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algebraic-stack_agda0000_doc_5256
module bee2 where open import Bee2.Crypto.Belt open import Data.ByteString.Utf8 open import Data.ByteString.IO open import Data.String using (toList) open import Data.Product using (proj₁) open import IO -- beltPBKDF : Password → ℕ → Salt → Kek main = run (writeBinaryFile "pbkdf2" (proj₁ (beltPBKDF (packStrict "zed...
algebraic-stack_agda0000_doc_5257
{-# OPTIONS --without-K --safe #-} module Dodo.Binary.Union where -- Stdlib imports open import Level using (Level; _⊔_) open import Data.Sum using (_⊎_; inj₁; inj₂; swap) open import Relation.Binary using (REL) -- Local imports open import Dodo.Binary.Equality -- # Definitions infixl 19 _∪₂_ _∪₂_ : {a b ℓ₁ ℓ₂ : ...
algebraic-stack_agda0000_doc_5258
postulate F : @0 Set → Set G : @0 Set → Set G A = F (λ { → A })
algebraic-stack_agda0000_doc_5259
{-# OPTIONS --without-K --rewriting #-} open import HoTT open import cohomology.Theory open import homotopy.PushoutSplit open import cw.CW module cw.cohomology.WedgeOfCells {i} (OT : OrdinaryTheory i) {n} (⊙skel : ⊙Skeleton {i} (S n)) where open OrdinaryTheory OT open import cohomology.Bouquet OT open import cw.We...
algebraic-stack_agda0000_doc_5260
{-# OPTIONS --safe --without-K #-} module Literals.Number where open import Agda.Builtin.FromNat public open Number ⦃ ... ⦄ public
algebraic-stack_agda0000_doc_5261
module StateSizedIO.Base where open import Size open import SizedIO.Base open import Data.Product record IOInterfaceˢ : Set₁ where field IOStateˢ : Set Commandˢ : IOStateˢ → Set Responseˢ : (s : IOStateˢ) → (m : Commandˢ s) → Set IOnextˢ : (s : IOStateˢ) → (m : Commandˢ s) → (Responseˢ...
algebraic-stack_agda0000_doc_5262
module Untyped.Abstract where open import Function open import Data.String open import Data.Nat open import Data.Unit open import Data.Product open import Data.List open import Data.Sum as Sum open import Data.Maybe open import Strict open import Debug.Trace open import Category.Monad open import Untyped.Monads po...
algebraic-stack_agda0000_doc_5263
-- Andreas, 2011-05-09 -- {-# OPTIONS -v tc.inj:40 -v tc.meta:30 #-} module Issue383b where postulate Σ : (A : Set) → (A → Set) → Set U : Set El : U → Set mutual data Ctxt : Set where _▻_ : (Γ : Ctxt) → (Env Γ → U) → Ctxt Env : Ctxt → Set Env (Γ ▻ σ) = Σ (Env Γ) λ γ → El (σ γ) postulate Δ : Ctx...
algebraic-stack_agda0000_doc_6944
------------------------------------------------------------------------ -- The Agda standard library -- -- Examples showing how the reflective ring solver may be used. ------------------------------------------------------------------------ module README.Tactic.RingSolver where -- You can ignore this bit! We're just...
algebraic-stack_agda0000_doc_6945
{-# OPTIONS --sized-types #-} -- {-# OPTIONS -v tc.size.solve:100 -v tc.meta.new:50 #-} module CheckSizeMetaBounds where open import Common.Size postulate Size< : (_ : Size) → Set {-# BUILTIN SIZELT Size< #-} data Nat {i : Size} : Set where zero : Nat suc : {j : Size< i} → Nat {j} → Nat one : Nat one = suc {...
algebraic-stack_agda0000_doc_6946
-- The bug documented below was exposed by the fix to issue 274. module Issue274 where open import Common.Level record Q a : Set (a ⊔ a) where record R a : Set a where field q : Q a A : Set₁ A = Set postulate ℓ : Level r : R (ℓ ⊔ ℓ) foo : R ℓ foo = r -- Issue274.agda:32,7-8 -- ℓ ⊔ ℓ !=< ℓ of type Leve...
algebraic-stack_agda0000_doc_6947
{-# OPTIONS --copatterns #-} module SplitResult where open import Common.Product test : {A B : Set} (a : A) (b : B) → A × B test a b = {!!} -- expected: -- proj₁ (test a b) = {!!} -- proj₂ (test a b) = {!!} testFun : {A B : Set} (a : A) (b : B) → A × B testFun = {!!} -- expected: -- testFun a b = {!!} record FunRe...
algebraic-stack_agda0000_doc_6948
{-# OPTIONS --without-K --rewriting #-} module lib.types.Suspension where open import lib.types.Suspension.Core public open import lib.types.Suspension.Flip public open import lib.types.Suspension.Iterated public open import lib.types.Suspension.IteratedFlip public open import lib.types.Suspension.IteratedTrunc publi...
algebraic-stack_agda0000_doc_6949
------------------------------------------------------------------------ -- The Agda standard library -- -- Rational numbers ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Rational where open import Data.Integer as ℤ using (ℤ; +_) open import D...
algebraic-stack_agda0000_doc_6950
module Data.Num.Redundant.Properties where open import Data.Num.Bij open import Data.Num.Redundant renaming (_+_ to _+R_) open import Data.Nat renaming (_<_ to _<ℕ_) open import Data.Nat.Etc open import Data.Nat.Properties.Simple open import Data.Sum open import Data.List hiding ([_]) open import Relation.Nullary op...
algebraic-stack_agda0000_doc_6951
-- Andreas, 2018-03-03, issue #2989 -- Internal error, fixable with additional 'reduce'. -- {-# OPTIONS --show-implicit --show-irrelevant #-} -- {-# OPTIONS -v tc.rec:70 -v tc:10 #-} postulate N : Set P : N → Set record Σ (A : Set) (B : A → Set) : Set where constructor pair field fst : A snd : B fst ...
algebraic-stack_agda0000_doc_6952
module Derivative where open import Sets open import Functor import Isomorphism ∂ : U -> U ∂ (K A) = K [0] ∂ Id = K [1] ∂ (F + G) = ∂ F + ∂ G ∂ (F × G) = ∂ F × G + F × ∂ G open Semantics -- Plugging a hole plug-∂ : {X : Set}(F : U) -> ⟦ ∂ F ⟧ X -> X -> ⟦ F ⟧ X plug-∂ (K _) () x pl...
algebraic-stack_agda0000_doc_6953
{-# OPTIONS --safe #-} module Cubical.Algebra.CommAlgebra where open import Cubical.Algebra.CommAlgebra.Base public open import Cubical.Algebra.CommAlgebra.Properties public
algebraic-stack_agda0000_doc_6954
-- Andreas, 2012-01-12 module Common.Irrelevance where open import Common.Level postulate .irrAxiom : ∀ {a}{A : Set a} → .A → A {-# BUILTIN IRRAXIOM irrAxiom #-} record Squash {a}(A : Set a) : Set a where constructor squash field .unsquash : A open Squash public
algebraic-stack_agda0000_doc_6955
-- define ∑ and ∏ as the bigOps of a Ring when interpreted -- as an additive/multiplicative monoid {-# OPTIONS --safe #-} module Cubical.Algebra.Ring.BigOps where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Function open import Cubical.Data.Bool open import Cubical.Data.Nat using (ℕ ; zer...
algebraic-stack_agda0000_doc_6956
module UpTo where open import Level open import Relation.Binary using (Rel; IsEquivalence) open import Data.Product open import Categories.Support.Equivalence open import Categories.Category open import Categories.2-Category open import Categories.Functor open import Categories.NaturalTransformation renaming (id to ...
algebraic-stack_agda0000_doc_6957
open import Oscar.Prelude open import Oscar.Class.IsDecidable open import Oscar.Data.Fin open import Oscar.Data.Decidable open import Oscar.Data.Proposequality module Oscar.Class.IsDecidable.Fin where instance IsDecidableFin : ∀ {n} → IsDecidable (Fin n) IsDecidableFin .IsDecidable._≟_ ∅ ∅ = ↑ ∅ IsDecidableFi...
algebraic-stack_agda0000_doc_6958
------------------------------------------------------------------------------ -- Even predicate ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} {-# OPTIONS --...
algebraic-stack_agda0000_doc_6959
{-# OPTIONS --without-K --safe #-} module Categories.Category.Instance.LawvereTheories where -- Category of Lawvere Theories open import Level open import Categories.Category.Core using (Category) open import Categories.Functor.Cartesian using (CartesianF) open import Categories.NaturalTransformation.NaturalIsomorph...
algebraic-stack_agda0000_doc_6768
------------------------------------------------------------------------------ -- Testing the η-expansion ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} {-# O...
algebraic-stack_agda0000_doc_6769
module Text.Greek.SBLGNT.Mark where open import Data.List open import Text.Greek.Bible open import Text.Greek.Script open import Text.Greek.Script.Unicode ΚΑΤΑ-ΜΑΡΚΟΝ : List (Word) ΚΑΤΑ-ΜΑΡΚΟΝ = word (Ἀ ∷ ρ ∷ χ ∷ ὴ ∷ []) "Mark.1.1" ∷ word (τ ∷ ο ∷ ῦ ∷ []) "Mark.1.1" ∷ word (ε ∷ ὐ ∷ α ∷ γ ∷ γ ∷ ε ∷ ∙λ ∷ ί ∷ ο ...
algebraic-stack_agda0000_doc_6770
{-# OPTIONS --without-K #-} module FinNatLemmas where open import Data.Empty using (⊥-elim) open import Data.Product using (_×_; _,_) open import Data.Nat using (ℕ; zero; suc; _+_; _*_; _<_; _≤_; _∸_; z≤n; s≤s; module ≤-Reasoning) open import Data.Nat.Properties using (m+n∸n≡m; m≤m+n; +-∸-assoc; cancel-+-left) o...
algebraic-stack_agda0000_doc_6771
open import Agda.Builtin.Bool open import Agda.Builtin.Equality test : (A : Set) (let X = _) (x : X) (p : A ≡ Bool) → Bool test .Bool true refl = false test .Bool false refl = true
algebraic-stack_agda0000_doc_6772
-- Andreas, 2014-09-23 -- Syntax declaration for overloaded constructor. module _ where module A where syntax c x = ⟦ x ⟧ data D2 (A : Set) : Set where c : A → D2 A data D1 : Set where c : D1 open A test : D2 D1 test = ⟦ c ⟧ -- Should work.
algebraic-stack_agda0000_doc_6773
module Issue1419 where module A where module M where module B where module M where open A open B module N (let open M) where module LotsOfStuff where
algebraic-stack_agda0000_doc_6774
------------------------------------------------------------------------ -- The Agda standard library -- -- A simple example of a program using the foreign function interface ------------------------------------------------------------------------ module README.Foreign.Haskell where -- In order to be considered safe ...
algebraic-stack_agda0000_doc_6775
{-# OPTIONS --sized-types #-} module Sized.Data.List where import Lvl open import Lang.Size open import Type private variable ℓ ℓ₁ ℓ₂ : Lvl.Level private variable T A A₁ A₂ B B₁ B₂ Result : Type{ℓ} private variable s s₁ s₂ : Size data List(s : Size){ℓ} (T : Type{ℓ}) : Type{ℓ} where ∅ : List(s)(T) -- An emp...
algebraic-stack_agda0000_doc_6776
{-# OPTIONS --without-K --rewriting #-} open import HoTT {- The cofiber space of [winl : X → X ∨ Y] is equivalent to [Y], - and the cofiber space of [winr : Y → X ∨ Y] is equivalent to [X]. -} module homotopy.WedgeCofiber {i} (X Y : Ptd i) where module CofWinl where module Into = CofiberRec {f = winl} (pt Y...
algebraic-stack_agda0000_doc_6777
module Issue1278.A (X : Set1) where data D : Set where d : D
algebraic-stack_agda0000_doc_6778
-- Combinators for logical reasoning {-# OPTIONS --without-K --safe --exact-split #-} module Constructive.Combinators where -- agda-stdlib open import Data.Empty open import Data.Sum as Sum open import Data.Product as Prod open import Function.Base open import Relation.Nullary using (¬_; Dec; yes; no) open import Rel...
algebraic-stack_agda0000_doc_6779
module Sessions.Semantics.Commands where open import Prelude open import Data.Fin open import Sessions.Syntax.Types open import Sessions.Syntax.Values mutual data Cmd : Pred RCtx 0ℓ where fork : ∀[ Comp unit ⇒ Cmd ] mkchan : ∀ α → ε[ Cmd ] send : ∀ {a α} → ∀[ (Endptr (a ! α) ...
algebraic-stack_agda0000_doc_6780
{-# OPTIONS --cubical --safe #-} module Relation.Nullary.Decidable.Properties where open import Relation.Nullary.Decidable open import Level open import Relation.Nullary.Stable open import Data.Empty open import HLevels open import Data.Empty.Properties using (isProp¬) open import Data.Unit open import Data.Empty De...
algebraic-stack_agda0000_doc_6781
-- Semantics of syntactic traversal and substitution module Semantics.Substitution.Traversal where open import Syntax.Types open import Syntax.Context renaming (_,_ to _,,_) open import Syntax.Terms open import Syntax.Substitution.Kits open import Syntax.Substitution.Instances open import Semantics.Types open import...
algebraic-stack_agda0000_doc_6782
------------------------------------------------------------------------ -- The Agda standard library -- -- Endomorphisms on a Set ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Function.Endomorphism.Propositional {a} (A : Set a) where open import A...
algebraic-stack_agda0000_doc_6783
-- MIT License -- Copyright (c) 2021 Luca Ciccone and Luca Padovani -- Permission is hereby granted, free of charge, to any person -- obtaining a copy of this software and associated documentation -- files (the "Software"), to deal in the Software without -- restriction, including without limitation the rights to use...
algebraic-stack_agda0000_doc_14672
{-# OPTIONS --without-K #-} module Util.HoTT.Univalence.Axiom where open import Util.HoTT.Equiv open import Util.HoTT.Univalence.Statement open import Util.Prelude open import Util.Relation.Binary.PropositionalEquality using (Σ-≡⁻) private variable α β γ : Level A B C : Set α postulate univalence : ∀ {...
algebraic-stack_agda0000_doc_14673
------------------------------------------------------------------------ -- The Agda standard library -- -- IO ------------------------------------------------------------------------ module IO where open import Coinduction open import Data.Unit open import Data.String open import Data.Colist open import Function imp...
algebraic-stack_agda0000_doc_14674
-- {-# OPTIONS -v tc.cover.cover:10 -v tc.cover.splittree:100 -v tc.cover.strategy:100 -v tc.cc:100 #-} module Issue365 where {- Basic data types -} data Nat : Set where zero : Nat succ : Nat -> Nat data Fin : Nat -> Set where fzero : {n : Nat} -> Fin (succ n) fsucc : {n : Nat} -> Fin n -> Fin (succ n) data Vec...
algebraic-stack_agda0000_doc_14675
module Operator.Equals {ℓ} where import Lvl open import Data.Boolean open import Functional open import Relator.Equals{ℓ} open import Type{ℓ} -- Type class for run-time checking of equality record Equals(T : Type) : Type where infixl 100 _==_ field _==_ : T → T → Bool field ⦃ completeness ⦄ : ∀{a b...
algebraic-stack_agda0000_doc_14676
open import Data.Product using ( ∃ ; _×_ ; _,_ ; proj₁ ; proj₂ ) open import Relation.Unary using ( _∈_ ) open import Web.Semantic.DL.TBox.Interp using ( Δ ; _⊨_≈_ ) renaming ( Interp to Interp′ ; emp to emp′ ) open import Web.Semantic.DL.Signature using ( Signature ) open import Web.Semantic.Util using ( False ; id...
algebraic-stack_agda0000_doc_14677
{-# OPTIONS --cubical #-} module Cubical.Categories.Everything where import Cubical.Categories.Category import Cubical.Categories.Functor import Cubical.Categories.NaturalTransformation import Cubical.Categories.Presheaves import Cubical.Categories.Sets import Cubical.Categories.Type
algebraic-stack_agda0000_doc_14678
------------------------------------------------------------------------ -- The Agda standard library -- -- Vectors defined by recursion ------------------------------------------------------------------------ -- What is the point of this module? The n-ary products below are intended -- to be used with a fixed n, in w...
algebraic-stack_agda0000_doc_14679
open import Prelude open import RW.Utils.Monads -- Some Error monad utilities, a là Haskell. module RW.Utils.Error where open import Data.String open Monad {{...}} -- Error Typeclass record IsError {a}(A : Set a) : Set a where field showError : A → String open IsError {{...}} instance ...
algebraic-stack_agda0000_doc_14680
-- Andreas, 2018-04-10, issue #3581, reported by 3abc, test case by Andrea -- Regression in the termination checker introduced together -- with collecting function calls also in the type signatures -- (fix of #1556). open import Agda.Builtin.Bool open import Agda.Builtin.Nat I = Bool i0 = true i1 = false record Pat...
algebraic-stack_agda0000_doc_14681
------------------------------------------------------------------------------ -- Testing Agda internal terms: @Var Nat Args@ when @Args = []@ ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS...
algebraic-stack_agda0000_doc_14682
{-# OPTIONS --universe-polymorphism #-} module Categories.Groupoid where open import Level open import Categories.Category import Categories.Morphisms record Groupoid {o ℓ e} (C : Category o ℓ e) : Set (o ⊔ ℓ ⊔ e) where private module C = Category C open C using (_⇒_) open Categories.Morphisms C field ...
algebraic-stack_agda0000_doc_14683
------------------------------------------------------------------------ -- Lemmas ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe --exact-split #-} module Math.Combinatorics.ListFunction.Properties.Lemma where open import Data.List hiding (_∷ʳ_) import Data.Li...
algebraic-stack_agda0000_doc_14684
module _ where open import Agda.Builtin.Equality using (_≡_; refl) -- First example -- module M (A : Set) where record R : Set where data D : Set where open R (record {}) postulate x : A F : D → Set₁ F _ rewrite refl {x = x} = Set -- Second example -- record ⊤ : Set where no-eta-equality ...
algebraic-stack_agda0000_doc_14685
{-# OPTIONS --sized-types #-} open import FRP.JS.Bool using ( Bool ; true ; false ) renaming ( _≟_ to _≟b_ ) open import FRP.JS.Nat using ( ℕ ) open import FRP.JS.Float using ( ℝ ) renaming ( _≟_ to _≟n_ ) open import FRP.JS.String using ( String ) renaming ( _≟_ to _≟s_ ) open import FRP.JS.Array using ( Array ) rena...
algebraic-stack_agda0000_doc_14686
-- Testing the version option on a file with errors. -- -- N.B. It is necessary to change the Issue1244a.out file when using -- different versions of Agda. foo : Set → Set foo a = b
algebraic-stack_agda0000_doc_14687
module Luau.Addr where open import Agda.Builtin.Bool using (true; false) open import Agda.Builtin.Equality using (_≡_) open import Agda.Builtin.Nat using (Nat; _==_) open import Agda.Builtin.String using (String) open import Agda.Builtin.TrustMe using (primTrustMe) open import Properties.Dec using (Dec; yes; no) open ...
algebraic-stack_agda0000_doc_14320
{-# OPTIONS --rewriting #-} open import Common.Prelude open import Common.Equality {-# BUILTIN REWRITE _≡_ #-} postulate f g : Nat → Nat f-zero : f zero ≡ g zero f-suc : ∀ n → f n ≡ g n → f (suc n) ≡ g (suc n) r : (n : Nat) → f n ≡ g n r zero = f-zero r (suc n) = f-suc n refl where rn : f n ≡ g n ...
algebraic-stack_agda0000_doc_14321
{-# OPTIONS --cubical-compatible #-} module Common.Equality where open import Agda.Builtin.Equality public open import Common.Level subst : ∀ {a p}{A : Set a}(P : A → Set p){x y : A} → x ≡ y → P x → P y subst P refl t = t cong : ∀ {a b}{A : Set a}{B : Set b}(f : A → B){x y : A} → x ≡ y → f x ≡ f y cong f refl = refl...
algebraic-stack_agda0000_doc_14322
module _ {T : Type{ℓₒ}} ⦃ equiv : Equiv{ℓₑ}(T) ⦄ where instance PredSet-setLike : SetLike{C = PredSet{ℓ}(T) ⦃ equiv ⦄} (_∈_) SetLike._⊆_ PredSet-setLike = _⊆_ SetLike._≡_ PredSet-setLike = _≡_ SetLike.[⊆]-membership PredSet-setLike = [↔]-intro intro _⊆_.proof SetLike.[≡]-membership PredSet-setLik...
algebraic-stack_agda0000_doc_14323
{-# OPTIONS --cubical --safe #-} module Cubical.Structures.CommRing where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.HLevels open import Cubical.Data.Sigma open import Cubical.Foundations.SIP renaming (SNS-PathP to SNS) open import Cubical.Structures...
algebraic-stack_agda0000_doc_14324
{-# OPTIONS --cubical #-} open import Cubical.Core.Glue open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.Univalence open import Cubical.Foundations.Isomorphism open import Cubical.Data.Nat open import Cubical.Data.Empty open import Cubical.Data.Unit open imp...
algebraic-stack_agda0000_doc_14325
------------------------------------------------------------------------ -- The Agda standard library -- -- This module is DEPRECATED. Please use `Data.Vec.Functional` instead. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} -- Disabled to prevent warnings f...
algebraic-stack_agda0000_doc_14326
open import Oscar.Prelude open import Oscar.Class open import Oscar.Class.Unit open import Oscar.Class.Leftunit module Oscar.Class.Leftunit.ToUnit where module _ {𝔞} {𝔄 : Ø 𝔞} {𝔢} {𝔈 : Ø 𝔢} {ℓ} {_↦_ : 𝔄 → 𝔄 → Ø ℓ} (let _↦_ = _↦_; infix 4 _↦_) {ε : 𝔈} {_◃_ : 𝔈 → 𝔄 → 𝔄} (let _◃_ = _◃_; infix 16 _◃_...
algebraic-stack_agda0000_doc_14327
module Lectures.One where -- Check background color -- Check fontsize -- Ask questions at *any* time data ⊤ : Set where tt : ⊤ data ⊥ : Set where absurd : ⊥ → {P : Set} → P absurd () -- Introduce most common key bindings -- C-c C-l load -- C-c C-, show context -- C-c C-. show context + type -- C-c C-...
algebraic-stack_agda0000_doc_14328
{-# OPTIONS --without-K --exact-split --allow-unsolved-metas #-} module 13-propositional-truncation where import 12-univalence open 12-univalence public -- Section 13 Propositional truncations, the image of a map, and the replacement axiom -- Section 13.1 Propositional truncations -- Definition 13.1.1 type-hom-Pr...
algebraic-stack_agda0000_doc_14329
------------------------------------------------------------------------ -- The Agda standard library -- -- Convenient syntax for reasoning with a partial setoid ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Relation.Binary module Relation.Bin...
algebraic-stack_agda0000_doc_14330
module Issue1232.Fin where data Fin : Set where zero : Fin
algebraic-stack_agda0000_doc_14331
{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9. Copyright (c) 2021, Oracle and/or its affiliates. Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl -} import LibraBFT.Impl.Consensus.ConsensusTypes.Vote as Vote ...
algebraic-stack_agda0000_doc_14332
{-# OPTIONS --without-K --safe #-} module Polynomial.Simple.AlmostCommutativeRing where import Algebra.Solver.Ring.AlmostCommutativeRing as Complex open import Level open import Relation.Binary open import Algebra open import Algebra.Structures open import Algebra.FunctionProperties import Algebra.Morphism as Morphis...
algebraic-stack_agda0000_doc_14333
{-# OPTIONS --without-K --rewriting #-} open import lib.Basics open import lib.NType2 open import lib.types.Bool open import lib.types.Empty open import lib.types.Paths open import lib.types.Pi open import lib.types.Sigma {- This file contains various lemmas that rely on lib.types.Paths or functional extensionality f...
algebraic-stack_agda0000_doc_14334
open import Signature -- | One signature for terms and one for predicates. module Logic (Σ Δ : Sig) (V : Set) where open import Data.Empty renaming (⊥ to Ø) open import Data.Unit open import Data.Sum open import Data.Product renaming (Σ to ∐) open import Data.Nat open import Data.Fin FinSet : Set → Set FinSet X = ∃ ...
algebraic-stack_agda0000_doc_14335
-- Andreas, 2017-01-24, issue #2429 -- Respect subtyping also for irrelevant lambdas! -- Subtyping: (.A → B) ≤ (A → B) -- Where a function is expected, we can put one which does not use its argument. id : ∀{A B : Set} → (.A → B) → A → B id f = f test : ∀{A B : Set} → (.A → B) → A → B test f = λ .a → f a -- Should w...
algebraic-stack_agda0000_doc_6512
{-# OPTIONS --cubical --safe #-} module Function.Surjective.Base where open import Path open import Function.Fiber open import Level open import HITs.PropositionalTruncation open import Data.Sigma Surjective : (A → B) → Type _ Surjective f = ∀ y → ∥ fiber f y ∥ SplitSurjective : (A → B) → Type _ SplitSurjective f =...
algebraic-stack_agda0000_doc_6513
module T where postulate x : Set postulate y : Set postulate p : Set -> Set e : Set e = p y
algebraic-stack_agda0000_doc_6514
open import Agda.Builtin.Reflection open import Agda.Builtin.Unit @0 A : Set₁ A = Set macro @0 m : Term → TC ⊤ m B = bindTC (quoteTC A) λ A → unify A B B : Set₁ B = m
algebraic-stack_agda0000_doc_6515
module Prelude.Bool where open import Prelude.Unit open import Prelude.Empty open import Prelude.Equality open import Prelude.Decidable open import Prelude.Function open import Agda.Builtin.Bool public infix 0 if_then_else_ if_then_else_ : ∀ {a} {A : Set a} → Bool → A → A → A if true then x else y = x if false the...
algebraic-stack_agda0000_doc_6516
module Prelude.Char where open import Prelude.Bool postulate Char : Set {-# BUILTIN CHAR Char #-} private primitive primCharEquality : (c c' : Char) -> Bool postulate eof : Char {-# COMPILED_EPIC eof () -> Int = foreign Int "eof" () #-} charEq : Char -> Char -> Bool charEq = primCharEquality
algebraic-stack_agda0000_doc_6517
-- Andreas, 2018-06-15, issue #1086 -- Reported by Andrea -- Fixed by Jesper in https://github.com/agda/agda/commit/242684bca62fabe43e125aefae7526be4b26a135 open import Common.Bool open import Common.Equality and : (a b : Bool) → Bool and true b = b and false b = false test : ∀ a b → and a b ≡ true → a ≡ true test ...
algebraic-stack_agda0000_doc_6518
------------------------------------------------------------------------ -- Encoder and decoder instances for Atom.χ-ℕ-atoms ------------------------------------------------------------------------ module Coding.Instances.Nat where open import Atom -- The code-Var and code-Const instances are hidden: they are replac...
algebraic-stack_agda0000_doc_6519
{-# OPTIONS --warning=error --without-K --guardedness --safe #-} open import LogicalFormulae open import Numbers.Naturals.Definition open import Setoids.Setoids open import Numbers.Naturals.Order open import Vectors module Sequences where record Sequence {a : _} (A : Set a) : Set a where coinductive field he...
algebraic-stack_agda0000_doc_6520
{- Properties and Formulae about Cardinality This file contains: - Relation between abstract properties and cardinality in special cases; - Combinatorial formulae, namely, cardinality of A+B, A×B, ΣAB, ΠAB, etc; - A general form of Pigeonhole Principle; - Maximal value of numerical function on finite sets; - Set trun...
algebraic-stack_agda0000_doc_6521
------------------------------------------------------------------------ -- The Agda standard library -- -- Decidable setoid membership over vectors. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Relation.Binary using (DecSetoid) module Data.V...
algebraic-stack_agda0000_doc_6522
module _ where open import Agda.Primitive.Cubical postulate PathP : ∀ {ℓ} (A : I → Set ℓ) → A i0 → A i1 → Set ℓ {-# BUILTIN PATHP PathP #-}
algebraic-stack_agda0000_doc_6523
module #8 where {- Define multiplication and exponentiation using recN. Verify that (N, +, 0, ×, 1) is a semiring using only indN. You will probably also need to use symmetry and transitivity of equality, Lemmas 2.1.1 and 2.1.2. -} open import Data.Nat recₙ : ∀{c}{C : Set c} → C → (ℕ → C → C) → ℕ → C recₙ c₀ c...
algebraic-stack_agda0000_doc_6524
--------------------------------------- -- Pairs of sets --------------------------------------- {-# OPTIONS --allow-unsolved-meta #-} module sv20.assign2.SetTheory.Pairs where -- Everything involving pairs, be them unordered -- or ordered pairs. Also the definition of power set -- and cartesian product between sets...
algebraic-stack_agda0000_doc_6525
postulate A : Set I : ..(_ : A) → Set R : A → Set f : ∀ ..(x : A) (r : R x) → I x -- can now be used here ^
algebraic-stack_agda0000_doc_6526
module examplesPaperJFP.VariableListForDispatchOnly where open import Data.Product hiding (map) open import Data.List open import NativeIO open import StateSizedIO.GUI.WxBindingsFFI open import Relation.Binary.PropositionalEquality data VarList : Set₁ where [] : VarList addVar : (A : Set) → Var A → VarLi...
algebraic-stack_agda0000_doc_6527
{-# OPTIONS --without-K #-} open import lib.Basics {- The generic nonrecursive higher inductive type with one point constructor and one paths constructor. -} module lib.types.Generic1HIT {i j} (A : Type i) (B : Type j) (g h : B → A) where {- data T : Type where cc : A → T pp : (b : B) → cc (f' b) ≡ cc (g b) ...
algebraic-stack_agda0000_doc_15104
-- Problem 2: Multiplication for matrices (from the matrix algebra DSL). module P2 where -- 2a: Type the variables in the text. -- (This answer uses Agda syntax, but that is not required.) postulate Nat : Set postulate V : Nat -> Set -> Set postulate Fin : Nat -> Set Op : Set -> Set Op a = a -> a -> a postulate su...
algebraic-stack_agda0000_doc_15105
{-# OPTIONS --without-K --safe #-} module C where open import Data.Empty open import Data.Unit open import Data.Sum open import Data.Product open import Relation.Binary.PropositionalEquality open import Singleton infixr 70 _×ᵤ_ infixr 60 _+ᵤₗ_ infixr 60 _+ᵤᵣ_ infixr 50 _⊚_ -----------------------------------------...
algebraic-stack_agda0000_doc_15106
{-# OPTIONS --universe-polymorphism #-} module Categories.Product where open import Level open import Function using () renaming (_∘_ to _∙_) open import Data.Product using (_×_; Σ; _,_; proj₁; proj₂; zip; map; <_,_>; swap) open import Categories.Category private map⁎ : ∀ {a b p q} {A : Set a} {B : A → Set b} {P :...
algebraic-stack_agda0000_doc_15107
open import Nat open import Prelude open import List open import core open import judgemental-erase open import sensibility open import moveerase module checks where -- these three judmgements lift the action semantics judgements to relate -- an expression and a list of pair-wise composable actions to the -- exp...
algebraic-stack_agda0000_doc_15108
{-# OPTIONS --no-import-sorts #-} open import Agda.Primitive renaming (Set to _X_X_) test : _X_X₁_ test = _X_X_
algebraic-stack_agda0000_doc_15109
{-# OPTIONS --without-K #-} open import Agda.Primitive using (Level; lsuc) open import Relation.Binary.PropositionalEquality.Core using (_≡_; cong) open import Data.Empty using (⊥; ⊥-elim) open import Data.Product using (proj₁; proj₂; Σ-syntax; _,_) open import Function.Base using (_∘_) variable ℓ ℓ′ : Level A C ...
algebraic-stack_agda0000_doc_15110
{-# OPTIONS --cubical --safe #-} module Cubical.Homotopy.Loopspace where open import Cubical.Core.Everything open import Cubical.Data.Nat open import Cubical.Foundations.Prelude open import Cubical.Foundations.Pointed open import Cubical.Foundations.GroupoidLaws {- loop space of a pointed type -} Ω : {ℓ : Level} →...
algebraic-stack_agda0000_doc_15111
module Sets.ImageSet.Oper where open import Data open import Functional open import Logic open import Logic.Propositional open import Logic.Predicate import Lvl open import Sets.ImageSet open import Structure.Function open import Structure.Setoid renaming (_≡_ to _≡ₛ_) open import Type open import Type.Dependent ...
algebraic-stack_agda0000_doc_15112
open import Agda.Builtin.IO using (IO) open import Agda.Builtin.String using (String) open import Agda.Builtin.Unit using (⊤) data D : Set where c₁ c₂ : D f : D → Set → String f c₁ = λ _ → "OK" f c₂ = λ _ → "OK" -- The following pragma should refer to the generated Haskell name -- for f. {-# FOREIGN GHC {-# NOINL...
algebraic-stack_agda0000_doc_15113
{-# OPTIONS --no-unreachable-check #-} module Issue424 where data _≡_ {A : Set₁} (x : A) : A → Set where refl : x ≡ x f : Set → Set f A = A f A = A fails : (A : Set) → f A ≡ A fails A = refl -- The case tree compiler used to treat f as a definition with an -- absurd pattern.
algebraic-stack_agda0000_doc_15114
{-# OPTIONS --cubical --no-import-sorts #-} open import Cubical.Foundations.Everything renaming (_⁻¹ to _⁻¹ᵖ; assoc to ∙-assoc) open import Function.Base using (_∋_; _$_) open import MorePropAlgebra.Bundles import Cubical.Structures.CommRing as Std module MorePropAlgebra.Properties.CommRing {ℓ} (assumptions : CommR...
algebraic-stack_agda0000_doc_15115
------------------------------------------------------------------------ -- The Agda standard library -- -- Trie, basic type and operations ------------------------------------------------------------------------ -- See README.Data.Trie.NonDependent for an example of using a trie to -- build a lexer. {-# OPTIONS --wi...