> Nat -> Set) : Set where
field
leriPaste : (wl wr : Nat){h : Nat} -> X wl h -> X wr h -> X (wl + wr) h
toboPaste : {w : Nat}(ht hb : Nat) -> X w ht -> X w hb -> X w (ht + hb)
-- Show that a PasteKit is just what you need to turn a tiling of
-- stuff into some stuff. (1 mark)
pasteBox : {X : Nat -> Nat -> Set} -> PasteKit X -> Box X []> X
pasteBox {X} pk = go where
open PasteKit pk -- brings leriPaste and toboPaste into scope
go : Box X []> X
go b = {!!}
-- If you were wondering what any of this had to do with part 1, here we
-- go...
Matrix : Set -> Nat -> Nat -> Set
Matrix C w h = Vec (Vec C w) h
-- matrices are "sized stuff", represented as a vector the right height
-- of rows which are vectors the right width of some sort of unit "cell".
-- Using the equipment you built in part 1, give matrices their PasteKit.
-- (1 mark)
matrixPasteKit : {C : Set} -> PasteKit (Matrix C)
matrixPasteKit = {!!}
---------------------------------------------------------------------------
-- INTERLUDE: TESTING WITH TEXT --
---------------------------------------------------------------------------
-- Turn a list into a vector, either by truncating or padding with
-- a given dummy element.
paddy : {X : Set} -> X -> List X -> {n : Nat} -> Vec X n
paddy _ _ {zero} = []
paddy x [] {suc n} = x :: paddy x [] {n}
paddy x (y :: ys) {suc n} = y :: paddy x ys {n}
-- Use that to make vectors of characters from strings, padding with space.
[-_-] : String -> {n : Nat} -> Vec Char n
[- s -] = paddy ' ' (primStringToList s)
-- Now we can have character matrices of a given size
_*C*_ : Nat -> Nat -> Set
w *C* h = Matrix Char w h
-- Here are some.
mat43-1 : 4 *C* 3
mat43-1 = [- "post" -] :: [- "cake" -] :: [- "flop" -] :: []
mat43-2 : 4 *C* 3
mat43-2 = [- "horn" -] :: [- "walk" -] :: [- "ping" -] :: []
mat22 : 2 *C* 2
mat22 = [- "go" -] :: [- "do" -] :: []
mat62 : 6 *C* 2
mat62 = [- "getter" -] :: [- "gooder" -] :: []
-- Put them together as a tiling.
myTiling : Box _*C*_ 8 5
myTiling = tobo 3 (leri 4 [ mat43-1 ] 4 [ mat43-2 ] refl)
2 (leri 2 [ mat22 ] 6 [ mat62 ] refl) refl
-- Paste all the pieces and see what you get!
myText : 8 *C* 5
myText = pasteBox matrixPasteKit myTiling
---------------------------------------------------------------------------
-- CUT KITS, MATRICES --
---------------------------------------------------------------------------
-- A "cut kit" for sized stuff is whatever you need to cut stuff into
-- smaller pieces: left-and-right pieces, or top-and-bottom pieces.
record CutKit (X : Nat -> Nat -> Set) : Set where
field
cutLR : (w h wl wr : Nat) -> wl + wr == w ->
X w h -> X wl h /*/ X wr h
cutTB : (w h ht hb : Nat) -> ht + hb == h ->
X w h -> X w ht /*/ X w hb
-- Equip matrices with their CutKit. (1 mark)
matrixCutKit : {C : Set} -> CutKit (Matrix C)
matrixCutKit {C} = {!!}
---------------------------------------------------------------------------
-- HOLES --
---------------------------------------------------------------------------
-- We might want to make sure that, whatever other basic tiles are in play,
-- we can have tiles which are "missing", as if we had cut rectangular
-- holes in a piece of paper.
data HoleOr (X : Nat -> Nat -> Set)(w h : Nat) : Set where
Hole : HoleOr X w h
[_] : X w h -> HoleOr X w h
-- A HoleOr X is (you guessed it) either a hole or an X.
-- Show that if X has a CutKit, so has HoleOr X. What do you get when you
-- cut up a hole? (1 mark)
holeCutKit : {X : Nat -> Nat -> Set} -> CutKit X -> CutKit (HoleOr X)
holeCutKit {X} ck = {!!}
---------------------------------------------------------------------------
-- A BIT OF FUN --
---------------------------------------------------------------------------
-- Show that you can turn holes into spaces.
holeSpace : HoleOr _*C*_ []> _*C*_
holeSpace Hole = vec (vec ' ')
holeSpace [ x ] = x
-- Show how to render a tiling made of text or holes as text.
renderHoleOrText : Box (HoleOr _*C*_) []> _*C*_
renderHoleOrText = pasteBox matrixPasteKit o mapBox holeSpace
-- Make a test example and see!
myTest : {!!} *C* {!!}
myTest = renderHoleOrText {!!}
---------------------------------------------------------------------------
-- NEXT TIME... --
---------------------------------------------------------------------------
-- Have a wee think about what you might need to equip Box X with a CutKit.
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
module HaskellSetup where
{- This is the low-level stuff that hooks into the ncurses library, together
with the Haskell versions of the Agda types. You should not need to bother
reading or modifying this file. -}
import Debug.Trace
import Foreign
import Foreign.C (CInt(..))
import ANSIEscapes
import System.IO
import System.Environment
import Control.Applicative
import Control.Concurrent
foreign import ccall
initscr :: IO ()
foreign import ccall "endwin"
endwin :: IO CInt
foreign import ccall "refresh"
refresh :: IO CInt
foreign import ccall "&LINES"
linesPtr :: Ptr CInt
foreign import ccall "&COLS"
colsPtr :: Ptr CInt
scrSize :: IO (Int, Int)
scrSize = do
lnes <- peek linesPtr
cols <- peek colsPtr
return (fromIntegral cols, fromIntegral lnes)
data Modifier = Normal | Shift | Control deriving Show
data Key = Char Char | Arrow Modifier Direction | Enter | Backspace | Delete | Escape | Tab deriving Show
data Event = Key Key | Resize Nat Nat
data Nat = Zero | Suc Nat
toNat :: Int -> Nat
toNat 0 = Zero
toNat n = Suc (toNat (n - 1))
fromNat :: Nat -> Int
fromNat Zero = 0
fromNat (Suc n) = 1 + fromNat n
data Colour
= Black | Red | Green | Yellow
| Blue | Magenta | Cyan | White
data Action
= GoRowCol Nat Nat
| SendText [Char]
| Move Direction Nat
| FgText Colour
| BgText Colour
act :: Action -> IO ()
act (GoRowCol y x) = do
resetCursor
forward (fromNat x)
down (fromNat y)
act (SendText s) = putStr s
act (Move d n) = moveCursor d (fromNat n)
act (FgText Black) = escape "0;30m"
act (FgText Red) = escape "1;31m"
act (FgText Green) = escape "1;32m"
act (FgText Yellow) = escape "1;33m"
act (FgText Blue) = escape "1;34m"
act (FgText Magenta) = escape "1;35m"
act (FgText Cyan) = escape "1;36m"
act (FgText White) = escape "1;37m"
act (BgText Black) = escape "40m"
act (BgText Red) = escape "41m"
act (BgText Green) = escape "42m"
act (BgText Yellow) = escape "43m"
act (BgText Blue) = escape "44m"
act (BgText Magenta) = escape "45m"
act (BgText Cyan) = escape "46m"
act (BgText White) = escape "47m"
getEscapeKey :: [(String, Key)] -> IO (Maybe Key)
getEscapeKey [] = return Nothing
getEscapeKey sks = case lookup "" sks of
Just k -> return (Just k)
_ -> do
c <- getChar
getEscapeKey [(cs, k) | (d : cs, k) <- sks, d == c]
directions :: [(Char, Direction)]
directions = [('A', DU), ('B', DD),
('C', DR), ('D', DL)]
escapeKeys :: [(String, Key)]
escapeKeys =
[([c], Arrow Normal d) | (c, d) <- directions] ++
[("1;2" ++ [c], Arrow Shift d) | (c, d) <- directions] ++
[("1;5" ++ [c], Arrow Control d) | (c, d) <- directions] ++
[("3~", Delete)]
keyReady :: IO (Maybe Key)
keyReady = do
b <- hReady stdin
if not b then return Nothing else do
c <- getChar
case c of
'\n' -> return $ Just Enter
'\r' -> return $ Just Enter
'\b' -> return $ Just Backspace
'\DEL' -> return $ Just Backspace
'\t' -> return $ Just Tab
_ | c >= ' ' -> return $ Just (Char c)
'\ESC' -> do
b <- hReady stdin
if not b then return $ Just Escape else do
c <- getChar
case c of
'[' -> getEscapeKey escapeKeys
_ -> return $ Just Escape
_ -> return $ Nothing
pni :: (Int, Int) -> (Nat, Nat)
pni (y, x) = (toNat y, toNat x)
mainLoop ::
s -> (Event -> s -> (s, [Action])) ->
IO ()
mainLoop start reactor = do
hSetBuffering stdout NoBuffering
hSetBuffering stdin NoBuffering
initscr
innerLoop (0, 0) start
endwin
return ()
where
innerLoop oldSize state0 = do
refresh
size@(w, h) <- scrSize
let (state1, acts) = if size /= oldSize
then reactor (Resize (toNat w) (toNat h)) state0
else (state0, [])
mapM_ act acts
mc <- keyReady
case mc of
Nothing -> threadDelay 100 >> innerLoop size state1
Just k -> do
let (state2, acts) = reactor (Key k) state1
mapM_ act acts
innerLoop size state2
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
# Exercise 6
I thought I should provide an overview of both the content and the
procedure. But first, strategic thinkers will need to know the
**deadline**, which was 23:59.59 on Monday 25 May 2015. **DEADLINE
EXTENSION:** you now have until 5pm on Wednesday 27 May 2015. That is,
I am giving you as much time as I can, still leaving enough of a
window to mark your stuff (not in your presence, this time) before the
deadline which will be imposed on me to return your scores to the exam
board. (That deadline turned out to be later than I had anticipated,
so I'm passing the benefit on to you.) You're playing for the last 25
of the 100 available marks.
**Request.** If you think you're done with exercise 6 before the
deadline, please let me know. It will significantly reduce my stress
levels if I can mark as much of your work as early as possible. Note
that I will still accept revised submissions up to the deadline (and
git will let me know that I need to look again). I'm afraid I can't
release scores early, but you'll more or less be able to tell what
your solutions are worth, anyway.
## What's it about?
The incremental release of this exercise rather obscures the big
picture, so let me try to sketch it. What you're writing is a simple
window manager, with overlapping windows. It'll be text-based and run
inside a shell window, just like the editor in exercise 5. At the end
of the day, you should have two windows with different stuff happening
in them: you should be able to switch focus between them, move them
and resize them.
## How does that break down?
It's a five episode story, hopefully not with cliffhangers.
1. **Vectors** where you learn the basics of working with lists whose
size is policed by types. We'll be using vectors of vectors
(matrices) to manage rectangular blocks of text.
2. **Boxes** where you learn to work with rectangular tilings built up
from basic components by putting things the same height side by
side or arranging two things the same width vertically.
3. **Cutting** where you learn to cut tilings as required, and to
overlay one tiling in front of another, seeing stuff at the back
through the holes in the front: the key technology for overlapping
windows.
4. **Display** where you learn to construct tilings of display
updates, and to send them to the screen. Of course, updates which
happen out of view should result in no action. Here, we'll start to
compile executables built from the pieces and control content from
the keyboard.
5. **Applications** where you learn to build interactive systems which
get keystrokes and give updates, then hang them in a framework
which supports *two* of them in separate windows, cooperatively.
Edit: we're ahead of the game; episode 4 already has two windows!
## Mac Users
Don't use a regular terminal for this, as shift-up and shift-down
aren't handled properly. Give [iterm2](http://iterm2.com/) a go
instead. I'm grateful to Dan Piponi for this valuable clue.
## Support
We have two lecture slots booked for Tuesdays at 2pm in LT209. We
should probably use both for orientation: week 11 for episodes 1 to 3;
week 12 for episodes 4 and 5.
If you are in need of clarification about the intended meaning of
things I've written, please use the myplace forum: others probably
need the same help. If you have questions about *your code*, please
contact me privately.
I am willing to offer lab help if a bunch of you think that would be
useful, or one-on-one advice by appointment. Don't stay unproductively
stuck. I won't be out of town much, but I mightn't be in my office
much, so showing up at LT1317 unexpected is not the best strategy (but
I won't object if you try your luck). My currently scheduled
disappearances are as follows: 7 May is election day, when I vote (you
should, too) then sleep until polls close and it's time to spend all
night throwing things at the telly; 8 May is the day after election
day, when it will probably hurt; 12 May sees a meeting in Dundee about
Type Inference.
Support each other. Learn together; code separately. By all means talk
about the difficulties you get into, the better to gain understanding,
but make sure your code comes from your understanding, not from
somebody else's code.
| {
"repo_name": "pigworker/CS410-14",
"stars": "64",
"repo_language": "Agda",
"file_name": "README.md",
"mime_type": "text/plain"
} |
# Contribution
Your contribution is warmly welcome!
If you see something incorrect, please use an issue or contact with me directly.
If you want add or improve something - just make a fork & PR, fell free. Work on develop branch.
---
# Contribution Guidelines
Please note that this project is released with a
[Contributor Code of Conduct](code-of-conduct.md). By participating in this
project you agree to abide by its terms.
---
Ensure your pull request adheres to the following guidelines:
- Make sure you take care of this
- And this as well
- And don't forget to check this
Thank you for your suggestions!
## Updating your PR
A lot of times, making a PR adhere to the standards above can be difficult.
If the maintainers notice anything that we'd like changed, we'll ask you to
edit your PR before we merge it. There's no need to open a new PR, just edit
the existing one. If you're not sure how to do that,
[here is a guide](https://github.com/RichardLitt/knowledge/blob/master/github/amending-a-commit-guide.md)
on the different ways you can update your PR so that we can merge it.
## TODO:
:white_check_mark: Good to see - languages versions.
:white_check_mark: More awesome resources.
:white_check_mark: Sort alphabetically (ie. relevant sources in a specific sections)
## Translations
For translations please make other branch for your changes & before PR (ie. for Spain will be: es_ES etc).
See here (example): [awesome-astronomy](https://github.com/mbiesiad/awesome-astronomy) and here: [awesome-astronomy-pl_PL](https://github.com/mbiesiad/awesome-astronomy/tree/pl_PL)
If you want, you can also add 'Translated by:' (ie. @JohnSmith) with link to your GitHub account or Twitter handle. Thank you!
| {
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"stars": "84",
"repo_language": "None",
"file_name": "readme.md",
"mime_type": "text/plain"
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# Contributor Covenant Code of Conduct
## Our Pledge
In the interest of fostering an open and welcoming environment, we as
contributors and maintainers pledge to making participation in our project and
our community a harassment-free experience for everyone, regardless of age, body
size, disability, ethnicity, gender identity and expression, level of experience,
nationality, personal appearance, race, religion, or sexual identity and
orientation.
## Our Standards
Examples of behavior that contributes to creating a positive environment
include:
* Using welcoming and inclusive language
* Being respectful of differing viewpoints and experiences
* Gracefully accepting constructive criticism
* Focusing on what is best for the community
* Showing empathy towards other community members
Examples of unacceptable behavior by participants include:
* The use of sexualized language or imagery and unwelcome sexual attention or
advances
* Trolling, insulting/derogatory comments, and personal or political attacks
* Public or private harassment
* Publishing others' private information, such as a physical or electronic
address, without explicit permission
* Other conduct which could reasonably be considered inappropriate in a
professional setting
## Our Responsibilities
Project maintainers are responsible for clarifying the standards of acceptable
behavior and are expected to take appropriate and fair corrective action in
response to any instances of unacceptable behavior.
Project maintainers have the right and responsibility to remove, edit, or
reject comments, commits, code, wiki edits, issues, and other contributions
that are not aligned to this Code of Conduct, or to ban temporarily or
permanently any contributor for other behaviors that they deem inappropriate,
threatening, offensive, or harmful.
## Scope
This Code of Conduct applies both within project spaces and in public spaces
when an individual is representing the project or its community. Examples of
representing a project or community include using an official project e-mail
address, posting via an official social media account, or acting as an appointed
representative at an online or offline event. Representation of a project may be
further defined and clarified by project maintainers.
## Enforcement
Instances of abusive, harassing, or otherwise unacceptable behavior may be
reported by contacting the project team at mbopensource+awesome(at)gmail(dot)com. All
complaints will be reviewed and investigated and will result in a response that
is deemed necessary and appropriate to the circumstances. The project team is
obligated to maintain confidentiality with regard to the reporter of an incident.
Further details of specific enforcement policies may be posted separately.
Project maintainers who do not follow or enforce the Code of Conduct in good
faith may face temporary or permanent repercussions as determined by other
members of the project's leadership.
## Attribution
This Code of Conduct is adapted from the [Contributor Covenant][homepage], version 1.4,
available at [http://contributor-covenant.org/version/1/4][version]
[homepage]: http://contributor-covenant.org
[version]: http://contributor-covenant.org/version/1/4/
| {
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"stars": "84",
"repo_language": "None",
"file_name": "readme.md",
"mime_type": "text/plain"
} |
# Awesome Translations [](https://awesome.re)
> The transfer of the meaning of a text from one language to another.
This list contains tools, books, articles, blogs, courses and everything related to translations ([t9n](https://en.wikipedia.org/wiki/Translation) - translation, [l10n](https://en.wikipedia.org/wiki/Language_localisation) - localization, [g11n](https://en.wikipedia.org/wiki/Language_localisation#Globalisation_versus_localisation) - globalization, [m17n](https://www.definify.com/word/multilingualization#:~:text=Noun,into%2C%20or%20for%20multiple%20languages) - multilingualization, [i18n](https://en.wikipedia.org/wiki/Language_localisation#Globalisation_versus_localisation) - internationalization, synonymous with globalization).
## Contents
- [Translations](#translations)
- [Platforms](#platforms)
- [Apps](#apps)
- [Tools](#tools)
- [Articles](#articles)
- [Blogs](#blogs)
- [Online Courses](#online-courses)
- [Books](#books)
- [Other](#other)
## Translations
- [English](https://github.com/mbiesiad/awesome-translations)
- [Polish](https://github.com/mbiesiad/awesome-translations/tree/pl_PL)
- [Spanish](https://web.archive.org/web/20220511155347/https://github.com/JoseDeFreitas/awesome-translations/tree/es_ES)
- [Italian](https://github.com/niedev/awesome-translations/tree/it_IT)
## Platforms
### Localization and translation platforms
- [Crowdin](https://crowdin.com/) - Closed source cloud-based localization technology and services company.
- [LocaleApp](https://www.localeapp.com/) - Effective app localization and translation.
- [Transifex](https://www.transifex.com/) - Proprietary, web-based translation platform, globalization management system (GMS).
- [Weblate](https://weblate.org/) - Copylefted libre web-based continuous translation platform.
- [SimpleLocalize](https://simplelocalize.io) - A simple translation management for software projects.
- [Tolgee](https://tolgee.io) - Open-source, developer & translator friendly platform enabling users to translate directly in the app they develop.
- [Lokalise](https://lokalise.com/) - Translation platform for developers.
- [Locize](https://locize.com/) - Proprietary translation platform.
### Project management
- [Zanata](http://zanata.org/) - Web-based translation platform for translators, content creators and developers to manage localisation projects.
- [Traduora](https://github.com/traduora/traduora) - A platform for manage translation workflow in teams.
### Platform-specific tools
- [GitLocalize](https://gitlocalize.com/) - Powerful localization platform that syncs with your GitHub repository and lets you continuously translate its content.
- [Respresso](https://respresso.io/) - Collaborative online resource manager for localizations, images, colors, etc. that generates platform-specific files and delivers them directly to your source code.
- [PO file editor](https://pofile.net/free-po-editor) - A free tool for translating PO files for localization with Gettext.
## Apps
### Automated translation
- [RTranslator](https://github.com/niedev/RTranslator) - A simultaneous translator app for Android based on Google's API.
- [Crow Translate](https://github.com/crow-translate/crow-translate) - A simple and lightweight translator for Linux and Windows that allows to translate and speak text using Google, Yandex and Bing translate API.
- [Copy Translator](https://github.com/CopyTranslator/CopyTranslator) - An app for Windows, Mac and Linux that automatically translate and adapt a text when copied in the clipboard.
- [LibreTranslate](https://github.com/uav4geo/LibreTranslate) - 100% Self-Hosted web app to translate text, based on Argos Translate.
### Translation software
- [OmegaT](https://omegat.org/) - Free translation memory application that works on Windows, macOS and Linux.
- [Argos Translate](https://github.com/argosopentech/argos-translate) - Completely open source offline translation app written in Python and based on OpenNMT. It can also be used as a Python library.
## Tools
### Automatic translation for end users
- [Bergamot](https://github.com/browsermt) - Client-side translation in the browser.
- [Crowdin MT](https://store.crowdin.com/crowdin-mt) - A machine learning translator based on translations from Crowdin Global translation memory.
### Translator libraries for developers
- [deep-translator](https://github.com/nidhaloff/deep-translator) - A flexible free and unlimited (depending on the translator used) library written in Python to translate between different languages in a simple way using multiple translators, it can also be used directly in the prompt.
- [Translator](https://github.com/UlionTse/translators) - A translator library based on the translation interface of Google, Yandex, Microsoft (Bing), Baidu, Alibaba, Tencent, NetEase (Youdao), Sogou, Deepl, etc.
### i18n frameworks for developers
- [I18next](https://www.i18next.com/) - Internationalization-framework written in and for JavaScript.
- [react-i18next](https://react.i18next.com/) - Powerful internationalization framework for React / React Native which is based on i18next.
- [MDN i18n](https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/API/i18n) - Functions to internationalize your browser extension. You can use these APIs to get localized strings from locale files packaged with your extension.
- [Ruby I18n](https://guides.rubyonrails.org/i18n.html) - Rails internationalization (i18n) API.
- [Quasar I18n](https://quasar.dev/options/app-internationalization) - App internationalization (i18n) in Quasar framework.
- [Vue I18n](https://kazupon.github.io/vue-i18n/) - Internationalization plugin for Vue.js.
- [i18n Ally](https://github.com/antfu/i18n-ally) - Extension for VSCode, all in one about i18n.
- [Translate](https://github.com/translate/translate) - A set of software and documentation designed to help make the lives of localizers both more productive and less frustrating.
- [Python-i18n](https://pypi.org/project/python-i18n/) - Python internationalization (i18n) package.
- [Jsproxy for Crowdin](https://store.crowdin.com/products/crowdin-proxy-translator) - Add-on to Crowdin.
- [Moment.js](https://momentjs.com/) - Parse, validate, manipulate and display dates and times in JavaScript.
- [WPML](https://wpml.org/) - A WordPress plugin that allows running multilingual websites with a single WordPress install.
- [FormatJS](https://formatjs.io/) - A modular collection of JavaScript libraries for internationalization that are focused on formatting numbers, dates, and strings for displaying to people.
- [Polyglot](https://github.com/untra/polyglot) - A fast, painless, open-source internationalization plugin for Jekyll blogs.
### Machine translation for developers
- [SwiftGoogleTranslate](https://github.com/maximbilan/SwiftGoogleTranslate) - A framework to use cloud translation API by Google in Swift.
- [attranslate](https://github.com/fkirc/attranslate) - A tool for semi-automated translations of cross-platform apps or websites.
### Other tools
- [npm i18n](https://www.npmjs.com/package/i18n) - Lightweight simple translation module with dynamic json storage.
- [Pootle](https://github.com/translate/pootle) - An online translation management tool with a translation interface focused on localization of applications' graphical user interfaces. It is used by LibreOffice.
- [Globalize](https://github.com/globalizejs/globalize) - A JavaScript library for internationalization and localization that leverage the official Unicode CLDR JSON data.
- [SimpleLocalize CLI](https://github.com/simplelocalize/simplelocalize-cli) - A CLI for finding translation keys in project files.
## Articles
### Introductions to internationalization
- [Stack Overflow Q&A-1](https://stackoverflow.com/questions/506743/localization-and-internationalization-whats-the-difference) - Localization and internationalization, what's the difference?
- [Stack Overflow Q&A-2](https://stackoverflow.com/questions/754520/what-is-the-actual-differences-between-i18n-l10n-g11n-and-specifically-what-does) - What is the actual differences between i18n/l10n/g11n and specifically what does each mean for development?
- [W3C](https://www.w3.org/International/questions/qa-i18n) - Localization vs. internationalization.
- [Internationalization vs. Localization: The Difference Between l10n and I18n](https://blog.crowdin.com/2022/07/14/internationalization-vs-localization) - Blog post about the difference between l10n and I18n from Crowdin.
### For developers
- [Angular and i18n](https://angular.io/guide/i18n) - Angular i18n guide.
- [Debian manuals](https://www.debian.org/doc/manuals/debian-reference/ch08.en.html) - Chapter 8: i18n and l10n.
- [Developer Chrome i18n](https://developer.chrome.com/webstore/i18n) - Internationalizing your app.
- [Software Globalization, Berkeley.edu - slides](https://lx.berkeley.edu/sites/default/files/berkeleylinguisticsdeptg11ncldr.pdf) - "Software globalization and adding languages on computers and mobile devices" by Craig Cummings (slides).
- [Flutter i18n](https://flutter.dev/docs/development/accessibility-and-localization/internationalization) - Internationalizing Flutter apps.
- [What is 'hreflang'?](https://simplelocalize.io/blog/posts/what-is-hreflang/) - What is `hreflang` attribute and how it can affect your SERP.
- [Globalization and localization in ASP.NET Core](https://learn.microsoft.com/en-us/aspnet/core/fundamentals/localization?view=aspnetcore-6.0) - Article about Globalization and localization in ASP.NET Core.
### Understanding computer-assisted translation
- [Computer-assisted translation](https://en.wikipedia.org/wiki/Computer-assisted_translation) - CAT (computer-aided translation) tools are typically understood to mean programs that specifically facilitate the actual translation process. This article describe: translation memory software, language search-engine software, terminology management software, alignment software, interactive machine translation, augmented translation.
### Machine translation
- [Approaches to Machine Translation](http://engineering.fuoye.edu.ng/journal/index.php/engineer/article/view/26/pdf) - A paper-review on different techniques for machine translation.
- [Neural Machine Translation](https://jair.org/index.php/jair/article/view/12007/26611) - A paper-review that trace back the origins of modern NMT architectures to word and sentence embeddings and earlier examples of the encoder-decoder network family. It will conclude with a short survey of more recent trends in the field.
## Blogs
- [Speakt](https://speakt.com/blog/) - Well-rounded resource, offering in-depth information from the best professionals in the industry on everything related to translation.
- [Lexico](https://www.lexico.com/) - Provides a collection of dictionaries of English and Spanish, and curiosities about many words and languages (in the "Explore" section). It is produced by Oxford University Press.
- [The Translator's Teacup](https://lingocode.com/translation-blog/) - Contains good tips for beginner translators.
- [Speaking of Translation](https://speakingoftranslation.com/) - Run by two outstanding experts in the field of translation and localization. You can listen to audio files covering their tips and opinions on the freelance translator's work.
- [eMpTy Pages](http://kv-emptypages.blogspot.com/) - Presents extremely detailed descriptions and opinions about localization management, collaborative translation platforms, translation management systems, machine translation, as well as the localization industry's biggest players.
## Online Courses
- [UWashingtonX's I18n and l10n](https://www.edx.org/professional-certificate/uwashingtonx-internationalization-and-localization) - A collection of 3 courses of internationalization and internationalization for digital products provided by the University of Washington.
- [Basic English Grammar and punctuation](https://www.coursera.org/learn/grammar-punctuation) - English grammar course for beginners provided by the University of California.
- [Intermediate English Grammar and punctuation](https://www.coursera.org/specializations/intermediate-grammar) - English grammar course for people with experience provided by the University of California.
- [Advanced English Grammar and punctuation](https://www.coursera.org/specializations/advanced-grammar-punctuation#courses) - English grammar course for experts provided by the University of California.
- [Natural Language Processing](https://www.coursera.org/specializations/natural-language-processing) - Teaches how to use machine learning to understand and manipulate human language. It requires a working knowledge of machine learning, intermediate Python experience including DL frameworks & proficiency in calculus, linear algebra, & statistics.
- [Machine Translation](https://www.coursera.org/learn/machinetranslation) - Explains the basic principles of translation algoritms. It is provided by the Karlsruhe Institute of Technology (Germany).
## Books
- [Statistical Machine Translation](https://www.cambridge.org/core/books/statistical-machine-translation/94EADF9F680558E13BE759997553CDE5#fndtn-information) - Establishes background in NLP and statistics, then develops the basics through to current research. By the end readers can build their own translation systems. The author is [Philipp Koehn](https://en.wikipedia.org/wiki/Philipp_Koehn).
- [Neural Machine Translation](https://www.cambridge.org/core/books/neural-machine-translation/7AAA628F88ADD64124EA008C425C0197#fndtn-information) - This introduction to machine translation starts from the basics of neural network methods and reaches the state of the art, while giving historical, linguistic, and applied context. Code examples in Python give a hands-on blueprint for implementation. The author is still Philipp Koehn.
- [Translation: An advanced resource book for students](https://www.amazon.com/Translation-advanced-resource-Routledge-Linguistics-ebook/dp/B07NPV8DSC/ref=cm_cr_arp_d_product_top?ie=UTF8) - Introduces the theory and practice of translation from a variety of linguistic and cultural angles. The authors are [Basil Hatim](https://scholar.google.com/citations?user=IVydQ-4AAAAJ&hl=en) and [Jeremy Munday](https://ahc.leeds.ac.uk/languages/staff/1006/professor-jeremy-munday).
## Other
- [Google Crowdsource](https://crowdsource.google.com/) - Crowdsourcing platform developed by Google intended to improve a host of Google services through the user-facing training of different algorithms (with translation and translation validation section).
- [Localizejs](https://localizejs.com/) - Translations for websites and applications to new languages and streamline translation workflow.
- [LocalizationLab](https://www.localizationlab.org/) - Global community of 7000+ contributors who support the translation and localization of Internet freedom tools.
- [Pontoon](https://pontoon.mozilla.org/) - Various Mozilla localization projects.
- [Watson Language Translator](https://www.ibm.com/cloud/watson-language-translator) - A service on the IBM Cloud that enables dynamically translation news, patents, or conversational documents.
- [Project Fluent](https://projectfluent.org) - A localization paradigm designed to unleash the entire expressive power of natural language translations.
- [ICU - International Components for Unicode](https://icu.unicode.org/) - A mature, widely used set of C/C++ and Java libraries providing Unicode and Globalization support for software applications.
- [Django docs - i18n](https://docs.djangoproject.com/en/4.1/topics/i18n/) - Part of the Django docs, focused on internationalization and localization.
- [Glocalization Strategy Playbook](https://github.com/GILT-Forum/Globalization-Strategy-Playbook) - A Guide for Localization and Globalization Professionals by the GILT forum.
- [DeepL Translator](https://www.deepl.com/) - A neural machine translation service launched in August 2017 and owned by Cologne based DeepL SE.
- [Amazon Translate](https://aws.amazon.com/translate/) - A neural machine translation service that delivers fast, high-quality, affordable, and customizable language translation.
- [ModernMT](https://www.modernmt.com/) - A self-learning machine translation service that improves from user corrections as user keep using it.
- [AutoML Translation Documentation](https://cloud.google.com/translate/automl/docs) - A documentation of AutoML Translation from Google.
- [Microsoft Translator](https://translator.microsoft.com/) - A multilingual machine translation cloud service provided by Microsoft.
## Contributing
Warmly welcome! Kindly go through [Contribution Guidelines](CONTRIBUTING.md) and [Code of Conduct](CODE-OF-CONDUCT.md) first.
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Please be sure about file' license or don't forget to add source info. Thanks.
| {
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# hackercon
A list of free software and IT security related conferences.
| Name | Location | Start | End |
| --- | --- | --- | --- |
| [linux.conf.au](https://lca2018.org/#/home) | Sydney, Australia | 2018-01-22 | 2018-01-26 |
| [FOSDEM](https://fosdem.org/2018/) | Brussels, Belgium | 2018-02-03 | 2018-02-04 |
| [OffensiveCon](https://www.offensivecon.org/) | Berlin, Germany | 2018-02-12 | 2018-02-17 |
| [Troopers](https://www.troopers.de/) | Heidelberg, Germany | 2018-03-14 | 2018-03-15 |
| [dknog](https://dknog.dk/) | Copenhagen, Denmark | 2018-03-08 | 2018-03-09 |
| [Chemnitzer Linux-Tage](https://chemnitzer.linux-tage.de/2018/en) | Chemnitz, Germany | 2018-03-10 | 2018-03-11 |
| [Black Hat Asia](https://www.blackhat.com/) | Singapore, Singapore | 2018-03-22 | 2018-03-23 |
| [foss-north](http://foss-north.se/) | Gothenbug, Sweden | 2018-04-23 | 2018-04-23 |
| [RuhrSec](https://www.ruhrsec.de/) | Bochum, Germany | 2018-05-17 | 2018-05-18 |
| [Security Fest](https://securityfest.com/) | Gothenburg, Sweden | 2018-06-01 | 2018-06-01 |
| [Area41](https://area41.io/) | Zürich, Switzerland | 2018-06-15 | 2018-06-16 |
| [Black Hat USA](https://www.blackhat.com/) | Las Vegas, USA | 2018-08-08 | 2018-08-09 |
| [Def Con](https://www.defcon.org/) | Las Vegas, USA | 2018-08-09 | 2017-08-12 |
| [USENIX WOOT](https://www.usenix.org/conference/woot18) | Baltimore, USA | 2018-08-13 | 2018-08-14 |
| [USENIX Security Symposium](https://www.usenix.org/) | Baltimore, USA | 2018-08-15 | 2018-08-17 |
| [DeepIntel](https://deepintel.net/) | Vienna, Austria | 2018-09-17 | 2018-09-18 |
| [Hack.lu](https://hack.lu/) | Luxembourg City, Luxembourg | 2018-10-16 | 2018-10-18 |
| [DeepSec](https://deepsec.net/) | Vienna, Austria | 2018-11-27 | 2018-11-30 |
| [Black Hat Europe](https://www.blackhat.com/) | London, UK | 2018-12-03 | 2018-12-06 |
| [Def Con](https://www.defcon.org/) | Las Vegas, USA | 2019-08-08 | 2019-08-11 |
Date unannounced
================
| Name | Location |
| --- | --- |
| [Kiwicon](https://www.kiwicon.org/) | Wellington, New Zealand |
| [Secure 2017](https://secure.edu.pl/) | October, Warsaw, Germany |
| [Texas Linux Fest](https://www.texaslinuxfest.org/) | Austin, TX, USA |
old
===
| Name | Location | Start | End |
| --- | --- | --- | --- |
| [ShmooCon](http://shmoocon.org/) | California, USA | 2017-01-30 | 2017-02-01 |
| [Enigma](https://www.usenix.org/conference/enigma2017/) | Washington D.C., USA | 2017-01-13 | 2017-01-15 |
| [FOSDEM](https://fosdem.org/) | Brussels, Belgium | 2017-02-04 | 2017-02-05 |
| [SCALE](https://socallinuxexpo.org/) | Pasadena, California, USA | 2017-03-02 | 2017-03-05 |
| [AsiaBSDCon](https://2017.asiabsdcon.org/) | Tokyo, Japan | 2017-03-09 | 2017-03-12 |
| [BSides Ljubljana](https://bsidesljubljana.si/) | Ljubljana, Slovenia | 2017-03-10 | 2017-03-10 |
| [Chemnitzer Linux-Tage](https://chemnitzer.linux-tage.de/) | Chemnitz, Germany | 2017-03-11 | 2017-03-12 |
| [CanSecWest](https://cansecwest.com/) | Vancouver, Canada | 2017-03-15 | 2017-03-17 |
| [FOSSASIA](https://fossasia.org/) | Singapore, Singapore | 2017-03-17 | 2017-03-19 |
| [Open Source Days](https://opensourcedays.org/) | Copenhagen, Denmark | 2017-03-18 | 2017-03-18 |
| [Troopers](https://www.troopers.de/) | Heidelberg, Germany | 2017-03-20 | 2017-03-24 |
| [GUUG FFG](https://www.guug.de/veranstaltungen/ffg2017/) | Darmstadt, Germany | 2017-03-21 | 2017-03-24 |
| [Black Hat Asia](https://www.blackhat.com/asia-17/) | Singapore, Singapore | 2017-03-28 | 2017-03-31 |
| [BSides Munich](http://bsidesmunich.org) | Munich, Germany | 2017-04-03 | 2017-04-03 |
| [Infiltrate](https://infiltratecon.com/) | Florida, USA | 2017-04-06 | 2017-04-07 |
| [newline](https://0x20.be/newline/2017/) | Ghent, Belgium | 2017-04-07 | 2017-04-09 |
| [Hack in the Box](https://conference.hitb.org/) | Amsterdam, Netherlands | 2017-04-10 | 2017-04-14 |
| [Easterhegg](http://www.easterhegg.eu/) | Frankfurt, Germany | 2017-04-14 | 2017-04-17 |
| [Augsburger Linux-Infotag](https://www.luga.de/Aktionen/LIT-2017/) | Augsburg, Germany | 2017-04-22 | 2017-04-22 |
| [Norcon](http://norcon.info/) | Chico, USA | 2017-04-22 | 2017-04-22 |
| [foss-north](http://foss-north.se/) | Gothenburg, Sweden | 2017-04-26 | 2017-04-26 |
| [IEEE Euro S&P](http://www.ieee-security.org/TC/EuroSP2017/) | Paris, France | 2017-04-26 | 2017-04-28 |
| [AtlSecCon](https://atlseccon.com/) | Halifax, Canada | 2017-04-27 | 2017-04-28 |
| [RuhrSec](https://www.ruhrsec.de/) | Bochum, Germany | 2017-05-02 | 2017-05-05 |
| [OSCON](https://conferences.oreilly.com/oscon/oscon-tx) | Austin/Texas, USA | 2017-05-08 | 2017-05-11 |
| [AppSec EU](https://2017.appsec.eu/) | Belfast, UK | 2017-05-08 | 2017-05-11 |
| [Hack In Paris](https://hackinparis.com/) | Paris, France | 2017-05-22 | 2017-05-23 |
| [PHDays](http://www.phdays.com/) | Mosco, Russia | 2017-05-23 | 2017-05-24 |
| [AusCERT](https://conference.auscert.org.au/) | Gold Goast, Australia | 2017-05-23 | 2017-05-26 |
| [PGCon](https://www.pgcon.org/) | Ottawa, Canada | 2017-05-23 | 2017-05-26 |
| [Nuit Du Hack](https://nuitduhack.com/en/) | Paris, France | 2017-05-24 | 2017-05-25 |
| [GPN](https://entropia.de/GPN) | Karlsruhe, Germany | 2017-05-25 | 2017-05-28 |
| [BerlinSides](http://berlinsides.org/) | Berlin, Germany | 2017-05-26 | 2017-05-28 |
| [SyScan360](https://www.syscan360.org/) | Seattle, USA | 2017-05-30 | 2017-05-31 |
| [Security Fest](https://www.securityfest.com/) | Gothenburg, Sweden | 2017-06-01 | 2017-06-01 |
| [WarCon](http://warcon.pl/) | Warsaw, Poland | 2017-06-02 | 2017-06-03 |
| [BSDCan](https://www.bsdcan.org/2017/) | Ottawa, Ontario, Canada | 2017-06-09 | 2017-06-10 |
| [RECON 2017](https://recon.cx/2017/montreal/) | Montreal, Québec, Canada | 2017-06-16 | 2017-06-18 |
| [CoSin](https://www.cosin.ch/) | Biel, Switzerland | 2017-06-16 | 2017-06-18 |
| [MOSEC](http://en.mosec.org/) | Shanghai, China | 2017-06-23 | 2017-06-23 |
| [PQCrypto](https://pqcrypto.org/) | Utrecht, Netherlands | 2017-06-26 | 2017-06-28 |
| [Groden](https://openlab-augsburg.de/groden17/) | Peißenberg, Germany | 2017-06-30 | 2017-07-02 |
| [RMLL](https://2017.rmll.info/) | Saint-Etienne, France | 2017-07-01 | 2017-07-07 |
| [HackOn](https://hackon.nl/) | Amsterdam, Netherlands | 2017-07-14 | 2017-07-16 |
| [ZeTeCo](https://wiki.zeteco.ch/) | Schaffhausen, Switzerland | 2017-07-21 | 2017-07-24 |
| [Black Hat USA](https://www.blackhat.com/) | Las Vegas, USA | 2017-07-22 | 2017-07-27 |
| [BSides LV](https://www.bsideslv.org/) | Las Vegas, USA | 2017-07-25 | 2017-07-26 |
| [Def Con](https://defcon.org/) | Las Vegas, USA | 2017-07-27 | 2017-07-30 |
| [GUADEC](https://wiki.gnome.org/GUADEC/2017) | Manchester, UK | 2017-07-28 | 2017-08-02 |
| [SHA2017](https://sha2017.org/) | Zeewolde, Netherlands | 2017-08-04 | 2017-08-08 |
| [DebConf](https://debconf.org/) | Montreal, Canada | 2017-08-06 | 2017-08-12 |
| [USENIX Security Symposium](https://www.usenix.org/) | Vancouver, Canada | 2017-08-16 | 2017-08-18 |
| [RustConf](http://rustconf.com/) | Portland, USA | 2017-08-18 | 2017-08-19 |
| [FrOSCon](https://www.froscon.de/) | Sankt Augustin, Germany | 2017-08-19 | 2017-08-20 |
| [AlligatorCon Europe](http://alligatorcon.pl/) | Krakow, Poland | 2017-08-25 | 2017-08-26 |
| [Bornhack](https://bornhack.dk/) | Bornholm, Denmark | 2017-08-27 | 2017-09-03 |
| [MRMCD](https://2017.mrmcd.net/) | Darmstadt, Germany | 2017-09-01 | 2017-09-03 |
| [Hack Open Air](https://hackenopenair.de/) | Peine, Germany | 2017-09-07 | 2017-09-10 |
| [vBSDcon](https://www.vbsdcon.com/) | Reston, Virginia, USA | 2017-09-08 | 2017-09-09 |
| [44CON](https://44con.com/) | London, UK | 2017-09-13 | 2017-09-15 |
| [SEC-T](https://www.sec-t.org/) | Stockholm, Sweden | 2017-09-14 | 2017-09-15 |
| [BalCCon](https://2k17.balccon.org/) | Novi Sad, Serbian | 2017-09-15 | 2017-09-17 |
| [BSides Zürich](https://bsideszh.ch/) | Zürich, Switzerland | 2017-09-17 | 2017-09-17 |
| [OWASP AppSec USA](https://2017.appsecusa.org/) | Florida, USA | 2017-09-19 | 2017-09-22 |
| [EuroBSDCon](https://2017.eurobsdcon.org/) | Paris, France | 2017-09-21 | 2017-09-24 |
| [BSides Zurich](https://bsideszh.ch/) | Zurich, Switzerland | 2017-09-23 | 2017-09-23 |
| [BruCON](http://brucon.org/) | Gent, Belgium | 2017-10-05 | 2017-10-06 |
| [VCFB](https://vcfb.de/) | Berlin, Germany | 2017-10-07 | 2017-10-08 |
| [Hack.lu](http://hack.lu/) | Luxembourg City, Luxembourg | 2017-10-16 | 2017-10-19 |
| [Datenspuren](https://www.datenspuren.de/) | Dresden, Germany | 2017-10-21 | 2017-10-22 |
| [Ruxcon](https://ruxcon.org.au/) | Melbourne, Australia | 2017-10-21 | 2017-10-22 |
| [MozFest](https://mozillafestival.org/) | London, UK | 2017-10-27 | 2017-10-29 |
| [ACM CCS](https://www.sigsac.org/ccs/CCS2017/) | Dallas, USA | 2017-10-30 | 2017-11-03 |
| [Hackfest](https://hackfest.ca/) | Quebec, Canada | 2017-10-31 | 2017-11-04 |
| [Driving IT](https://universe.ida.dk/driving-it/) | Copenhagen, Denmark | 2017-11-03 | 2017-11-03 |
| [OpenRheinRuhr](https://openrheinruhr.de/) | Oberhausen, Germany | 2017-11-04 | 2017-11-05 |
| [Nordic IT Security](http://www.nordicitsecurity.com/) | Stockholm, Sweden | 2017-11-07 | 2017-11-07 |
| [Øredev](http://oredev.org/) | Malmö, Sweden | 2017-11-06 | 2017-11-07 |
| [https://grehack.fr/](GreHack) | Grenoble, France | 2017-11-17 | 2017-11-17 |
| [T-DOSE](http://t-dose.org/) | Eindhoven, Netherlands | 2017-11-11 | 2017-11-12 |
| [BlackAlphs](https://www.blackalps.ch/) | Yverdon-Les-Bains, Switzerland | 2017-11-15 | 2017-11-16 |
| [Black Hat Europe](https://www.blackhat.com/) | London, UK | 2017-12-04 | 2017-12-07 |
| [34C3](https://events.ccc.de/) | Leipzig, Germany | 2017-12-27 | 2017-12-30 |
| [RealWorldCrypto](http://www.realworldcrypto.com/) | Zürich, Switzerland | 2018-01-10 | 2018-01-12 |
The list is more or less arbitrary compiled from conferences I know and hear
about. Naturally this means it has a strong bias towards events in central
Europe. Feel free to submit pull requests if you don't like this.
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# Changelog
## v2.2.0 (20/09/2022)
* Add support for USB bridged drives
## v2.1.1 (17/09/2022)
* Handle smartctl exit code != 0 and add smartprom_exit_code metric
## v2.1.0 (21/08/2022)
* Include new metric with SMART Health Status => smartprom_smart_passed
* Add model_family, model_name, serial_number and type attributes for each device
* The "drive" attribute now includes the full path. sda => /dev/sda
* Add more detailed log traces about discovered devices
* Update the Grafana dashboard
* Update Readme to include example metrics
## v2.0.1 (29/07/2022)
* Fix duplicated timeseries error. Resolves #36 (#37)
* Add missing raw metrics for sat devices. Resolves #25 (#38)
* Chore: Code cleanup
## v2.0.0 (28/07/2022)
* Breaking change: Convert the metrics name into lower case (#13)
* Update base Docker image and reduce image size. Resolves #17 (#31)
* Publish Docker images for ARM architecture. Resolves #19 (#34)
* Make refresh interval configurable. Revolves #24 (#29)
* Make exporter port and address configurable via environment variable (#27)
* Include zero value raw metrics (#15)
* Return more information on smartctl error. Resolves #23 (#28)
* Handle error when devices are not detected (#32)
* Using SMART tool to get the devices instead of glob (#14)
* Avoid Python stdout buffering (#33)
* Add Grafana dashboard. Resolves #18 (#30)
* Added gitignore (#12)
| {
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version: '3'
services:
smartctl-metrics:
build: ./
restart: unless-stopped
privileged: true
ports:
- 9902:9902
| {
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FROM python:3.10-alpine3.16
WORKDIR /usr/src
RUN apk add --no-cache smartmontools \
&& pip install prometheus_client \
# remove temporary files
&& rm -rf /root/.cache/ \
&& find / -name '*.pyc' -delete
COPY ./smartprom.py /smartprom.py
EXPOSE 9902
ENTRYPOINT ["/usr/local/bin/python", "-u", "/smartprom.py"]
# HELP
# docker build -t matusnovak/prometheus-smartctl:test .
| {
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#!/usr/bin/env python3
import json
import os
import subprocess
import time
from typing import Tuple
import prometheus_client
LABELS = ['drive', 'type', 'model_family', 'model_name', 'serial_number']
DRIVES = {}
METRICS = {}
# https://www.smartmontools.org/wiki/USB
SAT_TYPES = ['sat', 'usbjmicron', 'usbprolific', 'usbsunplus']
NVME_TYPES = ['nvme', 'sntasmedia', 'sntjmicron', 'sntrealtek']
SCSI_TYPES = ['scsi']
def run_smartctl_cmd(args: list) -> Tuple[str, int]:
"""
Runs the smartctl command on the system
"""
out = subprocess.Popen(args, stdout=subprocess.PIPE, stderr=subprocess.STDOUT)
stdout, stderr = out.communicate()
# exit code can be != 0 even if the command returned valid data
# see EXIT STATUS in
# https://www.smartmontools.org/browser/trunk/smartmontools/smartctl.8.in
if out.returncode != 0:
stdout_msg = stdout.decode('utf-8') if stdout is not None else ''
stderr_msg = stderr.decode('utf-8') if stderr is not None else ''
print(f"WARNING: Command returned exit code {out.returncode}. Stdout: '{stdout_msg}' Stderr: '{stderr_msg}'")
return stdout.decode("utf-8"), out.returncode
def get_drives() -> dict:
"""
Returns a dictionary of devices and its types
"""
disks = {}
result, _ = run_smartctl_cmd(['smartctl', '--scan-open', '--json=c'])
result_json = json.loads(result)
if 'devices' in result_json:
devices = result_json['devices']
for device in devices:
dev = device["name"]
disk_attrs = get_device_info(dev)
disk_attrs["type"] = device["type"]
disks[dev] = disk_attrs
print("Discovered device", dev, "with attributes", disk_attrs)
else:
print("No devices found. Make sure you have enough privileges.")
return disks
def get_device_info(dev: str) -> dict:
"""
Returns a dictionary of device info
"""
results, _ = run_smartctl_cmd(['smartctl', '-i', '--json=c', dev])
results = json.loads(results)
return {
'model_family': results.get("model_family", "Unknown"),
'model_name': results.get("model_name", "Unknown"),
'serial_number': results.get("serial_number", "Unknown")
}
def get_smart_status(results: dict) -> int:
"""
Returns a 1, 0 or -1 depending on if result from
smart status is True, False or unknown.
"""
status = results.get("smart_status")
return +(status.get("passed")) if status is not None else -1
def smart_sat(dev: str) -> dict:
"""
Runs the smartctl command on a internal or external "sat" device
and processes its attributes
"""
results, exit_code = run_smartctl_cmd(['smartctl', '-A', '-H', '-d', 'sat', '--json=c', dev])
results = json.loads(results)
attributes = {
'smart_passed': (0, get_smart_status(results)),
'exit_code': (0, exit_code)
}
data = results['ata_smart_attributes']['table']
for metric in data:
code = metric['id']
name = metric['name']
value = metric['value']
# metric['raw']['value'] contains values difficult to understand for temperatures and time up
# that's why we added some logic to parse the string value
value_raw = metric['raw']['string']
try:
# example value_raw: "33" or "43 (Min/Max 39/46)"
value_raw = int(value_raw.split()[0])
except:
# example value_raw: "20071h+27m+15.375s"
if 'h+' in value_raw:
value_raw = int(value_raw.split('h+')[0])
else:
print(f"Raw value of sat metric '{name}' can't be parsed. raw_string: {value_raw} "
f"raw_int: {metric['raw']['value']}")
value_raw = None
attributes[name] = (int(code), value)
if value_raw is not None:
attributes[f'{name}_raw'] = (int(code), value_raw)
return attributes
def smart_nvme(dev: str) -> dict:
"""
Runs the smartctl command on a internal or external "nvme" device
and processes its attributes
"""
results, exit_code = run_smartctl_cmd(['smartctl', '-A', '-H', '-d', 'nvme', '--json=c', dev])
results = json.loads(results)
attributes = {
'smart_passed': get_smart_status(results),
'exit_code': exit_code
}
data = results['nvme_smart_health_information_log']
for key, value in data.items():
if key == 'temperature_sensors':
for i, _value in enumerate(value, start=1):
attributes[f'temperature_sensor{i}'] = _value
else:
attributes[key] = value
return attributes
def smart_scsi(dev: str) -> dict:
"""
Runs the smartctl command on a "scsi" device
and processes its attributes
"""
results, exit_code = run_smartctl_cmd(['smartctl', '-A', '-H', '-d', 'scsi', '--json=c', dev])
results = json.loads(results)
attributes = {
'smart_passed': get_smart_status(results),
'exit_code': exit_code
}
for key, value in results.items():
if type(value) == dict:
for _label, _value in value.items():
if type(_value) == int:
attributes[f"{key}_{_label}"] = _value
elif type(value) == int:
attributes[key] = value
return attributes
def collect():
"""
Collect all drive metrics and save them as Gauge type
"""
global LABELS, DRIVES, METRICS, SAT_TYPES, NVME_TYPES, SCSI_TYPES
for drive, drive_attrs in DRIVES.items():
typ = drive_attrs['type']
try:
if typ in SAT_TYPES:
attrs = smart_sat(drive)
elif typ in NVME_TYPES:
attrs = smart_nvme(drive)
elif typ in SCSI_TYPES:
attrs = smart_scsi(drive)
else:
continue
for key, values in attrs.items():
# Metric name in lower case
metric = 'smartprom_' + key.replace('-', '_').replace(' ', '_').replace('.', '').replace('/', '_') \
.lower()
# Create metric if it does not exist
if metric not in METRICS:
desc = key.replace('_', ' ')
code = hex(values[0]) if typ in SAT_TYPES else hex(values)
print(f'Adding new gauge {metric} ({code})')
METRICS[metric] = prometheus_client.Gauge(metric, f'({code}) {desc}', LABELS)
# Update metric
metric_val = values[1] if typ in SAT_TYPES else values
METRICS[metric].labels(drive=drive,
type=typ,
model_family=drive_attrs['model_family'],
model_name=drive_attrs['model_name'],
serial_number=drive_attrs['serial_number']).set(metric_val)
except Exception as e:
print('Exception:', e)
pass
def main():
"""
Starts a server and exposes the metrics
"""
global DRIVES
# Validate configuration
exporter_address = os.environ.get("SMARTCTL_EXPORTER_ADDRESS", "0.0.0.0")
exporter_port = int(os.environ.get("SMARTCTL_EXPORTER_PORT", 9902))
refresh_interval = int(os.environ.get("SMARTCTL_REFRESH_INTERVAL", 60))
# Get drives (test smartctl)
DRIVES = get_drives()
# Start Prometheus server
prometheus_client.start_http_server(exporter_port, exporter_address)
print(f"Server listening in http://{exporter_address}:{exporter_port}/metrics")
while True:
collect()
time.sleep(refresh_interval)
if __name__ == '__main__':
main()
| {
"repo_name": "matusnovak/prometheus-smartctl",
"stars": "101",
"repo_language": "Python",
"file_name": "build.yml",
"mime_type": "text/plain"
} |
# Prometheus S.M.A.R.T ctl metrics exporter
This is a simple exporter for the [Prometheus metrics](https://prometheus.io/) using [smartctl](https://www.smartmontools.org/). The script `smartprom.py` also comes with `smartprom.service` so that you can run this script in the background on your Linux OS via `systemctl`. The script will use port `9902`, you can change it by changing it directly in the script. This script exports all of the data available from the smartctl.
## Install
_Note: You don't have to do this if you use the Docker image._
1. Copy the `smartprom.service` file into `/etc/systemd/system` folder.
2. Copy the `smartprom.py` file anywhere into your system.
3. Modify `ExecStart=` in the `smartprom.service` so that it points to `smartprom.py` in your system.
4. Run `chmod +x smartprom.py`
5. Install `prometheus_client` for the root user, example: `sudo -H python3 -m pip install prometheus_client`
6. Run `systemctl enable smartprom` and `systemctl start smartprom`
7. Your metrics will now be available at `http://localhost:9902`
## Docker usage
No extra configuration needed, should work out of the box. The `privileged: true` is required in order for `smartctl` to be able to access drives from the host.
Docker image is here: <https://hub.docker.com/r/matusnovak/prometheus-smartctl>
The architectures supported by this image are: linux/386, linux/amd64, linux/arm/v6, linux/arm/v7, linux/arm64/v8, linux/ppc64le, linux/s390x
Example docker-compose.yml:
```yml
version: '3'
services:
smartctl-exporter:
image: matusnovak/prometheus-smartctl:latest
container_name: smartctl-exporter
privileged: true
ports:
- "9902:9902"
restart: unless-stopped
```
Your metrics will be available at <http://localhost:9902/metrics>
The exported metrics looks like these:
```shell
smartprom_smart_passed{drive="/dev/sda",model_family="Seagate BarraCuda 3.5 (SMR)",model_name="ST6000DM003-2CY296",serial_number="WCT362XM",type="sat"} 1.0
smartprom_exit_code{drive="/dev/sda",model_family="Seagate BarraCuda 3.5 (SMR)",model_name="ST6000DM003-2CY296",serial_number="WCT362XM",type="sat"} 0.0
smartprom_raw_read_error_rate{drive="/dev/sda",model_family="Seagate BarraCuda 3.5 (SMR)",model_name="ST6000DM003-2CY296",serial_number="WCT362XM",type="sat"} 83.0
smartprom_raw_read_error_rate_raw{drive="/dev/sda",model_family="Seagate BarraCuda 3.5 (SMR)",model_name="ST6000DM003-2CY296",serial_number="WCT362XM",type="sat"} 2.23179896e+08
smartprom_power_on_hours{drive="/dev/sda",model_family="Seagate BarraCuda 3.5 (SMR)",model_name="ST6000DM003-2CY296",serial_number="WCT362XM",type="sat"} 73.0
smartprom_power_on_hours_raw{drive="/dev/sda",model_family="Seagate BarraCuda 3.5 (SMR)",model_name="ST6000DM003-2CY296",serial_number="WCT362XM",type="sat"} 24299.0
smartprom_airflow_temperature_cel{drive="/dev/sda",model_family="Seagate BarraCuda 3.5 (SMR)",model_name="ST6000DM003-2CY296",serial_number="WCT362XM",type="sat"} 60.0
smartprom_airflow_temperature_cel_raw{drive="/dev/sda",model_family="Seagate BarraCuda 3.5 (SMR)",model_name="ST6000DM003-2CY296",serial_number="WCT362XM",type="sat"} 40.0
...
```
## Configuration
All configuration is done with environment variables.
- `SMARTCTL_REFRESH_INTERVAL`: (Optional) The refresh interval of the metrics. A larger value reduces CPU usage. The default is `60` seconds.
- `SMARTCTL_EXPORTER_PORT`: (Optional) The address the exporter should listen on. The default is `9902`.
- `SMARTCTL_EXPORTER_ADDRESS`: (Optional) The address the exporter should listen on. The default is to listen on all addresses.
## Grafana dashboard
There is a reference Grafana dashboard in [grafana/grafana_dashboard.json](./grafana/grafana_dashboard.json).
| {
"repo_name": "matusnovak/prometheus-smartctl",
"stars": "101",
"repo_language": "Python",
"file_name": "build.yml",
"mime_type": "text/plain"
} |
name: build
on:
push:
tags:
- '*'
branches:
- '*'
jobs:
build:
name: Docker
runs-on: ubuntu-latest
steps:
- name: Checkout
uses: actions/checkout@v2
- name: Downcase repo
run: echo REPOSITORY=matusnovak/prometheus-smartctl >> $GITHUB_ENV
- name: Docker metadata
id: docker_metadata
uses: docker/metadata-action@v3
with:
images: ${{ env.REPOSITORY }}
# images: ${{ env.REPOSITORY }},ghcr.io/${{ env.REPOSITORY }}
flavor: |
latest=true
prefix=
suffix=
tags: |
type=sha
type=ref,event=tag
- name: Set up QEMU
uses: docker/[email protected]
- name: Set up Docker Buildx
uses: docker/setup-buildx-action@v1
- name: Login to DockerHub
uses: docker/login-action@v1
with:
username: ${{ secrets.DOCKER_USERNAME }}
password: ${{ secrets.DOCKER_PASSWORD }}
# - name: Login to GitHub Container Registry
# uses: docker/login-action@v1
# with:
# registry: ghcr.io
# username: ${{ github.repository_owner }}
# password: ${{ secrets.GH_PAT }}
- name: Build and push Docker image
uses: docker/build-push-action@v2
with:
context: .
file: ./Dockerfile
platforms: linux/386,linux/amd64,linux/arm/v6,linux/arm/v7,linux/arm64/v8,linux/ppc64le,linux/s390x
push: ${{ github.event_name != 'pull_request' }}
tags: ${{ steps.docker_metadata.outputs.tags }}
labels: ${{ steps.docker_metadata.outputs.labels }}
| {
"repo_name": "matusnovak/prometheus-smartctl",
"stars": "101",
"repo_language": "Python",
"file_name": "build.yml",
"mime_type": "text/plain"
} |
const fs = require('fs');
const path = require('path');
const transactionsPath = path.join(__dirname, 'cadence', 'transactions', '/')
const scriptsPath = path.join(__dirname, 'cadence', 'scripts', '/')
const convertCadenceToJs = async () => {
const resultingJs = await require('cadence-to-json')({
transactions: [ transactionsPath ],
scripts: [ scriptsPath ],
config: require('./flow.json')
})
fs.writeFile('lib/CadenceToJson.json', JSON.stringify(resultingJs), (err) => {
if (err) {
console.error("Failed to read CadenceToJs JSON");
process.exit(1)
}
})
}
convertCadenceToJs() | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
const json = require("./lib/CadenceToJson.json");
export { json };
import contracts from "./lib/cadut-generated/contracts/index.js";
import scripts from "./lib/cadut-generated/scripts/index.js";
import transactions from "./lib/cadut-generated/transactions/index.js";
import {
setEnvironment,
getEnvironment,
extendEnvironment,
} from "@onflow/flow-cadut";
let contractNames = Object.keys(json.vars["testnet"]);
for (let index in contractNames) {
const contractName = contractNames[index];
extendEnvironment({
name: contractName.replace("0x", ""),
testnet: json.vars["testnet"][contractName],
mainnet: json.vars["mainnet"][contractName],
});
}
const getAddressMaps = async function () {
const addressMaps = {};
setEnvironment("mainnet");
addressMaps["mainnet"] = await getEnvironment();
setEnvironment("testnet");
addressMaps["testnet"] = await getEnvironment();
return addressMaps;
};
export { getAddressMaps, contracts, scripts, transactions }; | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
{
"name": "flow-catalog",
"version": "0.2.1",
"lockfileVersion": 2,
"requires": true,
"packages": {
"": {
"name": "flow-catalog",
"version": "0.2.1",
"license": "ISC",
"dependencies": {
"@onflow/fcl": "^1.2.0",
"@onflow/flow-cadut": "^0.2.0-alpha.8",
"install": "^0.13.0",
"npm": "^8.18.0"
},
"devDependencies": {
"@babel/core": "^7.19.3",
"@babel/preset-env": "^7.19.3",
"@onflow/flow-cadut-generator": "^0.0.1",
"@onflow/types": "^0.0.6",
"babel-jest": "^28.0.3",
"babel-loader": "^8.2.5",
"cadence-to-json": "^1.0.3",
"cypress": "^9.7.0",
"flow-js-testing": "^0.2.3-alpha.6",
"jest": "^28.0.3",
"webpack": "^5.74.0",
"webpack-cli": "^4.10.0"
}
},
"node_modules/@ampproject/remapping": {
"version": "2.2.0",
"resolved": "https://registry.npmjs.org/@ampproject/remapping/-/remapping-2.2.0.tgz",
"integrity": "sha512-qRmjj8nj9qmLTQXXmaR1cck3UXSRMPrbsLJAasZpF+t3riI71BXed5ebIOYwQntykeZuhjsdweEc9BxH5Jc26w==",
"dev": true,
"dependencies": {
"@jridgewell/gen-mapping": "^0.1.0",
"@jridgewell/trace-mapping": "^0.3.9"
},
"engines": {
"node": ">=6.0.0"
}
},
"node_modules/@babel/code-frame": {
"version": "7.18.6",
"resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.18.6.tgz",
"integrity": "sha512-TDCmlK5eOvH+eH7cdAFlNXeVJqWIQ7gW9tY1GJIpUtFb6CmjVyq2VM3u71bOyR8CRihcCgMUYoDNyLXao3+70Q==",
"dev": true,
"dependencies": {
"@babel/highlight": "^7.18.6"
},
"engines": {
"node": ">=6.9.0"
}
},
"node_modules/@babel/compat-data": {
"version": "7.19.3",
"resolved": "https://registry.npmjs.org/@babel/compat-data/-/compat-data-7.19.3.tgz",
"integrity": "sha512-prBHMK4JYYK+wDjJF1q99KK4JLL+egWS4nmNqdlMUgCExMZ+iZW0hGhyC3VEbsPjvaN0TBhW//VIFwBrk8sEiw==",
"dev": true,
"engines": {
"node": ">=6.9.0"
}
},
"node_modules/@babel/core": {
"version": "7.19.3",
"resolved": "https://registry.npmjs.org/@babel/core/-/core-7.19.3.tgz",
"integrity": "sha512-WneDJxdsjEvyKtXKsaBGbDeiyOjR5vYq4HcShxnIbG0qixpoHjI3MqeZM9NDvsojNCEBItQE4juOo/bU6e72gQ==",
"dev": true,
"dependencies": {
"@ampproject/remapping": "^2.1.0",
"@babel/code-frame": "^7.18.6",
"@babel/generator": "^7.19.3",
"@babel/helper-compilation-targets": "^7.19.3",
"@babel/helper-module-transforms": "^7.19.0",
"@babel/helpers": "^7.19.0",
"@babel/parser": "^7.19.3",
"@babel/template": "^7.18.10",
"@babel/traverse": "^7.19.3",
"@babel/types": "^7.19.3",
"convert-source-map": "^1.7.0",
"debug": "^4.1.0",
"gensync": "^1.0.0-beta.2",
"json5": "^2.2.1",
"semver": "^6.3.0"
},
"engines": {
"node": ">=6.9.0"
},
"funding": {
"type": "opencollective",
"url": "https://opencollective.com/babel"
}
},
"node_modules/@babel/generator": {
"version": "7.19.3",
"resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.19.3.tgz",
"integrity": "sha512-fqVZnmp1ncvZU757UzDheKZpfPgatqY59XtW2/j/18H7u76akb8xqvjw82f+i2UKd/ksYsSick/BCLQUUtJ/qQ==",
"dev": true,
"dependencies": {
"@babel/types": "^7.19.3",
"@jridgewell/gen-mapping": "^0.3.2",
"jsesc": "^2.5.1"
},
"engines": {
"node": ">=6.9.0"
}
},
"node_modules/@babel/generator/node_modules/@jridgewell/gen-mapping": {
"version": "0.3.2",
"resolved": "https://registry.npmjs.org/@jridgewell/gen-mapping/-/gen-mapping-0.3.2.tgz",
"integrity": "sha512-mh65xKQAzI6iBcFzwv28KVWSmCkdRBWoOh+bYQGW3+6OZvbbN3TqMGo5hqYxQniRcH9F2VZIoJCm4pa3BPDK/A==",
"dev": true,
"dependencies": {
"@jridgewell/set-array": "^1.0.1",
"@jridgewell/sourcemap-codec": "^1.4.10",
"@jridgewell/trace-mapping": "^0.3.9"
},
"engines": {
"node": ">=6.0.0"
}
},
"node_modules/@babel/helper-annotate-as-pure": {
"version": "7.18.6",
"resolved": "https://registry.npmjs.org/@babel/helper-annotate-as-pure/-/helper-annotate-as-pure-7.18.6.tgz",
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"dependencies": {
"@babel/types": "^7.18.6"
},
"engines": {
"node": ">=6.9.0"
}
},
"node_modules/@babel/helper-builder-binary-assignment-operator-visitor": {
"version": "7.18.9",
"resolved": "https://registry.npmjs.org/@babel/helper-builder-binary-assignment-operator-visitor/-/helper-builder-binary-assignment-operator-visitor-7.18.9.tgz",
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"@babel/types": "^7.18.9"
},
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}
},
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"resolved": "https://registry.npmjs.org/@babel/helper-compilation-targets/-/helper-compilation-targets-7.19.3.tgz",
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"dev": true,
"dependencies": {
"@babel/compat-data": "^7.19.3",
"@babel/helper-validator-option": "^7.18.6",
"browserslist": "^4.21.3",
"semver": "^6.3.0"
},
"engines": {
"node": ">=6.9.0"
},
"peerDependencies": {
"@babel/core": "^7.0.0"
}
},
"node_modules/@babel/helper-create-class-features-plugin": {
"version": "7.19.0",
"resolved": "https://registry.npmjs.org/@babel/helper-create-class-features-plugin/-/helper-create-class-features-plugin-7.19.0.tgz",
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"@babel/helper-environment-visitor": "^7.18.9",
"@babel/helper-function-name": "^7.19.0",
"@babel/helper-member-expression-to-functions": "^7.18.9",
"@babel/helper-optimise-call-expression": "^7.18.6",
"@babel/helper-replace-supers": "^7.18.9",
"@babel/helper-split-export-declaration": "^7.18.6"
},
"engines": {
"node": ">=6.9.0"
},
"peerDependencies": {
"@babel/core": "^7.0.0"
}
},
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"version": "7.19.0",
"resolved": "https://registry.npmjs.org/@babel/helper-create-regexp-features-plugin/-/helper-create-regexp-features-plugin-7.19.0.tgz",
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"dev": true,
"dependencies": {
"@babel/helper-annotate-as-pure": "^7.18.6",
"regexpu-core": "^5.1.0"
},
"engines": {
"node": ">=6.9.0"
},
"peerDependencies": {
"@babel/core": "^7.0.0"
}
},
"node_modules/@babel/helper-define-polyfill-provider": {
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"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
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const path = require("path");
module.exports = {
target: "node",
entry: path.resolve(__dirname, "index.js"),
output: {
path: path.resolve(__dirname, "dist"),
filename: "index_bundle.js",
library: {
name: "flowCatalog",
type: "umd",
},
},
module: {
rules: [
{
test: /\.(js)$/,
exclude: /node_modules/,
use: "babel-loader",
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mode: "development",
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"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
# NFT Catalog
The NFT Catalog is an on chain registry listing NFT collections that exists on Flow which adhere to the NFT metadata standard. This empowers dApp developers to easily build on top of and discover interoperable NFT collections on Flow.
## Live Site
Checkout the catalog [site](https://www.flow-nft-catalog.com/) to submit your NFT collection both on testnet and mainnet.
## NPM Module
We exposed an interface to the catalog via a consumable NPM module. This library will expose a number of methods that can be called to interact with the catalog. The module can be found here with installation instructions below: https://www.npmjs.com/package/flow-catalog
### Methods
Method signatures and their associating parameters/responses can be found in the `cadence/` folder of this repo.
#### Scripts
```
checkForRecommendedV1Views
genTx
getAllNftsAndViewsInAccount
getAllNftsInAccount
getExamplenftCollectionLength
getExamplenftType
getNftAndViewsInAccount
getNftCatalog
getNftCatalogCount
getNftCatalogIdentifiers
getNftCatalogProposals
getNftCatalogProposalsCount
getNftCollectionsForNftType
getNftIdsInAccount
getNftInAccount
getNftInAccountFromPath
getNftMetadataForCollectionIdentifier
getNftProposalForId
getNftsCountInAccount
getNftsInAccount
getNftsInAccountFromIds
getNftsInAccountFromPath
getSupportedGeneratedScripts
getSupportedGeneratedTransactions
hasAdminProxy
isCatalogAdmin
```
#### Transactions
```
addToNftCatalog
addToNftCatalogAdmin
approveNftCatalogProposal
mintExampleNft
mintNonstandardNft
proposeNftToCatalog
rejectNftCatalogProposal
removeFromNftCatalog
removeNftCatalogProposal
sendAdminCapabilityToProxy
setupExamplenftCollection
setupNftCatalogAdminProxy
setupNonstandardnftCollection
setupStorefront
transferExamplenft
updateNftCatalogEntry
withdrawNftProposalFromCatalog
```
### Installation
```
npm install flow-catalog
```
or
```
yarn add flow-catalog
```
### Usage
Methods can be imported as follows, all nested methods live under the `scripts` or `transactions` variable.
NOTE: In order to properly bootstrap the method, you will need to run and `await` on the `getAddressMaps()` method, passing it into all of the methods as shown below.
```
import { getAddressMaps, scripts } from "flow-catalog";
const main = async () => {
const addressMap = await getAddressMaps();
console.log(await scripts.getNftCatalog(addressMap));
};
main();
```
The response of any method is a tuple-array, with the first element being the result, and the second being the error (if applicable).
For example, the result of the method above would look like -
```
[
{
BILPlayerCollection: {
contractName: 'Player',
contractAddress: '0x9e6cdb88e34fa1f3',
nftType: [Object],
collectionData: [Object],
collectionDisplay: [Object]
},
...
SoulMadeComponent: {
contractName: 'SoulMadeComponent',
contractAddress: '0x421c19b7dc122357',
nftType: [Object],
collectionData: [Object],
collectionDisplay: [Object]
}
},
null
]
```
## Contract Addresses
`NFTCatalog.cdc`: This contract contains the NFT Catalog
| Network | Address |
| ------- | ------------------ |
| Mainnet | 0x49a7cda3a1eecc29 |
| Testnet | 0x324c34e1c517e4db |
`NFTRetrieval.cdc`: This contract contains helper functions to make it easier to discover NFTs within accounts and from the catalog
| Network | Address |
| ------- | ------------------ |
| Mainnet | 0x49a7cda3a1eecc29 |
| Testnet | 0x324c34e1c517e4db |
## Submitting a Collection to the NFT Catalog
1. Visit [here](https://www.flow-nft-catalog.com/v)
2. Enter the address containing the NFT contract which contains the collection and select the contract
<img width="1509" alt="Screen Shot 2023-02-08 at 9 40 01 AM" src="https://user-images.githubusercontent.com/5430668/217561873-54beb50e-0ea2-46fb-b9f8-8dbe758ee12f.png">
3. Enter the storage path where the NFTs are stored and enter an address that holds a sample NFT or log in if you have access to an account that owns the NFT
<img width="1508" alt="Screen Shot 2023-02-08 at 9 42 54 AM" src="https://user-images.githubusercontent.com/5430668/217562366-e6cbf3cb-38b8-45cb-943e-e20185565743.png">
4. The application will verify that your NFT collection implements the required Metadata views.
1. The required metadata views include…
1. NFT Display
1. How to display an individual NFT part of the collection
2. External URL
1. A website for the NFT collection
3. Collection Data
1. Information needed to store and retrieve an NFT
4. Collection Display
1. How to display information about the NFT collection the NFT belongs to
5. Royalties
1. Any royalties that should be accounted for during marketplace transactions
2. You can find sample implementations of all these views in this example NFT [contract](https://github.com/onflow/flow-nft/blob/master/contracts/ExampleNFT.cdc).
3. If you are not implementing a view, the app will communicate this and you can update your NFT contract and try resubmitting.
<img width="738" alt="Screen Shot 2023-02-08 at 9 46 56 AM" src="https://user-images.githubusercontent.com/5430668/217563435-86863297-183b-4345-9615-61f9d4212fe9.png">
5. Submit proposal transaction to the NFT catalog by entering a unique url safe identifier for the collection and a message including any additional context (like contact information).
<img width="1503" alt="Screen Shot 2023-02-08 at 9 48 45 AM" src="https://user-images.githubusercontent.com/5430668/217563785-65065f51-37bc-49c7-8b3e-ba5d1dda3b24.png">
6. Once submitted you can view all proposals [here](https://www.flow-nft-catalog.com/proposals/mainnet) to track the review of your NFT.
If you would like to make a proposal manually, you may submit the following transaction with all parameters filled in: [https://github.com/dapperlabs/nft-catalog/blob/main/cadence/transactions/propose_nft_to_catalog.cdc](https://github.com/dapperlabs/nft-catalog/blob/main/cadence/transactions/propose_nft_to_catalog.cdc)
Proposals should be reviewed and approved within a few days. Reasons for a proposal being rejected may include:
- Providing duplicate path or name information of an existing collection on the catalog
- Providing a not url safe or inaccurate name as the identifier
## Using the Catalog (For marketplaces and other NFT applications)
All of the below examples use the catalog in mainnet, you may replace the imports to the testnet address when using the testnet network.
**Example 1 - Retrieve all NFT collections on the catalog**
```cadence
import NFTCatalog from 0x49a7cda3a1eecc29
/*
The catalog is returned as a `String: NFTCatalogMetadata`
The key string is intended to be a unique identifier for a specific collection.
The NFTCatalogMetadata contains collection-level views corresponding to each
collection identifier.
Due to the large size of the response, only the first 10 entries are returned.
*/
pub fun main(): {String: NFTCatalog.NFTCatalogMetadata} {
let catalogKeys = NFTCatalog.getCatalogKeys()
let keys = catalogKeys.slice(from: 0, upTo: 10)
let collections: {String: NFTCatalog.NFTCatalogMetadata} = {}
for key in keys {
collections[key] = catalog[key]
}
return collections
}
```
**Example 2 - Retrieve all collection names in the catalog**
```cadence
import NFTCatalog from 0x49a7cda3a1eecc29
pub fun main(): [String] {
let catalogKeys: {String: NFTCatalog.NFTCatalogMetadata} = NFTCatalog.getCatalogKeys()
let catalogNames: [String] = []
for collectionIdentifier in catalogKeys {
catalogNames.append(catalog[collectionIdentifier]!.collectionDisplay.name)
}
return catalogNames
}
```
**Example 3 - Retrieve NFT collections and counts owned by an account**
```cadence
import MetadataViews from 0x1d7e57aa55817448
import NFTCatalog from 0x49a7cda3a1eecc29
import NFTRetrieval from 0x49a7cda3a1eecc29
pub fun main(ownerAddress: Address): {String: Number} {
let account = getAuthAccount(ownerAddress)
let items: {String: Number} = {}
NFTCatalog.forEachCatalogKey(fun (collectionIdentifier: String):Bool {
let value = NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier)!
let keyHash = String.encodeHex(HashAlgorithm.SHA3_256.hash(collectionIdentifier.utf8))
let tempPathStr = "catalog".concat(keyHash)
let tempPublicPath = PublicPath(identifier: tempPathStr)!
account.link<&{MetadataViews.ResolverCollection}>(
tempPublicPath,
target: value.collectionData.storagePath
)
let collectionCap = account.getCapability<&AnyResource{MetadataViews.ResolverCollection}>(tempPublicPath)
if !collectionCap.check() {
return true
}
let count = NFTRetrieval.getNFTCountFromCap(collectionIdentifier: collectionIdentifier, collectionCap: collectionCap)
if count != 0 {
items[collectionIdentifier] = count
}
return true
})
return items
}
```
`Sample Response...`
```text
{
"schmoes_prelaunch_token": 1
}
```
**Example 4 - Retrieve all NFTs including metadata owned by an account**
```cadence
import MetadataViews from 0x1d7e57aa55817448
import NFTCatalog from 0x49a7cda3a1eecc29
import NFTRetrieval from 0x49a7cda3a1eecc29
pub struct NFT {
pub let id: UInt64
pub let name: String
pub let description: String
pub let thumbnail: String
pub let externalURL: String
pub let storagePath: StoragePath
pub let publicPath: PublicPath
pub let privatePath: PrivatePath
pub let publicLinkedType: Type
pub let privateLinkedType: Type
pub let collectionName: String
pub let collectionDescription: String
pub let collectionSquareImage: String
pub let collectionBannerImage: String
pub let collectionExternalURL: String
pub let royalties: [MetadataViews.Royalty]
init(
id: UInt64,
name: String,
description: String,
thumbnail: String,
externalURL: String,
storagePath: StoragePath,
publicPath: PublicPath,
privatePath: PrivatePath,
publicLinkedType: Type,
privateLinkedType: Type,
collectionName: String,
collectionDescription: String,
collectionSquareImage: String,
collectionBannerImage: String,
collectionExternalURL: String,
royalties: [MetadataViews.Royalty]
) {
self.id = id
self.name = name
self.description = description
self.thumbnail = thumbnail
self.externalURL = externalURL
self.storagePath = storagePath
self.publicPath = publicPath
self.privatePath = privatePath
self.publicLinkedType = publicLinkedType
self.privateLinkedType = privateLinkedType
self.collectionName = collectionName
self.collectionDescription = collectionDescription
self.collectionSquareImage = collectionSquareImage
self.collectionBannerImage = collectionBannerImage
self.collectionExternalURL = collectionExternalURL
self.royalties = royalties
}
}
pub fun main(ownerAddress: Address): {String: [NFT]} {
let account = getAuthAccount(ownerAddress)
let items: [MetadataViews.NFTView] = []
let data: {String: [NFT]} = {}
NFTCatalog.forEachCatalogKey(fun (collectionIdentifier: String):Bool {
let value = NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier)!
let keyHash = String.encodeHex(HashAlgorithm.SHA3_256.hash(collectionIdentifier.utf8))
let tempPathStr = "catalog".concat(keyHash)
let tempPublicPath = PublicPath(identifier: tempPathStr)!
account.link<&{MetadataViews.ResolverCollection}>(
tempPublicPath,
target: value.collectionData.storagePath
)
let collectionCap = account.getCapability<&AnyResource{MetadataViews.ResolverCollection}>(tempPublicPath)
if !collectionCap.check() {
return true
}
let views = NFTRetrieval.getNFTViewsFromCap(collectionIdentifier: collectionIdentifier, collectionCap: collectionCap)
let items: [NFT] = []
for view in views {
let displayView = view.display
let externalURLView = view.externalURL
let collectionDataView = view.collectionData
let collectionDisplayView = view.collectionDisplay
let royaltyView = view.royalties
if (displayView == nil || externalURLView == nil || collectionDataView == nil || collectionDisplayView == nil || royaltyView == nil) {
// Bad NFT. Skipping....
return true
}
items.append(
NFT(
id: view.id,
name: displayView!.name,
description: displayView!.description,
thumbnail: displayView!.thumbnail.uri(),
externalURL: externalURLView!.url,
storagePath: collectionDataView!.storagePath,
publicPath: collectionDataView!.publicPath,
privatePath: collectionDataView!.providerPath,
publicLinkedType: collectionDataView!.publicLinkedType,
privateLinkedType: collectionDataView!.providerLinkedType,
collectionName: collectionDisplayView!.name,
collectionDescription: collectionDisplayView!.description,
collectionSquareImage: collectionDisplayView!.squareImage.file.uri(),
collectionBannerImage: collectionDisplayView!.bannerImage.file.uri(),
collectionExternalURL: collectionDisplayView!.externalURL.url,
royalties: royaltyView!.getRoyalties()
)
)
}
data[collectionIdentifier] = items
return true
})
return data
}
```
`Sample Response...`
```text
{
"FlovatarComponent": [],
"schmoes_prelaunch_token": [
s.aa16be98aac20e8073f923261531cbbdfae1464f570f5be796b57cdc97656248.NFT(
id: 1006,
name: "Schmoes Pre Launch Token #1006",
description: "",
thumbnail: "https://gateway.pinata.cloud/ipfs/QmXQ1iBke5wjcjYG22ACVXsCvtMJKEkwFiMf96UChP8uJq",
externalURL: "https://schmoes.io",
storagePath: /storage/SchmoesPreLaunchTokenCollection,
publicPath: /public/SchmoesPreLaunchTokenCollection,
privatePath: /private/SchmoesPreLaunchTokenCollection,
publicLinkedType: Type<&A.6c4fe48768523577.SchmoesPreLaunchToken.Collection{A.1d7e57aa55817448.NonFungibleToken.CollectionPublic,A. 1d7e57aa55817448.NonFungibleToken.Receiver,A.1d7e57aa55817448.MetadataViews.ResolverCollection}>(),
privateLinkedType: Type<&A.6c4fe48768523577.SchmoesPreLaunchToken.Collection{A.1d7e57aa55817448.NonFungibleToken.CollectionPublic,A.1d7e57aa55817448.NonFungibleToken.Provider,A.1d7e57aa55817448.MetadataViews.ResolverCollection}>(),
collectionName: "Schmoes Pre Launch Token",
collectionDescription: "",
collectionSquareImage: "https://gateway.pinata.cloud/ipfs/QmXQ1iBke5wjcjYG22ACVXsCvtMJKEkwFiMf96UChP8uJq",
collectionBannerImage: "https://gateway.pinata.cloud/ipfs/QmXQ1iBke5wjcjYG22ACVXsCvtMJKEkwFiMf96UChP8uJq",
royalties: []
)
],
"Flovatar": []
}
```
**Example 5 - Retrieve all NFTs including metadata owned by an account for large wallets**
For Wallets that have a lot of NFTs you may run into memory issues. The common pattern to get around this for now is to retrieve just the ID's in a wallet by calling the following script
```cadence
import MetadataViews from 0x1d7e57aa55817448
import NFTCatalog from 0x49a7cda3a1eecc29
import NFTRetrieval from 0x49a7cda3a1eecc29
pub fun main(ownerAddress: Address): {String: [UInt64]} {
let account = getAuthAccount(ownerAddress)
let items: {String: [UInt64]} = {}
NFTCatalog.forEachCatalogKey(fun (key: String):Bool {
let value = NFTCatalog.getCatalogEntry(collectionIdentifier: key)!
let keyHash = String.encodeHex(HashAlgorithm.SHA3_256.hash(key.utf8))
let tempPathStr = "catalogIDs".concat(keyHash)
let tempPublicPath = PublicPath(identifier: tempPathStr)!
account.link<&{MetadataViews.ResolverCollection}>(
tempPublicPath,
target: value.collectionData.storagePath
)
let collectionCap = account.getCapability<&AnyResource{MetadataViews.ResolverCollection}>(tempPublicPath)
if !collectionCap.check() {
return true
}
let ids = NFTRetrieval.getNFTIDsFromCap(collectionIdentifier: key, collectionCap: collectionCap)
if ids.length > 0 {
items[key] = ids
}
return true
})
return items
}
```
and then use the ids to retrieve the full metadata for only those ids by calling the following script and passing in a map of collectlionIdentifer -> [ids]
```cadence
import MetadataViews from 0x1d7e57aa55817448
import NFTCatalog from 0x49a7cda3a1eecc29
import NFTRetrieval from 0x49a7cda3a1eecc29
pub struct NFT {
pub let id: UInt64
pub let name: String
pub let description: String
pub let thumbnail: String
pub let externalURL: String
pub let storagePath: StoragePath
pub let publicPath: PublicPath
pub let privatePath: PrivatePath
pub let publicLinkedType: Type
pub let privateLinkedType: Type
pub let collectionName: String
pub let collectionDescription: String
pub let collectionSquareImage: String
pub let collectionBannerImage: String
pub let collectionExternalURL: String
pub let royalties: [MetadataViews.Royalty]
init(
id: UInt64,
name: String,
description: String,
thumbnail: String,
externalURL: String,
storagePath: StoragePath,
publicPath: PublicPath,
privatePath: PrivatePath,
publicLinkedType: Type,
privateLinkedType: Type,
collectionName: String,
collectionDescription: String,
collectionSquareImage: String,
collectionBannerImage: String,
collectionExternalURL: String,
royalties: [MetadataViews.Royalty]
) {
self.id = id
self.name = name
self.description = description
self.thumbnail = thumbnail
self.externalURL = externalURL
self.storagePath = storagePath
self.publicPath = publicPath
self.privatePath = privatePath
self.publicLinkedType = publicLinkedType
self.privateLinkedType = privateLinkedType
self.collectionName = collectionName
self.collectionDescription = collectionDescription
self.collectionSquareImage = collectionSquareImage
self.collectionBannerImage = collectionBannerImage
self.collectionExternalURL = collectionExternalURL
self.royalties = royalties
}
}
pub fun main(ownerAddress: Address, collections: {String: [UInt64]}): {String: [NFT]} {
let data: {String: [NFT]} = {}
let account = getAuthAccount(ownerAddress)
for collectionIdentifier in collections.keys {
if NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier) != nil {
let value = NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier)!
let identifierHash = String.encodeHex(HashAlgorithm.SHA3_256.hash(collectionIdentifier.utf8))
let tempPathStr = "catalog".concat(identifierHash)
let tempPublicPath = PublicPath(identifier: tempPathStr)!
account.link<&{MetadataViews.ResolverCollection}>(
tempPublicPath,
target: value.collectionData.storagePath
)
let collectionCap = account.getCapability<&AnyResource{MetadataViews.ResolverCollection}>(tempPublicPath)
if !collectionCap.check() {
return data
}
let views = NFTRetrieval.getNFTViewsFromIDs(collectionIdentifier: collectionIdentifier, ids: collections[collectionIdentifier]!, collectionCap: collectionCap)
let items: [NFT] = []
for view in views {
let displayView = view.display
let externalURLView = view.externalURL
let collectionDataView = view.collectionData
let collectionDisplayView = view.collectionDisplay
let royaltyView = view.royalties
if (displayView == nil || externalURLView == nil || collectionDataView == nil || collectionDisplayView == nil || royaltyView == nil) {
// Bad NFT. Skipping....
continue
}
items.append(
NFT(
id: view.id,
name: displayView!.name,
description: displayView!.description,
thumbnail: displayView!.thumbnail.uri(),
externalURL: externalURLView!.url,
storagePath: collectionDataView!.storagePath,
publicPath: collectionDataView!.publicPath,
privatePath: collectionDataView!.providerPath,
publicLinkedType: collectionDataView!.publicLinkedType,
privateLinkedType: collectionDataView!.providerLinkedType,
collectionName: collectionDisplayView!.name,
collectionDescription: collectionDisplayView!.description,
collectionSquareImage: collectionDisplayView!.squareImage.file.uri(),
collectionBannerImage: collectionDisplayView!.bannerImage.file.uri(),
collectionExternalURL: collectionDisplayView!.externalURL.url,
royalties: royaltyView!.getRoyalties()
)
)
}
data[collectionIdentifier] = items
}
}
return data
}
```
**Example 6 - Retrieve all MetadataViews for NFTs in a wallet**
If you're looking for some MetadataViews that aren't in the [core view list](https://github.com/onflow/flow-nft/blob/master/contracts/MetadataViews.cdc#L36) you can leverage this script to grab all the views each NFT supports. Note: You lose some typing here but get more data.
```cadence
import MetadataViews from 0x1d7e57aa55817448
import NFTCatalog from 0x49a7cda3a1eecc29
import NFTRetrieval from 0x49a7cda3a1eecc29
pub struct NFTCollectionData {
pub let storagePath: StoragePath
pub let publicPath: PublicPath
pub let privatePath: PrivatePath
pub let publicLinkedType: Type
pub let privateLinkedType: Type
init(
storagePath: StoragePath,
publicPath: PublicPath,
privatePath: PrivatePath,
publicLinkedType: Type,
privateLinkedType: Type,
) {
self.storagePath = storagePath
self.publicPath = publicPath
self.privatePath = privatePath
self.publicLinkedType = publicLinkedType
self.privateLinkedType = privateLinkedType
}
}
pub fun main(ownerAddress: Address): {String: {String: AnyStruct}} {
let account = getAuthAccount(ownerAddress)
let items: [MetadataViews.NFTView] = []
let data: {String: {String: AnyStruct}} = {}
NFTCatalog.forEachCatalogKey(fun (collectionIdentifier: String):Bool {
let value = NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier)!
let keyHash = String.encodeHex(HashAlgorithm.SHA3_256.hash(collectionIdentifier.utf8))
let tempPathStr = "catalog".concat(keyHash)
let tempPublicPath = PublicPath(identifier: tempPathStr)!
account.link<&{MetadataViews.ResolverCollection}>(
tempPublicPath,
target: value.collectionData.storagePath
)
let collectionCap = account.getCapability<&AnyResource{MetadataViews.ResolverCollection}>(tempPublicPath)
if !collectionCap.check() {
return true
}
var views = NFTRetrieval.getAllMetadataViewsFromCap(collectionIdentifier: collectionIdentifier, collectionCap: collectionCap)
if views.keys.length == 0 {
return true
}
// Cadence doesn't support function return types, lets manually get rid of it
let nftCollectionDisplayView = views[Type<MetadataViews.NFTCollectionData>().identifier] as! MetadataViews.NFTCollectionData?
let collectionDataView = NFTCollectionData(
storagePath: nftCollectionDisplayView!.storagePath,
publicPath: nftCollectionDisplayView!.publicPath,
privatePath: nftCollectionDisplayView!.providerPath,
publicLinkedType: nftCollectionDisplayView!.publicLinkedType,
privateLinkedType: nftCollectionDisplayView!.providerLinkedType,
)
views.insert(key: Type<MetadataViews.NFTCollectionData>().identifier, collectionDataView)
data[collectionIdentifier] = views
return true
})
return data
}
```
**Example 7 - Setup a user’s account to receive a specific collection**
1. Run the following script to retrieve some collection-level information for an NFT collection identifier from the catalog
```cadence
// Assuming file name is `get_nft_collection_data.cdc`
import MetadataViews from 0x1d7e57aa55817448
import NFTCatalog from 0x49a7cda3a1eecc29
import NFTRetrieval from 0x49a7cda3a1eecc29
pub struct NFTCollection {
pub let contractName: String
pub let contractAddress: String
pub let storagePath: StoragePath
pub let publicPath: PublicPath
pub let privatePath: PrivatePath
pub let publicLinkedType: Type
pub let privateLinkedType: Type
pub let collectionName: String
pub let collectionDescription: String
pub let collectionSquareImage: String
pub let collectionBannerImage: String
init(
contractName: String,
contractAddress: String,
storagePath: StoragePath,
publicPath: PublicPath,
privatePath: PrivatePath,
publicLinkedType: Type,
privateLinkedType: Type,
collectionName: String,
collectionDescription: String,
collectionSquareImage: String,
collectionBannerImage: String
) {
self.contractName = contractName
self.contractAddress = contractAddress
self.storagePath = storagePath
self.publicPath = publicPath
self.privatePath = privatePath
self.publicLinkedType = publicLinkedType
self.privateLinkedType = privateLinkedType
self.collectionName = collectionName
self.collectionDescription = collectionDescription
self.collectionSquareImage = collectionSquareImage
self.collectionBannerImage = collectionBannerImage
}
}
pub fun main(collectionIdentifier : String) : NFTCollection? {
pre {
NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier) != nil : "Invalid collection identifier"
}
let contractView = NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier)!
let collectionDataView = NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier)!.collectionData
let collectionDisplayView = NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier)!.collectionDisplay
return NFTCollection(
contractName: contractView.contractName,
contractAddress: contractView.contractAddress.toString(),
storagePath: collectionDataView!.storagePath,
publicPath: collectionDataView!.publicPath,
privatePath: collectionDataView!.privatePath,
publicLinkedType: collectionDataView!.publicLinkedType,
privateLinkedType: collectionDataView!.privateLinkedType,
collectionName: collectionDisplayView!.name,
collectionDescription: collectionDisplayView!.description,
collectionSquareImage: collectionDisplayView!.squareImage.file.uri(),
collectionBannerImage: collectionDisplayView!.bannerImage.file.uri()
)
}
```
2. This script result can then be used to form a transaction by inserting the relevant variables from above into a transaction template like the following:
```cadence
// Assuming file name is `setup_collection_template.cdc`
import NonFungibleToken from 0x1d7e57aa55817448
import MetadataViews from 0x1d7e57aa55817448
import {CONTRACT_NAME} from {CONTRACT_ADDRESS}
transaction {
prepare(signer: AuthAccount) {
// Create a new empty collection
let collection <- {CONTRACT_NAME}.createEmptyCollection()
// save it to the account
signer.save(<-collection, to: {STORAGE_PATH})
// create a public capability for the collection
signer.link<&{PUBLIC_LINKED_TYPE}>(
{PUBLIC_PATH},
target: {STORAGE_PATH}
)
// create a private capability for the collection
signer.link<&{PRIVATE_LINKED_TYPE}>(
{PRIVATE_PATH},
target: {STORAGE_PATH}
)
}
}
```
We can achieve this with JavaScript, for example:
```javascript
import { readFileSync, writeFileSync } from "fs";
import * as fcl from "@onflow/fcl";
fcl.config()
.put("accessNode.api", "https://rest-mainnet.onflow.org")
.put("flow.network", "mainnet");
const args = process.argv.slice(2);
const collectionIdentifier = args[0];
if (collectionIdentifier === undefined) {
console.error("You need to pass the Collection identifier as an argument.");
process.exit(1);
}
try {
const scriptPath = new URL("get_nft_collection_data.cdc", import.meta.url);
const scriptCode = readFileSync(scriptPath, { encoding: "utf8" });
const nftCollection = await fcl.query({
cadence: scriptCode,
args: (arg, t) => [arg(collectionIdentifier, t.String)],
});
console.log(nftCollection);
const filePath = new URL("setup_collection_template.cdc", import.meta.url);
const transactionTemplate = readFileSync(filePath, { encoding: "utf8" });
const transaction = transactionTemplate
.replaceAll("{CONTRACT_NAME}", nftCollection.contractName)
.replaceAll("{CONTRACT_ADDRESS}", nftCollection.contractAddress)
.replaceAll(
"{STORAGE_PATH}",
`/${nftCollection.storagePath.domain}/${nftCollection.storagePath.identifier}`
)
.replaceAll(
"{PUBLIC_PATH}",
`/${nftCollection.publicPath.domain}/${nftCollection.publicPath.identifier}`
)
.replaceAll(
"{PRIVATE_PATH}",
`/${nftCollection.privatePath.domain}/${nftCollection.privatePath.identifier}`
)
.replaceAll(
"{PUBLIC_LINKED_TYPE}",
nftCollection.publicLinkedType.typeID.replace(/A\.\w{16}\./g, "")
)
.replaceAll(
"{PRIVATE_LINKED_TYPE}",
nftCollection.privateLinkedType.typeID.replace(/A\.\w{16}\./g, "")
);
const transactionPath = `setup_${nftCollection.contractName}_collection.cdc`;
writeFileSync(transactionPath, transaction);
console.log(transaction);
} catch (err) {
console.error(err.message);
}
```
Running the above with:
```bash
node setupCollection.mjs "ChainmonstersRewards"
```
will generate a file called `setup_ChainmonstersRewards_collection.cdc`, containing:
```cadence
import NonFungibleToken from 0x1d7e57aa55817448
import MetadataViews from 0x1d7e57aa55817448
import ChainmonstersRewards from 0x93615d25d14fa337
transaction {
prepare(signer: AuthAccount) {
// Create a new empty collection
let collection <- ChainmonstersRewards.createEmptyCollection()
// save it to the account
signer.save(<-collection, to: /storage/ChainmonstersRewardCollection)
// create a public capability for the collection
signer.link<&ChainmonstersRewards.Collection{ChainmonstersRewards.ChainmonstersRewardCollectionPublic,NonFungibleToken.CollectionPublic,NonFungibleToken.Receiver,MetadataViews.ResolverCollection}>(
/public/ChainmonstersRewardCollection,
target: /storage/ChainmonstersRewardCollection
)
// create a private capability for the collection
signer.link<&ChainmonstersRewards.Collection{ChainmonstersRewards.ChainmonstersRewardCollectionPublic,NonFungibleToken.CollectionPublic,NonFungibleToken.Provider,MetadataViews.ResolverCollection}>(
/private/ChainmonstersRewardsCollectionProvider,
target: /storage/ChainmonstersRewardCollection
)
}
}
```
## Developer Usage
### 1. [Install the Flow CLI](https://github.com/onflow/flow-cli)
### 2. [Install Node](https://nodejs.org/en/)
### 3. Clone the project
```sh
git clone --depth=1 https://github.com/onflow/nft-catalog.git
```
### 4. Install packages
- Run `npm install` in the root of the project
### 5. Run Test Suite
- Run `npm test` in the root of the project
## License
The works in these files:
- [FungibleToken.cdc](cadence/contracts/FungibleToken.cdc)
- [NonFungibleToken.cdc](cadence/contracts/NonFungibleToken.cdc)
- [ExampleNFT.cdc](cadence/contracts/ExampleNFT.cdc)
- [MetadataViews.cdc](cadence/contracts/MetadataViews.cdc)
- [NFTCatalog.cdc](cadence/contracts/NFTCatalog.cdc)
- [NFTCatalogAdmin.cdc](cadence/contracts/NFTCatalogAdmin.cdc)
- [NFTRetrieval.cdc](cadence/contracts/NFTRetrieval.cdc)
are under the [Unlicense](LICENSE).
| {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
#### Documentation
Has been moved to here:
[Docs](https://github.com/onflow/flow/tree/master/docs/content/nft-catalog) | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import MetadataViews from "../contracts/MetadataViews.cdc"
import NFTRetrieval from "../contracts/NFTRetrieval.cdc"
pub struct DisplayView {
pub let name : String
pub let description : String
pub let thumbnail : String
init (
name : String,
description : String,
thumbnail : String
) {
self.name = name
self.description = description
self.thumbnail = thumbnail
}
}
pub struct ExternalURLView {
pub let externalURL : String
init (
externalURL : String
) {
self.externalURL = externalURL
}
}
pub struct NFTCollectionDataView {
pub let storagePath : StoragePath
pub let publicPath : PublicPath
pub let privatePath: PrivatePath
pub let publicLinkedType: Type
pub let privateLinkedType: Type
init (
storagePath : StoragePath,
publicPath : PublicPath,
privatePath : PrivatePath,
publicLinkedType : Type,
privateLinkedType : Type,
) {
self.storagePath = storagePath
self.publicPath = publicPath
self.privatePath = privatePath
self.publicLinkedType = publicLinkedType
self.privateLinkedType = privateLinkedType
}
}
pub struct NFTCollectionDisplayView {
pub let collectionName : String
pub let collectionDescription: String
pub let collectionSquareImage : MetadataViews.Media
pub let collectionBannerImage : MetadataViews.Media
pub let externalURL : String
pub let socials : {String: MetadataViews.ExternalURL}
init (
collectionName : String,
collectionDescription : String,
collectionSquareImage : MetadataViews.Media,
collectionBannerImage : MetadataViews.Media,
externalURL : String,
socials : {String: MetadataViews.ExternalURL}
) {
self.collectionName = collectionName
self.collectionDescription = collectionDescription
self.collectionSquareImage = collectionSquareImage
self.collectionBannerImage = collectionBannerImage
self.externalURL = externalURL
self.socials = socials
}
}
pub struct RoyaltiesView {
pub let royalties: [MetadataViews.Royalty]
init (
royalties : [MetadataViews.Royalty]
) {
self.royalties = royalties
}
}
pub struct NFT {
pub let id : UInt64
pub let display : DisplayView?
pub let externalURL : ExternalURLView?
pub let nftCollectionData : NFTCollectionDataView?
pub let nftCollectionDisplay : NFTCollectionDisplayView?
pub let royalties : RoyaltiesView?
init(
id: UInt64,
display : DisplayView?,
externalURL : ExternalURLView?,
nftCollectionData : NFTCollectionDataView?,
nftCollectionDisplay : NFTCollectionDisplayView?,
royalties : RoyaltiesView?
) {
self.id = id
self.display = display
self.externalURL = externalURL
self.nftCollectionData = nftCollectionData
self.nftCollectionDisplay = nftCollectionDisplay
self.royalties = royalties
}
pub fun getMapping() : {String : AnyStruct} {
return {
"Id" : self.id,
"Display" : self.display,
"ExternalURL" : self.externalURL,
"NFTCollectionData" : self.nftCollectionData,
"NFTCollectionDisplay" : self.nftCollectionDisplay,
"Royalties" : self.royalties
}
}
}
pub fun main(ownerAddress: Address, storagePathIdentifier: String, nftID: UInt64): {String : AnyStruct} {
let owner = getAuthAccount(ownerAddress)
let tempPathStr = "getNFTsInAccountFromPathNFTCatalog"
let tempPublicPath = PublicPath(identifier: tempPathStr)!
owner.link<&{MetadataViews.ResolverCollection}>(
tempPublicPath,
target: StoragePath(identifier : storagePathIdentifier)!
)
let collectionCap = owner.getCapability<&AnyResource{MetadataViews.ResolverCollection}>(tempPublicPath)
assert(collectionCap.check(), message: "MetadataViews Collection is not set up properly, ensure the Capability was created/linked correctly.")
let collection = collectionCap.borrow()!
assert(collection.getIDs().length > 0, message: "No NFTs exist in this collection, ensure the provided account has at least 1 NFTs.")
return getNFTData(nftID: nftID, collection: collection)
}
pub fun getNFTData(nftID: UInt64, collection: &AnyResource{MetadataViews.ResolverCollection} ): {String : AnyStruct} {
let nftResolver = collection.borrowViewResolver(id: nftID)
let nftViews = MetadataViews.getNFTView(
id : nftID,
viewResolver: nftResolver
)
let displayView = nftViews.display
let externalURLView = nftViews.externalURL
let collectionDataView = nftViews.collectionData
let collectionDisplayView = nftViews.collectionDisplay
let royaltyView = nftViews.royalties
var display : DisplayView? = nil
if displayView != nil {
display = DisplayView(
name : displayView!.name,
description : displayView!.description,
thumbnail : displayView!.thumbnail.uri()
)
}
var externalURL : ExternalURLView? = nil
if externalURLView != nil {
externalURL = ExternalURLView(
externalURL : externalURLView!.url,
)
}
var nftCollectionData : NFTCollectionDataView? = nil
if collectionDataView != nil {
nftCollectionData = NFTCollectionDataView(
storagePath : collectionDataView!.storagePath,
publicPath : collectionDataView!.publicPath,
privatePath : collectionDataView!.providerPath,
publicLinkedType : collectionDataView!.publicLinkedType,
privateLinkedType : collectionDataView!.providerLinkedType,
)
}
var nftCollectionDisplay : NFTCollectionDisplayView? = nil
if collectionDisplayView != nil {
nftCollectionDisplay = NFTCollectionDisplayView(
collectionName : collectionDisplayView!.name,
collectionDescription : collectionDisplayView!.description,
collectionSquareImage : collectionDisplayView!.squareImage,
collectionBannerImage : collectionDisplayView!.bannerImage,
externalURL : collectionDisplayView!.externalURL.url,
socials : collectionDisplayView!.socials
)
}
var royalties : RoyaltiesView? = nil
if royaltyView != nil {
royalties = RoyaltiesView(
royalties : royaltyView!.getRoyalties()
)
}
return NFT(
id: nftID,
display : display,
externalURL : externalURL,
nftCollectionData : nftCollectionData,
nftCollectionDisplay : nftCollectionDisplay,
royalties : royalties
).getMapping()
} | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import NFTCatalog from "../contracts/NFTCatalog.cdc"
pub fun main(proposalIDs: [UInt64]): {UInt64 : NFTCatalog.NFTCatalogProposal} {
var data : {UInt64 : NFTCatalog.NFTCatalogProposal} = {}
for proposalID in proposalIDs {
assert(NFTCatalog.getCatalogProposalEntry(proposalID: proposalID) != nil, message: "Invalid Proposal ID")
data.insert(key: proposalID, NFTCatalog.getCatalogProposalEntry(proposalID: proposalID)!)
}
return data
} | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import NonFungibleToken from "../contracts/NonFungibleToken.cdc"
import ExampleNFT from "../contracts/ExampleNFT.cdc"
pub fun main(): String {
return Type<@ExampleNFT.NFT>().identifier
} | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import NFTCatalog from "../contracts/NFTCatalog.cdc"
pub fun main(nftTypeIdentifer: String): {String : Bool}? {
return NFTCatalog.getCollectionsForType(nftTypeIdentifier: CompositeType(nftTypeIdentifer)!.identifier)
} | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import NonFungibleToken from "../contracts/NonFungibleToken.cdc"
import ExampleNFT from "../contracts/ExampleNFT.cdc"
pub fun main(address: Address): Int {
let account = getAccount(address)
let collectionRef = account
.getCapability(ExampleNFT.CollectionPublicPath)
.borrow<&{NonFungibleToken.CollectionPublic}>()
?? panic("Could not borrow capability from public collection")
return collectionRef.getIDs().length
} | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import TransactionGeneration from "../contracts/TransactionGeneration.cdc"
pub fun main() : [String] {
return TransactionGeneration.getSupportedTx()
} | {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import TransactionGeneration from "../contracts/TransactionGeneration.cdc"
pub fun main(tx: String, collectionIdentifier: String, vaultIdentifier: String, merchantAddress: String) : String {
return TransactionGeneration.getTx(tx: tx, params: {
"collectionIdentifier": collectionIdentifier,
"vaultIdentifier": vaultIdentifier,
"merchantAddress": merchantAddress
})!
}
| {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import MetadataViews from "../contracts/MetadataViews.cdc"
import NFTCatalog from "../contracts/NFTCatalog.cdc"
import NFTRetrieval from "../contracts/NFTRetrieval.cdc"
pub struct NFT {
pub let id: UInt64
pub let name: String
pub let description: String
pub let thumbnail: String
pub let externalURL: String
pub let storagePath: StoragePath
pub let publicPath: PublicPath
pub let privatePath: PrivatePath
pub let publicLinkedType: Type
pub let privateLinkedType: Type
pub let collectionName: String
pub let collectionDescription: String
pub let collectionSquareImage: String
pub let collectionBannerImage: String
pub let collectionExternalURL: String
pub let royalties: [MetadataViews.Royalty]
init(
id: UInt64,
name: String,
description: String,
thumbnail: String,
externalURL: String,
storagePath: StoragePath,
publicPath: PublicPath,
privatePath: PrivatePath,
publicLinkedType: Type,
privateLinkedType: Type,
collectionName: String,
collectionDescription: String,
collectionSquareImage: String,
collectionBannerImage: String,
collectionExternalURL: String,
royalties: [MetadataViews.Royalty]
) {
self.id = id
self.name = name
self.description = description
self.thumbnail = thumbnail
self.externalURL = externalURL
self.storagePath = storagePath
self.publicPath = publicPath
self.privatePath = privatePath
self.publicLinkedType = publicLinkedType
self.privateLinkedType = privateLinkedType
self.collectionName = collectionName
self.collectionDescription = collectionDescription
self.collectionSquareImage = collectionSquareImage
self.collectionBannerImage = collectionBannerImage
self.collectionExternalURL = collectionExternalURL
self.royalties = royalties
}
}
pub fun main(ownerAddress: Address, collectionIdentifiers: [String]): {String: [NFT]} {
let account = getAuthAccount(ownerAddress)
let data: {String: [NFT]} = {}
for collectionIdentifier in collectionIdentifiers {
if NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier) != nil {
let value = NFTCatalog.getCatalogEntry(collectionIdentifier: collectionIdentifier)!
let identifierHash = String.encodeHex(HashAlgorithm.SHA3_256.hash(collectionIdentifier.utf8))
let tempPathStr = "catalog".concat(identifierHash)
let tempPublicPath = PublicPath(identifier: tempPathStr)!
account.link<&{MetadataViews.ResolverCollection}>(
tempPublicPath,
target: value.collectionData.storagePath
)
let collectionCap = account.getCapability<&AnyResource{MetadataViews.ResolverCollection}>(tempPublicPath)
if !collectionCap.check() {
continue
}
let views = NFTRetrieval.getNFTViewsFromCap(collectionIdentifier: collectionIdentifier, collectionCap: collectionCap)
let items: [NFT] = []
for view in views {
let displayView = view.display
let externalURLView = view.externalURL
let collectionDataView = view.collectionData
let collectionDisplayView = view.collectionDisplay
let royaltyView = view.royalties
if (displayView == nil || externalURLView == nil || collectionDataView == nil || collectionDisplayView == nil || royaltyView == nil) {
// Bad NFT. Skipping....
continue
}
items.append(
NFT(
id: view.id,
name: displayView!.name,
description: displayView!.description,
thumbnail: displayView!.thumbnail.uri(),
externalURL: externalURLView!.url,
storagePath: collectionDataView!.storagePath,
publicPath: collectionDataView!.publicPath,
privatePath: collectionDataView!.providerPath,
publicLinkedType: collectionDataView!.publicLinkedType,
privateLinkedType: collectionDataView!.providerLinkedType,
collectionName: collectionDisplayView!.name,
collectionDescription: collectionDisplayView!.description,
collectionSquareImage: collectionDisplayView!.squareImage.file.uri(),
collectionBannerImage: collectionDisplayView!.bannerImage.file.uri(),
collectionExternalURL: collectionDisplayView!.externalURL.url,
royalties: royaltyView!.getRoyalties()
)
)
}
data[collectionIdentifier] = items
}
}
return data
}
| {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
import NFTCatalog from "../contracts/NFTCatalog.cdc"
pub fun main(): [String] {
return NFTCatalog.getCatalogKeys()
}
| {
"repo_name": "onflow/nft-catalog",
"stars": "34",
"repo_language": "Cadence",
"file_name": "home.spec.ts",
"mime_type": "text/plain"
} |
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