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|---|---|
{-# OPTIONS --without-K --safe #-}
open import Categories.Category
module Categories.Diagram.Equalizer.Properties {o ℓ e} (C : Category o ℓ e) where
open import Categories.Diagram.Equalizer C
open import Categories.Morphism C
open import Categories.Morphism.Reasoning C
private
module C = Category C
open C
va... | {
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-- {-# OPTIONS --sized-types --show-implicit #-}
module _ where
open import Common.Size
data Either (A B : Set) : Set where
left : A → Either A B
right : B → Either A B
caseEither : ∀{A B C : Set} → Either A B → (A → C) → (B → C) → C
caseEither (left a) l r = l a
caseEither (right b) l r = r b
data Nat {i :... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Homomorphism proofs for exponentiation over polynomials
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Tactic.RingSolver.Core.Polynomial.... | {
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{-# OPTIONS --allow-unsolved-metas #-}
open import Agda.Primitive using (lzero; lsuc; _⊔_)
open import Relation.Binary.PropositionalEquality using (_≡_; refl; sym; trans; cong; subst; setoid)
open import Data.Product using (_×_; Σ; _,_; proj₁; proj₂; zip; map; <_,_>; swap)
import Function.Equality
open import Relation... | {
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module StateSized.GUI.ShipBitMap where
open import StateSizedIO.GUI.WxBindingsFFI
ship : Bitmap
ship = bitmap "./StateSized/GUI/ship.ico"
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module NativePolyIO where
open import Data.String.Base using (String) public
open import Level
record Unit {α} : Set α where
constructor unit
{-# HASKELL type AgdaUnit a = () #-}
{-# COMPILED_DATA Unit AgdaUnit () #-}
postulate
NativeIO : ∀ {ℓ} → Set ℓ → Set ℓ
nativeReturn : ∀ {a} {A : Set a} → A → NativeIO... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Products of nullary relations
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Relation.Nullary.Product where
open import Data.Bool.Base
open i... | {
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module Issue512 where
postulate
Level : Set
{-# BUILTIN LEVEL Level #-}
data _≡_ {a} {A : Set a} (x : A) : A → Set a where
refl : x ≡ x
{-# BUILTIN EQUALITY _≡_ #-}
{-# BUILTIN REFL refl #-}
data A : Set where
a b : A
proof : a ≡ a
proof = refl
f : A → A → A
f x y rewrite proof = ? -- gave error below (no... | {
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module Operations.Stateful where
import Data.Bool as B
open import Data.Fin
open import Data.Nat
open import Data.Vec hiding (head; tail)
open import Function
open import Relation.Binary.PropositionalEquality
open import Eval
open import Operations.Combinatorial
open import Types
alternator : Closed 𝔹 → Closed... | {
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module Categories.Initial where
open import Library
open import Categories
open import Categories.Sets
open Cat
record Init {a b} (C : Cat {a}{b})(I : Obj C) : Set (a ⊔ b) where
constructor init
field i : ∀{X} → Hom C I X
law : ∀{X}{f : Hom C I X} → i {X} ≅ f
ZeroSet : Init Sets ⊥
ZeroSet = record {i = ... | {
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-- Andreas, 2015-07-07 continuation of issue 665
-- Jesper, 2015-12-18 some of these don't work anymore with the new unifier,
-- but a few others that weren't accepted are now.
{-# OPTIONS --show-implicit #-}
-- {-# OPTIONS -v tc.with.strip:10 #-}
-- {-# OPTIONS -v tc.with.strip:60 -v tc.lhs:20 -v tc.lhs.unify:20 #-}... | {
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{-# OPTIONS --without-K --safe #-}
open import Level
open import Categories.Category using () renaming (Category to Setoid-Category)
open import Categories.Category.Monoidal using (Monoidal)
module Categories.Bicategory.Instance.EnrichedCats
{o ℓ e} {V : Setoid-Category o ℓ e} (M : Monoidal V) (v : Level) where
--... | {
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{-# OPTIONS --cubical --no-import-sorts #-}
open import Cubical.Foundations.Everything renaming (_⁻¹ to _⁻¹ᵖ; assoc to ∙-assoc)
open import Cubical.Relation.Nullary.Base renaming (¬_ to ¬ᵗ_)-- ¬ᵗ_
open import Cubical.Relation.Binary.Base
open import Cubical.Data.Sum.Base renaming (_⊎_ to infixr 4 _⊎_)
open import Cub... | {
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import Lvl
open import Type
module Type.Singleton.Proofs {ℓ : Lvl.Level} {X : Type{ℓ}} where
open import Functional
open import Function.Domains
open import Logic.Predicate
open import Relator.Equals
open import Relator.Equals.Proofs
open import Type.Properties.Empty
open import Type.Singleton
open import Type.P... | {
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module _ {a} {A : Set a} where
open import Agda.Builtin.Equality
open import Agda.Builtin.List
infix 4 _⊆_
postulate
_⊆_ : (xs ys : List A) → Set a
⊆-trans : ∀{xs ys zs} → xs ⊆ ys → ys ⊆ zs → xs ⊆ zs
private
variable
xs ys zs : List A
σ τ : ys ⊆ zs
x y : A
x≈y : x ≡ y
lemma : ∀ us (ρ : us ⊆ z... | {
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module B where
open import A
B : Set
B = A
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Nondependent heterogeneous N-ary products
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Product.Nary.NonDependent where
---------------... | {
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module Numeral.Finite.Category where
open import Functional
import Lvl
open import Numeral.Finite
open import Numeral.Natural
open import Type
open import Syntax.Function
-- Equality category on the type of finite natural numbers.
module _ where
open import Relator.Equals
open import Relator.Equals.Proofs.Eq... | {
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{-# OPTIONS --without-K --safe #-}
open import Definition.Typed.EqualityRelation
module Definition.LogicalRelation.Properties.Neutral {{eqrel : EqRelSet}} where
open EqRelSet {{...}}
open import Definition.Untyped
open import Definition.Untyped.Properties
open import Definition.Typed
open import Definition.Typed.Pro... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.types.Coproduct
open import lib.types.Paths
open import lib.types.Pointed
open import lib.types.Pushout
open import lib.types.PushoutFlattening
open import lib.types.PushoutFmap
open import lib.types.Sigma
open import lib.types.Span
open im... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Instance.StrictCats where
-- The (large) 'strict' category of (small) categories.
-- The difference here is that _≈_ is not |NaturalIsomorphism| but |_≈F_|
open import Level
open import Relation.Binary.PropositionalEquality using (refl)
open import Catego... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Ideals.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.Ideals.Prime.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_... | {
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-- {-# OPTIONS -v interaction:100 #-}
module Issue810 where
record T (A : Set) : Set where
constructor mkT
field unT : A
introHid : {A : Set} → T A
introHid = {!!}
data Sg {A : Set} : A → Set where
sg : (a : A) → Sg a
intro : ∀ {A}{a : A} → Sg a
intro = {!!}
intro′ : ∀ {A}(a : A) → Sg a
intro′ = {!!}
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{-# OPTIONS --without-K --safe #-}
module Definition.Typed.Consequences.InverseUniv where
open import Definition.Untyped
open import Definition.Typed
open import Definition.Typed.Consequences.Syntactic
import Tools.Sum as Sum
open import Tools.Sum using (_⊎_; inj₁; inj₂)
open import Tools.Product
open import Tools.E... | {
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{-# OPTIONS --cubical #-}
module Erased-cubical-Open-public.Cubical where
-- It instantiates and exports code from
-- Erased-cubical-Open-public.Erased.
open import Erased-cubical-Open-public.Erased Set public
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{-
The flattening lemma for pushouts (Lemma 8.5.3 in the HoTT book) proved in a cubical style.
The proof in the HoTT book (the core lying in Lemma 6.12.2, the flattening lemma for coequalizers)
consists mostly of long strings of equalities about transport. This proof follows almost
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module Issue794a where
open import Common.Prelude
open import Common.MAlonzo
postulate A : Set
id : .A → A → A
id x y = y
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{- Definition of vectors. Inspired by the Agda Standard Library -}
{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Data.Vec.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Nat
open import Cubical.Data.FinData
private
variable
ℓ ℓ' : Level
A : Type ℓ
infixr 5... | {
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{-# OPTIONS --without-K #-}
module HIT.Interval where
open import PathOperations
open import PathStructure.Id.Tr
open import Types
module I-Definition where
private
data #I : Set where
#0 : #I
#1 : #I
I : Set
I = #I
0ᵢ : I
0ᵢ = #0
1ᵢ : I
1ᵢ = #1
postulate
seg : 0ᵢ ≡ 1ᵢ
I-ind... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Some properties of equivalence closures.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Relation.Binary.Construct.Closure.Equivalence.Properti... | {
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module Bin-predicates where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; sym; cong)
open Eq.≡-Reasoning
open import Data.Nat using (ℕ; zero; suc; _+_; _*_)
open import Data.Nat.Properties using (+-identityʳ; +-suc; +-assoc; +-comm)
-- 2進数の表現
data Bin : Set where
⟨⟩ : Bin
_O : Bin →... | {
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module Issue1258-2 where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
data _==_ {A : Set}(x : A) : A -> Set where
refl : x == x
data Bool : Set where
true false : Bool
data Σ (A : Set) (B : A → Set) : Set where
_,_ : (x : A) → B x → Σ A B
_×_ : Set → Set → Set
A × B = Σ A (λ _ → B)
postulate f ... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Structures for types of functions
------------------------------------------------------------------------
-- The contents of this file should usually be accessed from `Function`.
{-# OPTIONS --without-K --safe... | {
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-- Andreas, 2016-07-28, issue #779
record P : Set where
postulate Bla : Set
field F : Set
-- Current error:
-- Missing definition for Bla
-- Expected:
-- Success, or error outlawing postulate before last field.
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{-
This is a HoTT-UF core library based on cubical type theory, where the
cubical machinery is hidden, using the HoTT Book terminology and
notation.
The point is that function extensionality, propositional truncation
and univalence compute (an example is given below).
For the moment, this requires the development ve... | {
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module Logic.Relations where
import Logic.Base
import Data.Bool
Rel : Set -> Set1
Rel A = A -> A -> Set
Reflexive : {A : Set} -> Rel A -> Set
Reflexive {A} _R_ = (x : A) -> x R x
Symmetric : {A : Set} -> Rel A -> Set
Symmetric {A} _R_ = (x y : A) -> x R y -> y R x
Transitive : {A : Set} -> Rel A -> Set
Transitiv... | {
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{- -}
-- starting from builtins
-- forgot what the point of this was...
module Oscar.Data6 where
open import Oscar.Category.Semigroupoid
open import Oscar.Category.Category
open import Oscar.Category.Morphism
open import Oscar.Category.Setoid
open import Oscar.Function
open import Agda.Builtin.Unit using () renaming... | {
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-- Currently postulates are not allowed in mutual blocks.
-- This might change.
module PostulateInMutual where
mutual
postulate A : Set
postulate B : Set
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{-# OPTIONS --without-K --rewriting #-}
module Conaturals where
open import Basics
open import Bool
open import lib.Basics
open import lib.types.Nat
open import lib.types.Bool
{-
_is-increasing-b : (ℕ → Bool) → Type _
P is-increasing-b = (n m : ℕ) → n ≤ m → (P n) holds-b → (P m) holds-b
increasing... | {
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module help where
open import univ
open import Base
-- Prelims
infixl 150 _#_
K : {A : S} -> S -> Fam A
K B = fam (\_ -> B) (\_ -> refS)
_#_ : {A : S}{F : Fam A} -> El (pi A F) -> (x : El A) -> El (F ! x)
el < f , _ > # x = f x
pFun : {A : S}{F : Fam A}(f : El (pi A F)){x y : El A}(x=y : x == y) ->
f # x =... | {
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{-# OPTIONS --without-K --safe #-}
module Definition.Conversion.Transitivity where
open import Definition.Untyped
open import Definition.Typed
open import Definition.Typed.Properties
open import Definition.Typed.RedSteps
open import Definition.Conversion
open import Definition.Conversion.Soundness
open import Definit... | {
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module Test where
import Lvl
{- TODO: Unsolved metas
module NumAndDivisionProofs where
open import Functional
open import Logic.Propositional{Lvl.𝟎}
open import Logic.Convenience{Lvl.𝟎}
open import Numeral.Natural
open import Numeral.Natural.Oper
open import Numeral.Natural.Relation
open import Numera... | {
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{-# OPTIONS --type-in-type --without-K #-}
{- Semi-simplicial types: A small demonstration that the "usual approach"
works if we postulate the required coherence for the functorial behaviour
of the "Skeleton" functor.
This coherence can be achieved in a 2-level system, where the required
functor law can b... | {
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record R : Set₁ where
field
_A : Set
P : Set → Set₁
P R.A = Set
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Data.Vec.Properties where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Univalence
import Cubical.Data.Empty as ⊥
open import Cubical.Data.Nat
o... | {
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open import Agda.Primitive using (_⊔_ ; lsuc ; Level)
import Categories.Category as Category
import Categories.Category.Cartesian as Cartesian
open import Categories.Object.Terminal using (Terminal)
open import Categories.Object.Product using (Product)
open import MultiSorted.AlgebraicTheory
open import MultiSorted.S... | {
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-- Andreas, 2017-08-14, issue #2682, test case by Ulf
-- WAS: CheckInternal treats abstract projections as not in scope,
-- while the type checker allows them.
-- Adapted solution: allow also in CheckInternal
-- {-# OPTIONS -v tc.rec.proj:20 #-}
-- {-# OPTIONS -v tc.deftype:25 #-}
-- {-# OPTIONS -v tc:20 #-}
abstra... | {
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module CoprodMonad where
open import functor
open import monad
data PlusT (t₁ t₂ : Set → Set) (a : Set) (p₁ : Triple t₁)(p₂ : Triple t₂) : Set where
T₁ : (t₁ (PlusT t₁ t₂ a p₁ p₂)) → PlusT t₁ t₂ a p₁ p₂
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{-# OPTIONS --safe #-}
module Cubical.Categories.Instances.CommRings where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Structure
open import Cubical.Data.Unit
open import Cubical.Data.Sigma
open import Cubica... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.HITs.AssocList.Properties where
open import Cubical.HITs.AssocList.Base as AL
open import Cubical.Foundations.Everything
open import Cubical.HITs.FiniteMultiset as FMS
open import Cubical.Data.Nat using (ℕ; zero; suc; _+_)
private
variable
ℓ : Level
A : Type... | {
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module Agda.Builtin.FromString where
open import Agda.Primitive
open import Agda.Builtin.String
record IsString {a} (A : Set a) : Set (lsuc a) where
field
Constraint : String → Set a
fromString : (s : String) {{_ : Constraint s}} → A
open IsString {{...}} public using (fromString)
{-# BUILTIN FROMSTRING ... | {
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{-# OPTIONS --cubical --safe #-}
module Data.Tree.Braun where
open import Prelude
open import Data.Nat
data Bal (n : ℕ) : ℕ → ℕ → Type where
one : Bal n n (1 + n * 2)
two : Bal n (suc n) (2 + n * 2)
data Tree {a} (A : Type a) : ℕ → Type a where
leaf : Tree A 0
node : ∀ {n m r} → (bal : Bal n m r) → A ... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- A solver for proving that one list is a sublist of the other.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Relation.Binary using (Rel; ... | {
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open import Relation.Binary.Core
module TreeSort.Everything {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_)
(trans≤ : Transitive _≤_) where
open import TreeSort.Impl1.Correctness.Order _≤_ tot≤ trans≤
open import TreeSort.Impl1.Correctness.Permutation _≤_ tot≤
o... | {
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------------------------------------------------------------------------
-- The reflexive transitive closures of McBride, Norell and Jansson
------------------------------------------------------------------------
-- This module could be placed under Relation.Binary. However, since
-- its primary purpose is to be used... | {
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open import Agda.Builtin.Bool
open import Agda.Builtin.Equality
idTrue : ∀ b → b ≡ true → Bool
idTrue b eq = {!!}
-- C-c C-c b RET gives us:
-- idTrue false eq = {!!}
-- idTrue true eq = {!!}
-- Now that we can leave `idTrue false eq` out because it's
-- trivially an impossible clause, it'd be nice to only get:
-- i... | {
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{-# OPTIONS --prop --without-K --rewriting #-}
module Calf.Types.List where
open import Calf.Prelude
open import Calf.Metalanguage
open import Data.List public using (List; []; _∷_; _∷ʳ_; [_]; length; _++_)
list : tp pos → tp pos
list A = U (meta (List (val A)))
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{-# OPTIONS --rewriting --allow-unsolved-metas #-}
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Rewrite
postulate
I : Set
A : I → Set
HEq : (i0 i1 : I) → A i0 → A i1 → Set
HEq-on-refl : (i : I) (a0 a1 : A i) → HEq i i a0 a1 ≡ I
{-# REWRITE HEq-on-refl #-}
record Con : Set where
field... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Code for converting Vec A n → B to and from n-ary functions
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Vec.N-ary where
open import D... | {
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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 LibraBFT.Concrete.Obligations
o... | {
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module empty where
----------------------------------------------------------------------
-- datatypes
----------------------------------------------------------------------
data ⊥ : Set where
----------------------------------------------------------------------
-- syntax
-------------------------------------------... | {
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module Dave.Equality where
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
infix 4 _≡_
{-# BUILTIN EQUALITY _≡_ #-}
sym : ∀ {A : Set} {x y : A} → x ≡ y → y ≡ x
sym refl = refl
trans : ∀ {A : Set} {x y z : A} → x ≡ y → y ≡ z → x ≡ z
trans refl b = b
cong : ∀ {A B : Set} (f : A → B) {x ... | {
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{-# OPTIONS --universe-polymorphism #-}
module UniversePolymorphicIO where
open import Common.Level
postulate
IO : ∀ {ℓ} → Set ℓ → Set ℓ
{-# IMPORT UniversePolymorphicIO #-}
{-# COMPILED_TYPE IO UniversePolymorphicIO.AgdaIO #-}
{-# BUILTIN IO IO #-}
postulate
return : ∀ {a} {A : Set a} → A → IO A
_>>=_ : ∀ ... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.Algebra.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Equiv.HalfAdjoint
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Function
o... | {
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open import Common.Prelude
open import Common.Reflect
module TermSplicing1 where
x = unquote Set
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{-# OPTIONS --prop --without-K --rewriting #-}
-- The basic CBPV metalanguage.
open import Calf.CostMonoid
module Calf.Metalanguage where
open import Calf.Prelude
open import Relation.Binary.PropositionalEquality
open import Data.Product
postulate
mode : □
pos : mode
neg : mode
tp : mode → □
val : tp po... | {
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open import Mockingbird.Forest using (Forest)
module Mockingbird.Forest.Combination.Vec.Base {b ℓ} (forest : Forest {b} {ℓ}) where
open import Data.Fin using (Fin; zero; suc; #_)
open import Data.Nat using (ℕ; zero; suc)
open import Data.Nat.Properties using (_≤?_)
open import Data.Vec as Vec using (Vec; _∷_)
open im... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Injections
------------------------------------------------------------------------
module Function.Injection where
open import Function as Fun using () renaming (_∘_ to _⟨∘⟩_)
open import Level
open import Rel... | {
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open import Oscar.Prelude
open import Oscar.Class
module Oscar.Class.Quadricity where
module Quadricity
{𝔞} {𝔄 : Ø 𝔞}
{𝔟} {𝔅 : Ø 𝔟}
{ℓ} (_↦_ : 𝔅 → 𝔅 → Ø ℓ) (let infix 4 _↦_; _↦_ = _↦_)
(_∧_ : 𝔅 → 𝔅 → 𝔅) (let infixr 15 _∧_; _∧_ = _∧_)
(_∼_ : 𝔄 → 𝔄 → 𝔅) (let infix 18 _∼_; _∼_ = _∼_)
(_⊛_ : 𝔄... | {
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module Data.Num.Redundant where
-- Base: 2
-- Digit: { 0, 1, 2 }
--
-- Numeral System which maxports efficient addition, substraction
-- and arithmetic shift.
open import Data.List using (List ; []; _∷_) public
open import Data.Nat renaming (_+_ to _+ℕ_; _<_ to _<ℕ_)
open import Data.Num.Bij
open import Data.Emp... | {
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module Data.Vec.Membership.Propositional.Distinct where
open import Data.Vec as Vec using (Vec; []; _∷_; _++_)
open import Data.Vec.Membership.Propositional
open import Data.Vec.Any hiding (map; index; head; tail)
open import Data.List as List using (List)
open import Relation.Binary.PropositionalEquality as P using... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.Data.DiffInt.Base where
open import Cubical.Foundations.Prelude
open import Cubical.HITs.SetQuotients.Base
open import Cubical.Data.Prod
open import Cubical.Data.Nat
rel : (ℕ ×Σ ℕ) → (ℕ ×Σ ℕ) → Type₀
rel (a₀ , b₀) (a₁ , b₁) = x ≡ y
where
x = a₀ + b₁
y = a₁ +... | {
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module SystemF.Substitutions where
open import Prelude hiding (subst)
open import SystemF.Syntax
open import Data.Fin.Substitution
open import Data.Star hiding (map)
open import Data.Vec hiding ([_])
open import SystemF.Substitutions.Types public
module TermTypeSubst where
module TermTypeApp {T} (l : Lift T Type)... | {
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{-
Theory about isomorphisms
- Definitions of [section] and [retract]
- Definition of isomorphisms ([Iso])
- Any isomorphism is an equivalence ([isoToEquiv])
-}
{-# OPTIONS --cubical --safe #-}
module Cubical.Foundations.Isomorphism where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
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module PiNF-syntax where
infixr 30 _⟷_
infixr 20 _◎_
------------------------------------------------------------------------------
-- First we define a universe of our value types
data B : Set where
ZERO : B
ONE : B
PLUS : B → B → B
NEG : B → B
TIMES : B → B → B
RECIP : B → B
--------------------... | {
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module Human.Maybe where
data Maybe (A : Set) : Set where
just : A -> Maybe A
nothing : Maybe A
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module Issue2575 where
import Issue2575.M
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module Issue373 where
data ⊤ : Set where
tt : ⊤
{-# COMPILED_DATA ⊤ () () #-}
data ℕ : Set where
zero : ℕ
suc : (n : ℕ) → ℕ
{-# BUILTIN NATURAL ℕ #-}
{-# IMPORT Imports.Nat #-}
data List (A : Set) : Set where
[] : List A
_∷_ : A → List A → List A
{-# BUILTIN LIST List #-}
{-# BUILTIN NIL [] #... | {
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module BuiltinMustBeConstructor where
data Nat : Set where
zero : Nat
one : Nat
suc : Nat -> Nat
suc x = x
{-# BUILTIN NATURAL Nat #-}
{-# BUILTIN SUC suc #-}
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{-# OPTIONS --without-K --safe #-}
module Categories.Functor.Construction.Zero where
-- The Zero functor maps everything to the initial object of a
-- category (when it exists). Note quite const.
open import Level
open import Categories.Category
open import Categories.Functor using (Functor)
open import Categories.O... | {
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{-
Theory about equivalences (definitions are in Core/Glue.agda)
- isEquiv is a proposition ([isPropIsEquiv])
- Any isomorphism is an equivalence ([isoToEquiv])
There are more statements about equivalences in Equiv/Properties.agda:
- if f is an equivalence then (cong f) is an equivalence
- if f is an equivalence th... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Definitions used in the reflection machinery
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Reflection.Definition where
open import Data.List... | {
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{-# OPTIONS --without-K --safe #-}
-- Quicksort
module Experiment.Induction where
-- agda-stdlib
open import Level
open import Data.List
open import Data.Product
open import Data.Nat as ℕ
open import Data.Nat.Induction as Ind
open import Relation.Binary as B
open import Relation.Unary as U
import Relation.Unary... | {
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module Syntacticosmos (Gnd : Set)(U : Set)(El : U -> Set) where
open import Basics
open import Pr
open import Nom
import Kind
open Kind Gnd U El public
import Cxt
open Cxt Kind public
import Loc
open Loc Kind public
import Term
open Term Gnd U El public
import Shift
open Shift Gnd U El public
import Eta
open Eta Gnd U... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.MonoidSolver.Examples where
open import Cubical.Foundations.Prelude
open import Cubical.Algebra.Monoid.Base
open import Cubical.Algebra.CommMonoid.Base
open import Cubical.Algebra.MonoidSolver.Reflection
private
variable
ℓ : Level
module ExamplesMonoid (M : Monoi... | {
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-- Andreas, 2019-02-17, issue #3417
--
-- We want to see highlighting for all the warnings,
-- even if the last thing is a hard error.
open import Agda.Builtin.Nat
reachable : Nat → Nat
reachable zer = 0
reachable (suc n) = suc (reachable n)
coverage : Nat → Nat
coverage zero = zero
Termination : Set
Termination = ... | {
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{-# OPTIONS --without-K #-}
open import Prelude
open import GSeTT.Syntax
open import GSeTT.Rules
open import GSeTT.Uniqueness-Derivations
module MCaTT.Desuspension where
↓GC : ∀ (Γ : Pre-Ctx) → Γ ⊢C → Pre-Ctx
↓GT : ∀ (Γ : Pre-Ctx) (A : Pre-Ty) → Γ ⊢T A → Pre-Ty
↓Gt : ∀ (Γ : Pre-Ctx) (A : Pre-Ty) (x : ℕ) → Γ ⊢... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Species.Constructions where
-- Construction of basic species
open import Level
open import Data.Empty
open import Data.Fin.Base as Fin using (Fin)
open import Data.Fin.Properties using (¬Fin0)
open import Data.Fin.Permutation using (↔⇒≡)
open import Data.N... | {
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{-# OPTIONS --without-K --safe #-}
module Data.Binary.Proofs.Semantics where
open import Relation.Binary.PropositionalEquality
open import Data.Binary.Operations.Unary
open import Data.Binary.Proofs.Unary
open import Data.Binary.Definitions
open import Data.Binary.Operations.Semantics
open import Data.Nat as ℕ using ... | {
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module std-reduction where
open import Esterel.Lang
open import Esterel.Lang.Properties
open import Esterel.Context
using (EvaluationContext ; EvaluationContext1 ; _⟦_⟧e ; _≐_⟦_⟧e ;
Context ; Context1 ; _⟦_⟧c ; _≐_⟦_⟧c)
open import Esterel.Environment as Env
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{-# OPTIONS --without-K #-}
module hott.equivalence.biinvertible where
open import sum
open import equality
open import function.core
open import function.isomorphism.core
open import function.isomorphism.utils
open import function.overloading
open import function.extensionality
open import hott.level.core
open import... | {
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data Nat : Set where
zero : Nat
suc : Nat → Nat
test : ∀{N M : Nat} → Nat → Nat → Nat
test L K = {!N L M!}
-- Andreas, 2016-07-10, issue 2088
-- Changed behavior:
-- The hidden variables N and M are made visible
-- only the visible L is split.
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-- pull in Haskell Ints
module int where
open import bool
open import string
open import list
open import char
open import functions
open import nat
postulate
int : Set
int0 : int
int1 : int
_+int_ : int → int → int
_*int_ : int → int → int
_-int_ : int → int → int
𝕃char-to-int : 𝕃 char → int
int-... | {
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{-# OPTIONS --overlapping-instances #-}
module Sort where
open import Data.Nat using (ℕ)
open import Data.Fin using (Fin)
open import Data.List using (List; _∷_; [])
open import Data.Variant using (Variants; inj; `_)
-- instance search methods
open import Data.List.Membership.Propositional.Instances
using (⦃h... | {
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{-# OPTIONS --safe #-}
open import Definition.Typed.EqualityRelation
module Definition.LogicalRelation.Substitution.Introductions.IdUPiPi {{eqrel : EqRelSet}} where
open EqRelSet {{...}}
open import Definition.Untyped as U hiding (wk)
open import Definition.Untyped.Properties
open import Definition.Typed
open import... | {
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module GUIgeneric.GUIModel where
open import GUIgeneric.Prelude renaming (inj₁ to secondButton; inj₂ to firstButton; WxColor to Color) hiding (IOInterfaceˢ)
open import GUIgeneric.GUIDefinitions renaming (add to add'; add' to add) --; ComponentEls to Frame)
open import GUIgeneric.GUI
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open import Coinduction using ( ∞ ; ♭ ; ♯_ )
open import Data.Bool using ( Bool ; true ; false )
open import Data.Nat using ( ℕ ; zero ; suc )
open import Data.Natural using ( Natural ; # ; % ; _+_ )
open import Data.Strict using ( Strict ; ! )
open import System.IO.Transducers.List using ( S⊆S&*T )
open import System.... | {
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open import Data.Product using (_×_; _,_)
open import IMP
open import OperationalSemantics
open import Hoare
soundness : ∀{P Q : assn} {c}
→ ⊢[ P ] c [ Q ]
→ ⊨[ P ] c [ Q ]
soundness Skip p Skip = p
soundness Loc p Loc = p
soundness (Comp r r₁) p (Comp z z₁) = soundness r₁ (soundness r p z) z₁
sou... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Data.Int where
open import Cubical.Data.Int.Base public
open import Cubical.Data.Int.Properties public
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-- Andreas, 2016-06-26 issue #2066, reported by Mietek Bak
-- already fixed on stable-2.5
open import Data.Nat using (ℕ ; zero ; suc ; _≟_)
open import Relation.Binary using (Decidable)
open import Relation.Binary.PropositionalEquality using (_≡_ ; _≢_ ; refl)
open import Relation.Nullary using (yes ; no)
data Tm : S... | {
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