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{-# OPTIONS --universe-polymorphism #-}
module Data.BitVector.Properties where
open import Algebra using (CommutativeRing)
open import Data.Bool using (_∧_; _∨_; _xor_)
renaming (Bool to Bit; false to 0#; true to 1#)
open import Data.Nat using (ℕ) renaming (zero to Nzero; suc to Nsuc)
open import Da... | {
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open import Signature
import Logic
module Model (Σ Δ : Sig) (V : Set) (Φ : Logic.Program Σ Δ V) where
open import Function
open import Data.Empty renaming (⊥ to Ø)
open import Data.Sum
open import Data.Product renaming (Σ to ∐)
open import Relation.Unary
open import Relation.Binary.PropositionalEquality hiding ([_])
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------------------------------------------------------------------------
-- Parsing of mixfix operators
------------------------------------------------------------------------
-- This module defines a grammar for the precedence graph g.
open import RecursiveDescent.Hybrid.Mixfix.Expr
module RecursiveDescent.Hybrid.... | {
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module Refactoring where
open import ParseTree hiding (after)
open import Data.List
open import Data.String hiding (_++_)
open import Data.Sum hiding (map)
open import Data.Product
open import ScopeParseTree
open import MatchUpNames
open import ScopeState
open import Data.Nat
open import InterpretCommand
open import Da... | {
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{-# OPTIONS --safe --warning=error --with-K #-}
open import Sets.EquivalenceRelations
open import Groups.Definition
open import Orders
open import Rings.Definition
open import Numbers.Integers.Integers
open import Numbers.Integers.Multiplication
open import Setoids.Setoids
open import LogicalFormulae
open import Sets.... | {
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{-# OPTIONS --universe-polymorphism #-}
module Categories.Monoidal.Cartesian where
open import Data.Product using (proj₁; proj₂) renaming (_×_ to _×₀_)
open import Data.Fin using (zero)
open import Categories.Category
open import Categories.Monoidal
open import Categories.Object.BinaryProducts
open import Categories.... | {
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{-# OPTIONS --sized-types #-}
open import Relation.Binary.Core
module Heapsort.Impl1.Correctness.Permutation {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_)
(trans≤ : Transitive _≤_) where
open import BBHeap _≤_ hiding (forget ; flatten)
open import BBHeap.Heap... | {
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open import Common.Prelude
open import Common.Equality
test : "foo" ≡ "bar" → Set₁
test refl = Set
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-- 2012-02-22
module CorrectPrintingOfVariablesInSortCheckingForData where
data Bool : Set where
true false : Bool
if_then_else_ : {A : Set2} → Bool → A → A → A
if true then a else b = a
if false then a else b = b
data foo : (y : Bool) → if y then Set else Set
data foo where
bar : foo true
-- This should pr... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Numbers.Naturals.Semiring -- for length
open import Lists.Definition
open import Lists.Fold.Fold
module Lists.Length where
length : {a : _} {A : Set a} (l : List A) → ℕ
length [] = zero
length (x :: l) = succ (length l)
lengt... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Functor.Bifunctor where
-- Bifunctor, aka a Functor from C × D to E
open import Level
open import Categories.Category
open import Categories.Functor
open import Categories.Functor.Construction.Constant
open import Categories.Category.Product
private
variable
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{-# OPTIONS --without-K #-}
module Agda.Builtin.Sigma where
open import Agda.Primitive
record Σ {a b} (A : Set a) (B : A → Set b) : Set (a ⊔ b) where
constructor _,_
field
fst : A
snd : B fst
open Σ public
infixr 4 _,_
{-# BUILTIN SIGMA Σ #-}
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------------------------------------------------------------------------
-- Code for converting Vec₁ n A → B to and from n-ary functions
------------------------------------------------------------------------
-- I want universe polymorphism.
module Data.Vec.N-ary1 where
open import Data.Nat
open import Data.Vec1
op... | {
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{-# OPTIONS --without-K --safe #-}
module PlainPi where
open import Data.Empty
open import Data.Unit
open import Data.Sum
open import Data.Product
open import Relation.Binary.PropositionalEquality
infixr 70 _×ᵤ_
infixr 60 _+ᵤ_
infixr 50 _⊚_
---------------------------------------------------------------------------... | {
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{-# OPTIONS --erased-cubical --safe #-}
module Transformation where
open import Data.Integer using (ℤ; +_; _-_; -_)
open import Data.List using (List; _∷_; []; map; reverse)
open import Data.Product using (_,_)
open import Note using (Note; tone; rest)
open import Pitch using (Pitch; transposePitch... | {
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------------------------------------------------------------------------------
-- Properties of the divisibility relation
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymo... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category
--(Binary) product of objects and morphisms
module Categories.Object.Product {o ℓ e} (C : Category o ℓ e) where
open import Categories.Object.Product.Core C public
open import Categories.Object.Product.Morphisms C public
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module examplesPaperJFP.finn where
open import Data.Nat
data Fin : ℕ → Set where
zero : {n : ℕ} → Fin (suc n)
suc : {n : ℕ} (i : Fin n) → Fin (suc n)
mutual
data Even : ℕ → Set where
0p : Even 0
sucp : {n : ℕ} → Odd n → Even (suc n)
data Odd : ℕ → Set where
sucp : {n : ℕ} → Even n... | {
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module CombiningProofs.WhereTranslation where
open import FOTC.Base
open import FOTC.Data.Nat
-- See Issue https://github.com/asr/apia/issues/81 ... | {
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-- (Pre)abelian categories
{-# OPTIONS --safe #-}
module Cubical.Categories.Abelian.Base where
open import Cubical.Categories.Additive.Base
open import Cubical.Categories.Category.Base
open import Cubical.Categories.Morphism
open import Cubical.Data.Sigma.Base
open import Cubical.Foundations.Prelude
private
variab... | {
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module Prelude.Eq where
open import Prelude.Level
infix 4 _==_
data _==_ {l : Level}{A : Set l} (x : A) : A → Set l where
refl : x == x
cong : {A : Set}{B : Set}{x y : A}(f : A → B) → x == y → f x == f y
cong f refl = refl
{-# BUILTIN EQUALITY _==_ #-}
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.NType2
open import lib.types.Group
open import lib.types.Sigma
open import lib.types.Truncation
module lib.groups.SubgroupProp where
record SubgroupProp {i} (G : Group i) j : Type (lmax i (lsucc j)) where
private
module G = Group G
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{-# OPTIONS --safe #-}
open import Generics.Prelude
open import Generics.Telescope
open import Generics.Desc
open import Generics.Mu
module Generics.Mu.Fold
{P I n} {D : DataDesc P I n}
{c} (X : ⟦ P , I ⟧xtel → Set c)
(alg : ∀ {pi} → ⟦ D ⟧Data X pi → X pi) where
private
variable
p : ⟦ P ⟧tel tt
V : E... | {
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{-# OPTIONS --safe #-}
module Cubical.Data.SumFin.Properties where
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Univalence
open import Cubical.Data.Empty as ⊥
open impo... | {
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module Basic.Compiler.Code where
open import Basic.AST
open import Basic.BigStep
open import Utils.Decidable
open import Utils.Monoid
open import Data.Fin using (Fin; #_)
open import Data.Vec hiding (_∷ʳ_; _++_; [_])
open import Data.Nat
open import Data.Bool renaming (not to notBool; if_then_else_ to ifBool_then_el... | {
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module ListNat where
data Nat : Set where
zero : Nat
succ : Nat -> Nat
data List (a : Set) : Set where
[] : List a
_::_ : a -> List a -> List a
infixr 30 _::_
[1,0,2] = one :: zero :: succ one :: []
where one = succ zero
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Structures.Subtype where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Data.NatPlusOne
open import Cubical.Data.Nat
open import Cubical.Data.Sigma
private
variable
ℓ ℓ' : Level
-- The type o... | {
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{-# OPTIONS --without-K #-}
module higher.circle.properties where
open import sum
open import equality
open import function.isomorphism
open import sets.empty
open import sets.bool
open import hott.equivalence
open import hott.univalence
open import higher.circle.core
non-simply-connected : ¬ (loop ≡ refl)
non-simply... | {
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-- Andreas, 2015-07-13 Better parse errors for illegal type signatures
1 : Set1
1 = Set
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{-# OPTIONS --without-K #-}
module Model.Quantification where
open import Model.RGraph as RG using (RGraph)
open import Model.Size as MS using (_<_ ; ⟦_⟧Δ ; ⟦_⟧n ; ⟦_⟧σ)
open import Model.Type.Core
open import Source.Size.Substitution.Theory
open import Source.Size.Substitution.Universe as SS using (Sub⊢ᵤ)
open import... | {
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module Tactic.Nat.Subtract.Refute where
open import Prelude
open import Builtin.Reflection
open import Tactic.Reflection.Quote
open import Tactic.Reflection.Substitute
open import Tactic.Reflection
open import Control.Monad.State
open import Tactic.Nat.Reflect
open import Tactic.Nat.NF
open import Tactic.Nat.Exp
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{-# OPTIONS --allow-unsolved-metas #-}
module simple where
module Nat where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
_+_ : Nat -> Nat -> Nat
zero + m = m
suc n + m = suc (n + m)
module N = Nat
z = N._+_ (N.suc N.zero) (N.suc N.zero)
zz = Nat._+_ (Nat.suc Nat.zero) (Nat.suc Nat.zero)
mo... | {
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module Numeral.Natural.LinearSearch where
open import Data.Boolean
open import Data.Boolean.Stmt
open import Data.List
import Data.List.Functions as List
open import Data.List.Relation.Membership using (_∈_)
open import Data.List.Relation.Membership.Proofs
open import Data.List.Relation.Quantification
open import... | {
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{-# OPTIONS --allow-unsolved-metas #-}
record R : Set₁ where
field
A : Set
f : A → A
record Double {a} (A : Set a) : Set a where
field
double : A → A
open Double {{...}}
-- Type error (incomplete patterns in Patterns.Match)
doubleR : Double R
R.A (double {{doubleR}} x) = R.A x
R.f (double {{double... | {
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{-
This files contains:
- Facts about constructions on finite sets, especially when they preserve finiteness.
-}
{-# OPTIONS --safe #-}
module Cubical.Data.FinSet.Constructors where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Equiv renaming (_∙ₑ_ t... | {
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module Prelude.Int where
open import Prelude.Unit
open import Prelude.Empty
open import Prelude.Nat
open import Prelude.Number
open import Prelude.String
open import Prelude.Semiring
open import Prelude.Equality
open import Prelude.Equality.Inspect
open import Prelude.Equality.Unsafe using (eraseEquality)
open import... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.Lattice where
open import Cubical.Algebra.Lattice.Base public
open import Cubical.Algebra.Lattice.Properties public
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{-# OPTIONS --without-K #-}
module algebra.semigroup.morphism where
open import level
open import algebra.semigroup.core
open import equality.core
open import hott.level
module _ {i}{j}
{X : Set i}⦃ sX : IsSemigroup X ⦄
{Y : Set j}⦃ sY : IsSemigroup Y ⦄ where
open IsSemigroup ⦃ ... ⦄
IsSemigro... | {
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{-# OPTIONS --safe #-}
{-
Constructions of "sets" in the cumulative hierarchy. Including:
- the empty set
- unions
- ω
- replacement
- separation
-}
module Cubical.HITs.CumulativeHierarchy.Constructions where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations... | {
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module A1 where
open import Data.Empty using (⊥)
open import Relation.Binary.PropositionalEquality using (_≡_; refl; subst)
open import Data.Unit using (⊤; tt)
open import Data.Bool using (Bool; false; true; _xor_)
open import Data.Sum using (_⊎_; inj₁; inj₂)
open import Data.Product using (_×_; _,_; Σ; Σ-syntax)
open... | {
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module x02-842Induction-hc where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; cong; sym)
open Eq.≡-Reasoning using (begin_; _≡⟨⟩_; _∎)
open import Data.Nat using (ℕ; zero; suc; _+_; _*_; _∸_)
-- associativity
_ : (3 + 4) + 5 ≡ 3 + (4 + 5)
_ =
begin
(3 + 4) + 5 ≡⟨⟩
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-- Instance arguments in records.
module Issue509 where
-- The instance version of _
⋯ : {A : Set} {{ x : A }} → A
⋯ {{ x }} = x
data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
record T (n : ℕ) : Set where
field
nextPrime : ℕ
T₁ : T (suc zero)
T₁ = record { nextPrime = suc (suc zero) }
T₂ : T (suc (suc zero))
T... | {
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{-# OPTIONS --without-K --exact-split --rewriting #-}
open import lib.Basics
open import lib.NConnected
open import Graphs.Definition
open import Coequalizers.Definition
{- We will consider two properties of graphs: if they are trees and if they are connected,
both are defined in terms of the geometric realisatio... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Integers, basic types and operations
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Integer.Base where
open import Data.Nat.Base as ℕ
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module DeBruijnExSubst where
open import Prelude -- using (_∘_) -- composition, identity
open import Data.Maybe
open import Logic.Identity renaming (subst to subst≡)
import Logic.ChainReasoning
module Chain = Logic.ChainReasoning.Poly.Homogenous _≡_ (\x -> refl) (\x y z -> trans)
open Chain
open import DeBruijn... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Sets.EquivalenceRelations
open import LogicalFormulae
open import Orders.Total.Definition
open import Orders.Partial.Definition
open import Setoids.Setoids
open import Functions.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Data.Nat.Lower where
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Function
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Prelude
open import Cubical.Foundati... | {
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------------------------------------------------------------------------
-- An observation about weak bisimilarity
------------------------------------------------------------------------
{-# OPTIONS --sized-types #-}
module Delay-monad.Bisimilarity.Observation where
open import Equality.Propositional
open import Lo... | {
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open import FRP.JS.String using ( String )
open import FRP.JS.Time using ( Time )
module FRP.JS.Date where
postulate
Date : Set
fromTime : Time → Date
toTime : Date → Time
toString : Date → String
toUTCString : Date → String
{-# COMPILED_JS fromTime require("agda-frp-time").date #-}
{-# COMPILED_JS toTime ... | {
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open import Relation.Binary.PropositionalEquality using (_≡_; _≢_; refl; sym)
module AKS.Nat.Combinatorial where
open import AKS.Nat.Base using (ℕ; _+_; _∸_; _*_; _≤_)
open ℕ
open import AKS.Nat.Properties using (*-identityʳ)
open import AKS.Nat.Properties using (0≤n; ≤-refl; m≤m+n; *-mono-≤; module ≤-Reasoning)
open... | {
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{-# OPTIONS --without-K #-}
module Lecture6 where
import Lecture5
open Lecture5 public
-- Section 6.1 Contractible types
is-contr : {i : Level} → UU i → UU i
is-contr A = Sigma A (λ a → (x : A) → Id a x)
center : {i : Level} {A : UU i} → is-contr A → A
center (dpair c C) = c
-- We make sure that the contraction i... | {
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{-# OPTIONS --without-K --safe #-}
open import Algebra.Construct.DirectProduct
module Construct.DirectProduct where
open import Algebra
import Algebra.Construct.DirectProduct as DirectProduct
open import Data.Product
open import Data.Product.Relation.Binary.Pointwise.NonDependent
open import Level using (Level; _⊔_)... | {
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{-# OPTIONS --without-K #-}
open import Base
module Homotopy.PullbackDef where
record pullback-diag (i : Level) : Set (suc i) where
constructor diag_,_,_,_,_
field
A : Set i
B : Set i
C : Set i
f : A → C
g : B → C
pullback-diag-raw-eq : ∀ {i} {A A' : Set i} (p : A ≡ A')
{B B' : Set i} (q :... | {
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-- Module shadowing using generated modules for records and datatypes
module Issue260b where
module R where
record R : Set where
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module UniDB.Subst.StarPrime where
open import UniDB.Subst.Core
open import UniDB.Morph.StarPrime
open import UniDB.Morph.Depth
module _
{T : STX} {{vrT : Vr T}} {{wkT : Wk T}} {{apTT : Ap T T}}
{Ξ : MOR} {{lkTΞ : Lk T Ξ}}
where
mutual
instance
iLkStar* : Lk T (Star* Ξ)
lk {{iLkStar*}} refl ... | {
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-- Basic intuitionistic propositional calculus, without ∨ or ⊥.
-- Hilbert-style formalisation of syntax.
-- Nested terms.
module BasicIPC.Syntax.Hilbert where
open import BasicIPC.Syntax.Common public
-- Derivations.
infix 3 _⊢_
data _⊢_ (Γ : Cx Ty) : Ty → Set where
var : ∀ {A} → A ∈ Γ → Γ ⊢ A
app : ∀... | {
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------------------------------------------------------------------------
-- Small parser combinator library used by Mixfix.Acyclic.Grammar
------------------------------------------------------------------------
-- Note that while Mixfix.Acyclic.Lib and Mixfix.Cyclic.Lib may appear
-- to be very similar, there are som... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- A Categorical view of the Sum type (Left-biased)
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Level
module Data.Sum.Categorical.Left {... | {
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{-# REWRITE #-}
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... |
{-# OPTIONS --without-K --exact-split --allow-unsolved-metas #-}
module SAT-solver where
import 14-univalence
open 14-univalence public
{- The literates are atomic propositions or negations thereof. We simply use
the natural numbers to encode the atomic propositions, and we use the
booleans to tell whether i... | {
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open import Data.Product using ( _,_ )
open import Data.Unit using ( ⊤ ; tt )
open import FRP.LTL.ISet.Core using ( ISet ; [_] ; _,_ )
module FRP.LTL.ISet.Unit where
T : ISet
T = [ (λ i → ⊤) , (λ i j i~j t → (tt , tt)) , (λ i j i⊑j t → tt) ]
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Extensional pointwise lifting of relations to vectors
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Vec.Relation.Binary.Pointwise.Extens... | {
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module IPC.Metatheory.Hilbert-BasicTarski where
open import IPC.Syntax.Hilbert public
open import IPC.Semantics.BasicTarski public
-- Soundness with respect to all models, or evaluation.
eval : ∀ {A Γ} → Γ ⊢ A → Γ ⊨ A
eval (var i) γ = lookup i γ
eval (app t u) γ = (eval t γ) (eval u γ)
eval ci γ = I
eval c... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Definition
open import Groups.Abelian.Definition
open import Groups.FiniteGroups.Definition
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Numbers.Naturals.Order.Lemmas
open import Se... | {
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------------------------------------------------------------------------------
-- Group theory properties
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# O... | {
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{-# OPTIONS --safe --experimental-lossy-unification #-}
module Cubical.Algebra.Ring.Properties where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Equiv.HalfAdjoint
open import Cubical.Foundations.HLevels
open impo... | {
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module SystemF.Everything where
open import SystemF.Syntax public
open import SystemF.WellTyped public
open import SystemF.Substitutions.Lemmas public
open import SystemF.Substitutions public
open import SystemF.NormalForm public
open TypeLemmas public hiding (var)
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data Nat : Set where
zero : Nat
suc : Nat → Nat
test : ∀{N M : Nat} → Nat → Nat → Nat
test N M = {!.N N .M!}
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module nodcap.NF.Show where
open import Data.String using (String)
open import nodcap.Base
open import nodcap.NF.Typing
import nodcap.Show as S
showTerm : {Γ : Environment} → ⊢ⁿᶠ Γ → String
showTerm {Γ} x = S.showTerm (fromNF x)
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{-# OPTIONS --without-K --safe #-}
-- This module shows that D<: typing is undecidable.
module DsubTermUndec where
open import Data.List as List
open import Data.List.All as All
open import Data.Nat as ℕ
open import Data.Maybe as Maybe
open import Data.Product
open import Data.Sum
open import Data.Empty renaming (⊥ t... | {
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{-# OPTIONS --warning=error --safe --without-K --guardedness #-}
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import LogicalFormulae
open import Numbers.Integers.Integers
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Subtraction
open import Numbers.Naturals.Naturals
open import ... | {
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{-
This second-order signature was created from the following second-order syntax description:
syntax Monoid | M
type
* : 0-ary
term
unit : * | ε
add : * * -> * | _⊕_ l20
theory
(εU⊕ᴸ) a |> add (unit, a) = a
(εU⊕ᴿ) a |> add (a, unit) = a
(⊕A) a b c |> add (add(a, b), c) = add (a, add(b, c))
-}
mod... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.Prelude
open import Level using (0ℓ)
-- This modu... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
module Haskell.Modules.Eq where
open import Haskell.Modules.ToBool
---... | {
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{-# OPTIONS --without-K --safe #-}
module Cats.Category.Cat.Facts.Exponential where
open import Data.Product using (_,_)
open import Level using (_⊔_)
open import Relation.Binary using (IsEquivalence)
open import Cats.Bifunctor using
(Bifunctor ; Bifunctor→Functor₁ ; transposeBifunctor₁ ; transposeBifunctor₁-resp)
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module OlderBasicILP.Indirect.Translation where
open import OlderBasicILP.Indirect public
import OlderBasicILP.Indirect.Hilbert.Sequential as HS
import OlderBasicILP.Indirect.Hilbert.Nested as HN
import OlderBasicILP.Indirect.Gentzen as G
open HS using () renaming (_⊢×_ to HS⟨_⊢×_⟩ ; _⊢_ to HS⟨_⊢_⟩) public
open HN u... | {
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{-# OPTIONS --allow-unsolved-metas #-}
open import Agda.Builtin.Nat
open import Agda.Builtin.Equality
data _≅_ {A : Set} (x : A) : {B : Set} → B → Set where
refl : x ≅ x
test₁ : (A : Set) (x y : A) (z : Nat) → x ≡ y → x ≅ (suc z) → y ≅ 1 → Nat
test₁ A (suc z) (suc zero) .z refl refl refl = {!!}
test₂ : (A : Set) ... | {
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open import Nat
open import Prelude
open import List
open import contexts
open import unions
module core where
-- types
data typ : Set where
_==>_ : typ → typ → typ
⟨⟩ : typ
⟨_×_⟩ : typ → typ → typ
D[_] : Nat → typ
-- arrow type constructors bind very tightly
infixr 25 _==>_
-- type co... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
module ClassicalLogic.ClassicalFive where
em = {A : Set} → (A || (A → False))
dne = {A : Set} → ((A → False) → False) → A
peirce = {A B : Set} → ((A → B) → A) → A
iad = {A B : Set} → (A → B) → ((A → False) || B)
dem = {A B : Set} → (((A ... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.ImplShared.Base.Types
open import LibraBFT.Abstra... | {
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module NativeInt where
open import Data.Integer.Base hiding (_+_)
postulate
Int : Set
toInt : ℤ -> Int
fromInt : Int -> ℤ
{-# COMPILE GHC Int = type Int #-}
{-# COMPILE GHC toInt fromInteger #-}
{-# COMPILE GHC fromInt toInteger #-}
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module Numeral.Natural.Oper.FlooredDivision.Proofs.DivisibilityWithRemainder where
open import Data
open import Functional
open import Numeral.Finite
import Numeral.Finite.Proofs as 𝕟
open import Numeral.Natural
open import Numeral.Natural.Oper
open import Numeral.Natural.Oper.FlooredDivision
open import Numeral... | {
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module Miscellaneous.HeterogenousId where
import Lvl
open import Logic
open import Logic.Propositional
open import Functional
open import Type
-- TODO: Will this work for getting function extensionality? Probably not?
data IdFn {ℓ} : ∀{T : Type{ℓ}} → T → T → Stmt{Lvl.𝐒(ℓ)} where
IdFn-intro : ∀{T}{x : T} → (Id... | {
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-- The part up to "data D" could be replaced by "open import
-- Common.Prelude", but at the time of writing that seems to slow down
-- the test by something like a factor of two or three (for the GHC
-- backend, on one system).
open import Agda.Builtin.IO
open import Agda.Builtin.String
open import Agda.Builtin.Unit
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Function setoids and related constructions
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Function.Equality where
import Function as Fun
open... | {
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{-# OPTIONS --allow-unsolved-metas #-}
open import Prelude hiding (⊤)
module Control.Monad.Free.State {ℓ} (S : Type ℓ) (isSetS : isSet S) where
open import Control.Monad.Free.Quotiented
open import Data.Unit.UniversePolymorphic
open import Algebra
open import Data.List
open import Data.List.Syntax
data StateF (A : ... | {
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module my-list where
open import level
open import bool
open import eq
open import maybe
open import nat
open import nat-thms
open import product-thms
open import product
data 𝕃 {ℓ} (A : Set ℓ) : Set ℓ where
[] : 𝕃 A
_::_ : (x : A) (xs : 𝕃 A) → 𝕃 A
{-# BUILTIN LIST 𝕃 #-}
{-# BUILTIN NIL [] #-}
{-# BUILTI... | {
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open import Agda.Builtin.Nat
open import Agda.Builtin.Sigma
open import Agda.Builtin.Equality
it : ∀ {a} {A : Set a} {{_ : A}} → A
it {{p}} = p
f : (a {b} {{c}} : Nat) → Nat
f = λ a {b} → it
g : (a b@(c , d) (e , f) : Σ Nat (λ _ → Nat)) → Nat
g = λ a b@(c , d) x@(e , _) → f (fst a) {d} {{e}}
h : ∀ {a} (b@(c , d) : ... | {
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{-
This module converts between the path types and the inductively
defined equality types.
-}
{-# OPTIONS --safe #-}
module Cubical.Data.Equality where
open import Cubical.Foundations.Prelude public
hiding ( _≡_ ; _≡⟨_⟩_ ; _∎ ; isPropIsContr)
renaming ( refl to reflPath
; transport to transportP... | {
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-- Andreas, issue #2482, reported by Guillaume Allais
-- Internal error because of wrong value for
-- number of parameters for data type.
-- {-# OPTIONS -v tc.data.sort:50 #-}
-- {-# OPTIONS -v tc.term.con:50 #-}
data D {b} (B : Set b) : Set b
-- This used to falsely compute the number of parameters to 1
data D B w... | {
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module UniDB.Morph.Sub where
open import UniDB.Spec
open import UniDB.Morph.Depth
--------------------------------------------------------------------------------
data Single (T : STX) : MOR where
single : {γ : Dom} (t : T γ) → Single T (suc γ) γ
instance
iLkSingle : {T : STX} {{vrT : Vr T}} → Lk T (Single T)
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-- Andreas, 2022-06-14, issue #4725 reported by nad
-- The termination checker needs to recognize
-- dotted variable and record patterns as patterns
-- for this example to pass.
-- These should be harmless even with --cubical
-- (dotted constructor patterns are not, see #4606).
-- Keep fingers crossed.
{-# OPTIONS --... | {
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module examplesPaperJFP.safeFibStackMachineObjectOriented where
open import Data.Nat
open import Data.List
open import Data.Vec
open import Data.Sum
open import Data.Fin renaming (_+_ to _+f_)
open import Data.Product
open import examplesPaperJFP.StatefulObject
open import examplesPaperJFP.StackBisim
open import exam... | {
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-- Andreas, 2021-09-06, issue #5545,
-- regression introduced by #5522 (fix for #5291).
--
-- Note: this test requires that there is no newline at the end of file.
-- So, it violates the whitespace requirement of fix-whitespace,
-- and needs to be an exception in the configuration of fix-whitespace.
{-# OPTIONS --allo... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.Prelude
import Data.Vec.Relation.Unary.All as ... | {
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module ZTF where
infixr 40 _◎_
open import Data.Integer
open import Data.Product
open import Relation.Binary.PropositionalEquality
------------------------------------------------------------------------------
-- Zero totalized fields
data B : Set where
ZERO : B
ONE : B
PLUS : B → B → B
TIMES : B ... | {
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------------------------------------------------------------------------
-- The unit type (in Set₁)
------------------------------------------------------------------------
module Data.Unit1 where
record ⊤₁ : Set₁ where
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{-# OPTIONS --without-K #-}
open import lib.Basics
open import lib.types.Pi
open import lib.types.Paths
open import lib.types.Sigma
module lib.types.Flattening {i j k}
(A : Type i) (B : Type j) (f g : B → A)
(C : A → Type k) (D : (b : B) → C (f b) ≃ C (g b)) where
{- The base HIT -}
import lib.types.Generic1HIT... | {
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{-
Definition of what it means to be a notion of relational structure
-}
{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Foundations.RelationalStructure where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.HLevels
open import Cubical.Fo... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.Relation.Nullary where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Data.Empty
private
variable
ℓ : Level
A : Type ℓ
-- Negation
infix 3 ¬_
¬_ : Type ℓ → Type ℓ
¬ A = A → ⊥
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