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algebraic-stack_agda0000_doc_12512
------------------------------------------------------------------------ -- A large class of algebraic structures satisfies the property that -- isomorphic instances of a structure are equal (assuming univalence) ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-...
algebraic-stack_agda0000_doc_12513
{-# OPTIONS --without-K --safe #-} module Categories.Category.Construction.Properties.Kleisli where open import Level import Relation.Binary.PropositionalEquality as ≡ open import Categories.Adjoint open import Categories.Adjoint.Properties open import Categories.Category open import Categories.Functor using (Functor...
algebraic-stack_agda0000_doc_12514
module Issue599 where data Bool : Set where true false : Bool -- standard lambda here foo : Bool → Bool foo = ? -- pattern matching lambda here bar : Bool → Bool bar = ?
algebraic-stack_agda0000_doc_12515
------------------------------------------------------------------------ -- The halting problem ------------------------------------------------------------------------ module Halting-problem where open import Equality.Propositional.Cubical open import Logical-equivalence using (_⇔_) open import Prelude hiding (const...
algebraic-stack_agda0000_doc_12516
module IrrelevantLambda where postulate A : Set P : .A -> Set f : ._ -> Set f = λ .x -> P x f' = λ .(x : _) -> P x f'' = λ .{x y z : _} -> P x g : ((.A -> Set) -> Set) -> Set g k = k f
algebraic-stack_agda0000_doc_12517
module Golden.InsertionSort where open import Agda.Builtin.Nat open import Agda.Builtin.List open import Agda.Builtin.Bool insert : Nat -> List Nat -> List Nat insert a [] = a ∷ [] insert x (a ∷ b) with x < a ... | true = x ∷ a ∷ b ... | false = a ∷ (insert x b) foldr : ∀ {a b : Set} → (a → b → b) → b → List a -> b ...
algebraic-stack_agda0000_doc_12518
------------------------------------------------------------------------ -- The Agda standard library -- -- Universe levels ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Level where -- Levels. open import Agda.Primitive as Prim public using (...
algebraic-stack_agda0000_doc_12519
{-# OPTIONS --safe #-} module Cubical.Algebra.MonoidSolver.Solver where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Structure open import Cubical.Data.FinData using (Fin) open import Cubical.Data.Nat using (ℕ) open import Cubical.Data.List open import Cubical.Data.Vec using (Vec; lookup) ...
algebraic-stack_agda0000_doc_12520
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Homotopy.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv.Properties private variable ℓ ℓ' : Level _∼_ : {X : Type ℓ} {Y : X → Type ℓ'} → (f g : (x : X) → Y x) → Type (ℓ-max ℓ ℓ') _∼_ {X = X} f g = (x : X...
algebraic-stack_agda0000_doc_12521
{-# OPTIONS --cubical --safe --postfix-projections #-} module Categories.Exercises where open import Prelude open import Categories open Category ⦃ ... ⦄ open import Categories.Product open Product public open HasProducts ⦃ ... ⦄ public -- module _ {ℓ₁} {ℓ₂} ⦃ c : Category ℓ₁ ℓ₂ ⦄ ⦃ hp : HasProducts c ⦄ where -- ...
algebraic-stack_agda0000_doc_12522
{-# OPTIONS --safe --warning=error --without-K #-} open import LogicalFormulae open import Numbers.Naturals.Semiring open import Numbers.Naturals.Multiplication open import Semirings.Definition open import Rings.Definition open import Setoids.Setoids module Numbers.Integers.RingStructure.Ring where open import Numbe...
algebraic-stack_agda0000_doc_12523
module Oscar.Data.Term.Injectivity {𝔣} (FunctionName : Set 𝔣) where open import Oscar.Data.Term FunctionName open import Data.Fin open import Data.Nat open import Data.Vec open import Relation.Binary.PropositionalEquality Term-i-inj : ∀ {m} {𝑥₁ 𝑥₂ : Fin m} → i 𝑥₁ ≡ i 𝑥₂ → 𝑥₁ ≡ 𝑥₂ Term-i-inj refl = refl Ter...
algebraic-stack_agda0000_doc_12524
{-# OPTIONS --without-K --exact-split --rewriting --overlapping-instances #-} open import lib.Basics open import lib.NConnected open import lib.NType2 open import lib.types.Truncation open import lib.types.Sigma open import lib.Equivalence open import lib.types.Fin open import lib.types.Coproduct open import Graphs.D...
algebraic-stack_agda0000_doc_12525
{-# OPTIONS --without-K #-} module TypeEquivalences where open import Data.Empty open import Data.Unit open import Data.Unit.Core open import Data.Nat renaming (_⊔_ to _⊔ℕ_) open import Data.Sum renaming (map to _⊎→_) open import Data.Product renaming (map to _×→_) open import Function renaming (_∘_ to _○_) -- explic...
algebraic-stack_agda0000_doc_12526
{-# OPTIONS --cubical #-} module HyperPositive where open import Prelude infixr 4 _↬_ {-# NO_POSITIVITY_CHECK #-} record _↬_ (A : Type a) (B : Type b) : Type (a ℓ⊔ b) where inductive; constructor hyp field invoke : ((A ↬ B) → A) → B open _↬_ open import Data.List using (List; _∷_; []; foldr) module _ {a b} {A ...
algebraic-stack_agda0000_doc_12527
open import Relation.Binary.Indexed module Relation.Binary.Indexed.EqReasoning {𝒾} {I : Set 𝒾} {𝒸 ℓ} (S : Setoid I 𝒸 ℓ) where open Setoid S import Relation.Binary.Indexed.PreorderReasoning as PreR open import Relation.Binary.Indexed.Extra using (Setoid⇒Preorder) open PreR (Setoid⇒Preorder S) public renamin...
algebraic-stack_agda0000_doc_4656
module Categories.Ran where open import Level open import Categories.Category open import Categories.Functor hiding (_≡_) open import Categories.NaturalTransformation record Ran {o₀ ℓ₀ e₀} {o₁ ℓ₁ e₁} {o₂ ℓ₂ e₂} {A : Category o₀ ℓ₀ e₀} {B : Category o₁ ℓ₁ e₁} {C : Category o₂ ℓ₂ e₂} (F : Functor...
algebraic-stack_agda0000_doc_4657
{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9. Copyright (c) 2020 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.Lemmas open import LibraBFT.H...
algebraic-stack_agda0000_doc_4658
module Thesis.Syntax where open import Thesis.Types public open import Thesis.Contexts public data Const : (τ : Type) → Set where unit : Const unit lit : ℤ → Const int plus : Const (int ⇒ int ⇒ int) minus : Const (int ⇒ int ⇒ int) cons : ∀ {t1 t2} → Const (t1 ⇒ t2 ⇒ pair t1 t2) fst : ∀ {t1 t2} → Con...
algebraic-stack_agda0000_doc_4659
open import Common.Reflection macro round-trip : Term → Tactic round-trip v hole = unify v hole module M (A : Set) where data D : Set where test : Set test = round-trip D
algebraic-stack_agda0000_doc_4660
module MissingWithClauses where data D : Set where c : D f : D -> D f c with c
algebraic-stack_agda0000_doc_4661
module PiInSet where Rel : Set -> Set1 Rel A = A -> A -> Set Reflexive : {A : Set} -> Rel A -> Set Reflexive {A} _R_ = forall x -> x R x Symmetric : {A : Set} -> Rel A -> Set Symmetric {A} _R_ = forall x y -> x R y -> y R x data True : Set where tt : True data False : Set where data Nat : Set where zero : Na...
algebraic-stack_agda0000_doc_4662
{-# OPTIONS --without-K --allow-unsolved-metas --exact-split #-} module 21-pushouts where import 20-pullbacks open 20-pullbacks public -- Section 14.1 {- We define the type of cocones with vertex X on a span. Since we will use it later on, we will also characterize the identity type of the type of cocones wit...
algebraic-stack_agda0000_doc_4663
{-# OPTIONS --without-K --safe #-} open import Categories.Category open import Categories.Category.Monoidal -- the definition used here is not very similar to what one usually sees in nLab or -- any textbook. the difference is that usually closed monoidal category is defined -- through a right adjoint of -⊗X, which ...
algebraic-stack_agda0000_doc_4664
{-# OPTIONS --universe-polymorphism #-} module Categories.Bifunctor where open import Level open import Data.Product using (_,_; swap) open import Categories.Category open import Categories.Functor public open import Categories.Product Bifunctor : ∀ {o ℓ e} {o′ ℓ′ e′} {o′′ ℓ′′ e′′} → Category o ℓ e → Category o′ ℓ′...
algebraic-stack_agda0000_doc_4665
module Cats.Functor.Op where open import Cats.Category.Base open import Cats.Category.Op using (_ᵒᵖ) open import Cats.Functor using (Functor) open Functor Op : ∀ {lo la l≈ lo′ la′ l≈′} → {C : Category lo la l≈} {D : Category lo′ la′ l≈′} → Functor C D → Functor (C ᵒᵖ) (D ᵒᵖ) Op F = record { fobj = fobj F ...
algebraic-stack_agda0000_doc_4666
module Tactic.Deriving.Quotable where open import Prelude open import Container.Traversable open import Tactic.Reflection open import Tactic.Reflection.Quote.Class open import Tactic.Deriving private -- Bootstrapping qVis : Visibility → Term qVis visible = con (quote visible) [] qVis hidden = con (quote hidd...
algebraic-stack_agda0000_doc_4667
open import Data.Product using ( _×_ ) open import FRP.LTL.ISet.Core using ( ISet ; ⌈_⌉ ; M⟦_⟧ ) open import FRP.LTL.Time using ( Time ) open import FRP.LTL.Time.Bound using ( fin ; _≺_ ) open import FRP.LTL.Time.Interval using ( [_⟩ ; sing ) module FRP.LTL.ISet.Until where data _Until_ (A B : ISet) (t : Time) : Set ...
algebraic-stack_agda0000_doc_4668
module Sets.ExtensionalPredicateSet where import Lvl open import Data open import Data.Boolean open import Data.Either as Either using (_‖_) open import Data.Tuple as Tuple using (_⨯_ ; _,_) open import Functional open import Function.Equals open import Function.Equals.Proofs open import Function.Inverse open imp...
algebraic-stack_agda0000_doc_4669
open import MLib.Prelude open import MLib.Algebra.PropertyCode open import MLib.Algebra.PropertyCode.Structures module MLib.Matrix.Plus {c ℓ} (struct : Struct bimonoidCode c ℓ) {m n : ℕ} where open import MLib.Matrix.Core open import MLib.Matrix.Equality struct open FunctionProperties -- Pointwise addition -- infi...
algebraic-stack_agda0000_doc_4670
{- Practical Relational Algebra Toon Nolten based on The Power Of Pi -} module relational-algebra where open import Data.Empty open import Data.Unit hiding (_≤_) open import Data.Bool open import Data.Nat open import Data.Integer hiding (show) open import Data.List open import...
algebraic-stack_agda0000_doc_4671
{-# OPTIONS --without-K --safe #-} open import Definition.Typed.EqualityRelation module Definition.LogicalRelation {{eqrel : EqRelSet}} where open EqRelSet {{...}} open import Definition.Untyped as U open import Definition.Typed open import Definition.Typed.Weakening open import Agda.Primitive open import Tools.Pro...
algebraic-stack_agda0000_doc_13024
{-# OPTIONS --safe --postfix-projections #-} module Cubical.Algebra.OrderedCommMonoid.PropCompletion where {- The completion of an ordered monoid, viewed as monoidal prop-enriched category. This is used in the construction of the upper naturals, which is an idea of David Jaz Myers presented here https://felix-...
algebraic-stack_agda0000_doc_13025
-- Andreas, 2018-10-18, re issue #2757 -- -- Extracted this snippet from the standard library -- as it caused problems during work in #2757 -- (runtime erasue using 0-quantity). -- {-# OPTIONS -v tc.lhs.unify:65 -v tc.irr:50 #-} open import Agda.Builtin.Size data ⊥ : Set where mutual data Conat (i : Size) : Set w...
algebraic-stack_agda0000_doc_13026
open import MJ.Types open import MJ.Classtable import MJ.Syntax as Syntax import MJ.Semantics.Values as Values -- -- Substitution-free interpretation of welltyped MJ -- module MJ.Semantics.Functional {c} (Σ : CT c) (ℂ : Syntax.Impl Σ) where open import Prelude open import Data.Vec hiding (init) open import Data.Ve...
algebraic-stack_agda0000_doc_13027
{-# OPTIONS --allow-unsolved-metas #-} module LiteralFormula where open import OscarPrelude open import IsLiteralFormula open import HasNegation open import Formula record LiteralFormula : Set where constructor ⟨_⟩ field {formula} : Formula isLiteralFormula : IsLiteralFormula formula open LiteralFormul...
algebraic-stack_agda0000_doc_13028
{-# OPTIONS --cubical --safe #-} module Cubical.Foundations.Bundle where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.Univalence open import Cubical.Foundations.Fibration open import Cubical.Foundations.Structure open import Cubical.Structures.TypeEqvTo...
algebraic-stack_agda0000_doc_13029
module Generic.Property.Reify where open import Generic.Core data ExplView : Visibility -> Set where yes-expl : ExplView expl no-expl : ∀ {v} -> ExplView v explView : ∀ v -> ExplView v explView expl = yes-expl explView v = no-expl ExplMaybe : ∀ {α} -> Visibility -> Set α -> Set α ExplMaybe v A with explView...
algebraic-stack_agda0000_doc_13030
module Issue1760g where data ⊥ : Set where {-# NO_POSITIVITY_CHECK #-} {-# NON_TERMINATING #-} mutual record U : Set where constructor roll field ap : U → U lemma : U → ⊥ lemma (roll u) = lemma (u (roll u)) bottom : ⊥ bottom = lemma (roll λ x → x)
algebraic-stack_agda0000_doc_13031
{-# OPTIONS --without-K --safe #-} open import Algebra.Structures.Bundles.Field module Algebra.Linear.Morphism.VectorSpace {k ℓᵏ} (K : Field k ℓᵏ) where open import Level open import Algebra.FunctionProperties as FP import Algebra.Linear.Morphism.Definitions as LinearMorphismDefinitions import Algebra.Morphism a...
algebraic-stack_agda0000_doc_13032
module helloworld where open import IO main = run (putStrLn "Hello World")
algebraic-stack_agda0000_doc_13033
{-# OPTIONS --without-K #-} module hott.types where open import hott.types.nat public open import hott.types.coproduct public
algebraic-stack_agda0000_doc_13034
module README where ---------------------------------------------------------------------- -- The Agda smallib library, version 0.1 ---------------------------------------------------------------------- -- -- This library implements a type theory which is described in the -- Appendix of the HoTT book. It also contains...
algebraic-stack_agda0000_doc_13035
{-# OPTIONS --without-K #-} open import HoTT open import cohomology.SuspAdjointLoopIso open import cohomology.WithCoefficients open import cohomology.Theory open import cohomology.Exactness open import cohomology.Choice {- A spectrum (family (Eₙ | n : ℤ) such that ΩEₙ₊₁ = Eₙ) - gives rise to a cohomology theory C wi...
algebraic-stack_agda0000_doc_13036
{-# OPTIONS --warning=error --safe --without-K #-} open import LogicalFormulae open import Agda.Primitive using (Level; lzero; lsuc; _⊔_) open import Functions.Definition open import Setoids.Setoids open import Setoids.Subset module Graphs.Definition where record Graph {a b : _} (c : _) {V' : Set a} (V : Setoid {a} ...
algebraic-stack_agda0000_doc_13037
{- A defintion of the real projective spaces following: [BR17] U. Buchholtz, E. Rijke, The real projective spaces in homotopy type theory. (2017) https://arxiv.org/abs/1704.05770 -} {-# OPTIONS --cubical --safe #-} module Cubical.HITs.RPn.Base where open import Cubical.Foundations.Prelude open impo...
algebraic-stack_agda0000_doc_13038
{-# OPTIONS --allow-unsolved-metas #-} open import Agda.Builtin.Bool postulate A : Set F : Bool → Set F true = A F false = A data D {b : Bool} (x : F b) : Set where variable b : Bool x : F b postulate f : D x → (P : F b → Set) → P x
algebraic-stack_agda0000_doc_13039
-- {-# OPTIONS -v scope.clash:20 #-} -- Andreas, 2012-10-19 test case for Issue 719 module ShadowModule2 where open import Common.Size as YesDuplicate import Common.Size as NotDuplicate private open module YesDuplicate = NotDuplicate -- should report: -- Duplicate definition of module YesDuplicate. -- NOT: Duplicate ...
algebraic-stack_agda0000_doc_4832
module CS410-Monoid where open import CS410-Prelude record Monoid (M : Set) : Set where field -- OPERATIONS ---------------------------------------- e : M op : M -> M -> M -- LAWS ---------------------------------------------- lunit : forall m -> op e m == m runit : forall m -> op m e...
algebraic-stack_agda0000_doc_4833
------------------------------------------------------------------------ -- A combinator for running two computations in parallel ------------------------------------------------------------------------ {-# OPTIONS --sized-types #-} module Delay-monad.Parallel where import Equality.Propositional as Eq open import Pr...
algebraic-stack_agda0000_doc_4834
{-# OPTIONS --allow-exec #-} open import Agda.Builtin.FromNat open import Data.Bool.Base using (T; Bool; if_then_else_) open import Data.String using (String; _++_; lines) open import Data.Nat.Base using (ℕ) open import Data.Fin using (Fin) import Data.Fin.Literals as Fin import Data.Nat.Literals as Nat open import D...
algebraic-stack_agda0000_doc_4835
module Theory where open import Data.List using (List; []; _∷_; _++_) open import Data.Fin using () renaming (zero to fzero; suc to fsuc) open import Relation.Binary using (Rel) open import Level using (suc; _⊔_) open import Syntax record Theory ℓ₁ ℓ₂ ℓ₃ : Set (suc (ℓ₁ ⊔ ℓ₂ ⊔ ℓ₃)) where field Sg : Signature ...
algebraic-stack_agda0000_doc_4836
module Prelude.Unit where data Unit : Set where unit : Unit
algebraic-stack_agda0000_doc_4837
------------------------------------------------------------------------ -- The Agda standard library -- -- Bounded vectors (inefficient implementation) ------------------------------------------------------------------------ -- Vectors of a specified maximum length. module Data.Star.BoundedVec where open import Dat...
algebraic-stack_agda0000_doc_4838
{-# OPTIONS --without-K --rewriting #-} open import HoTT module homotopy.SmashFmapConn where module _ {i} {j} {A : Type i} (B : A → Type j) where custom-assoc : {a₀ a₁ a₂ a₃ : A} {b₀ : B a₀} {b₁ b₁' b₁'' : B a₁} {b₂ : B a₂} {b₃ : B a₃} {p : a₀ == a₁} (p' : b₀ == b₁ [ B ↓ p ]) (q' : b₁ == b₁') (r' ...
algebraic-stack_agda0000_doc_4839
{-# OPTIONS --allow-unsolved-metas #-} ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ -- CS410 2017/18 Exercise 1 VECTORS AND FRIENDS (worth 25%) --------------------------------------------------------------...
algebraic-stack_agda0000_doc_4840
------------------------------------------------------------------------ -- The Agda standard library -- -- A categorical view of Vec ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Vec.Categorical {a n} where open import Category.Applicative us...
algebraic-stack_agda0000_doc_4841
-- A placeholder module so that we can write a main. Agda compilation -- does not work without a main so batch compilation is bound to give -- errors. For travis builds, we want batch compilation and this is -- module can be imported to serve that purpose. There is nothing -- useful that can be achieved from this modul...
algebraic-stack_agda0000_doc_4842
open import Mockingbird.Forest using (Forest) import Mockingbird.Forest.Birds as Birds -- The Master Forest module Mockingbird.Problems.Chapter18 {b ℓ} (forest : Forest {b} {ℓ}) ⦃ _ : Birds.HasStarling forest ⦄ ⦃ _ : Birds.HasKestrel forest ⦄ ...
algebraic-stack_agda0000_doc_4843
-- Andreas, 2017-01-12, re #2386 -- Correct error message for wrong BUILTIN UNIT data Bool : Set where true false : Bool {-# BUILTIN UNIT Bool #-} -- Error WAS: -- The builtin UNIT must be a datatype with 1 constructors -- when checking the pragma BUILTIN UNIT Bool -- Expected error: -- Builtin UNIT must be a sin...
algebraic-stack_agda0000_doc_4844
open import FRP.JS.Bool using ( not ) open import FRP.JS.Nat using ( ) renaming ( _≟_ to _≟n_ ) open import FRP.JS.String using ( _≟_ ; _≤_ ; _<_ ; length ) open import FRP.JS.QUnit using ( TestSuite ; ok ; test ; _,_ ) module FRP.JS.Test.String where tests : TestSuite tests = ( test "≟" ( ok "abc ≟ abc" ("ab...
algebraic-stack_agda0000_doc_4845
-- Andreas, 2017-11-06, issue #2840 reported by wenkokke Id : (F : Set → Set) → Set → Set Id F = F data D (A : Set) : Set where c : Id _ A -- WAS: internal error in positivity checker -- EXPECTED: success, or -- The target of a constructor must be the datatype applied to its -- parameters, _F_2 A isn't -- when ch...
algebraic-stack_agda0000_doc_4846
------------------------------------------------------------------------ -- This module proves that the context-sensitive language aⁿbⁿcⁿ can -- be recognised ------------------------------------------------------------------------ -- This is obvious given the proof in -- TotalRecognisers.LeftRecursion.ExpressiveStren...
algebraic-stack_agda0000_doc_4847
postulate Nat : Set Fin : Nat → Set Finnat : Nat → Set fortytwo : Nat finnatic : Finnat fortytwo _==_ : Finnat fortytwo → Finnat fortytwo → Set record Fixer : Set where field fix : ∀ {x} → Finnat x → Finnat fortytwo open Fixer {{...}} postulate Fixidentity : {{_ : Fixer}} → Set instance fixiden...
algebraic-stack_agda0000_doc_13248
module Categories.Setoids where open import Library open import Categories record Setoid {a b} : Set (lsuc (a ⊔ b)) where field set : Set a eq : set → set → Set b ref : {s : set} → eq s s sym' : {s s' : set} → eq s s' → eq s' s trn : {s s' s'' : set} → eq s s' → eq s...
algebraic-stack_agda0000_doc_13249
------------------------------------------------------------------------ -- Divisibility and coprimality ------------------------------------------------------------------------ module Data.Integer.Divisibility where open import Data.Function open import Data.Integer open import Data.Integer.Properties import Data.Na...
algebraic-stack_agda0000_doc_13250
module Issue18 where postulate D : Set data ∃ (A : D → Set) : Set where _,_ : (witness : D) → A witness → ∃ A
algebraic-stack_agda0000_doc_13251
{-# OPTIONS --cubical #-} module Cubical.README where ------------------------------------------------------------------------ -- An experimental library for Cubical Agda ----------------------------------------------------------------------- -- The library comes with a .agda-lib file, for use with the library -- man...
algebraic-stack_agda0000_doc_13252
module Lang.Function where import Lvl open import Data.Boolean open import Data.List as List using (List) open import Data.List.Functions.Positional as List open import Data.Option open import Data open import Lang.Reflection open import Syntax.Do open import Type -- A default value tactic for implicit arguments...
algebraic-stack_agda0000_doc_13253
postulate T C D : Set instance I : {{_ : C}} → D d : {{_ : D}} → T t : T t = d
algebraic-stack_agda0000_doc_13254
{-# OPTIONS --without-K --safe #-} module Categories.Diagram.Cone.Properties where open import Level open import Categories.Category open import Categories.Functor open import Categories.Functor.Properties open import Categories.NaturalTransformation import Categories.Diagram.Cone as Con import Categories.Morphism.R...
algebraic-stack_agda0000_doc_13255
{-# OPTIONS --safe #-} module Definition.Conversion.HelperDecidable where open import Definition.Untyped open import Definition.Untyped.Properties open import Definition.Typed open import Definition.Typed.Properties open import Definition.Conversion open import Definition.Conversion.Whnf open import Definition.Conver...
algebraic-stack_agda0000_doc_13256
record R (X : Set) : Set₁ where field P : X → Set f : ∀ {x : X} → P x → P x open R {{…}} test : ∀ {X} {{r : R X}} {x : X} → P x → P x test p = f p -- WAS: instance search fails with several candidates left -- SHOULD: succeed
algebraic-stack_agda0000_doc_13257
------------------------------------------------------------------------ -- The Agda standard library -- -- Heterogeneous equality ------------------------------------------------------------------------ {-# OPTIONS --with-K --safe #-} module Relation.Binary.HeterogeneousEquality where import Axiom.Extensionality.He...
algebraic-stack_agda0000_doc_13258
{-# OPTIONS --without-K #-} module Data.Word8.Primitive where open import Agda.Builtin.Bool using (Bool) open import Agda.Builtin.Nat using (Nat) {-# FOREIGN GHC import qualified Data.Word #-} {-# FOREIGN GHC import qualified Data.Bits #-} postulate Word8 : Set _==_ : Word8 → Word8 → Bool _/=_ : Word8 → Word8...
algebraic-stack_agda0000_doc_13259
------------------------------------------------------------------------------ -- Testing the --schematic-propositional-symbols option ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-un...
algebraic-stack_agda0000_doc_13260
module Formalization.ClassicalPropositionalLogic.NaturalDeduction.Consistency where import Lvl open import Formalization.ClassicalPropositionalLogic.NaturalDeduction open import Formalization.ClassicalPropositionalLogic.NaturalDeduction.Proofs open import Formalization.ClassicalPropositionalLogic.Syntax open impo...
algebraic-stack_agda0000_doc_13261
open import Structure.Operator.Field open import Structure.Setoid open import Type -- Operators for matrices over a field. module Numeral.Matrix.OverField {ℓ ℓₑ}{T : Type{ℓ}} ⦃ equiv : Equiv{ℓₑ}(T) ⦄ {_+ₛ_ _⋅ₛ_ : T → T → T} ⦃ field-structure : Field(_+ₛ_)(_⋅ₛ_) ⦄ where open Field(field-structure) renaming (_−_ to _−ₛ_...
algebraic-stack_agda0000_doc_13262
module Five where open import Relation.Binary.PropositionalEquality open ≡-Reasoning import Data.Nat as ℕ import Data.Nat.Properties as ℕₚ import Data.List as List import Data.List.Properties as Listₚ import Data.Product as Product open List using (List; []; _∷_; _++_) open ℕ using (ℕ; zero; suc; _+_) open Product u...
algebraic-stack_agda0000_doc_13263
open import Prelude renaming (lift to finlift) hiding (id; subst) module Implicits.Substitutions.Lemmas.LNMetaType where open import Implicits.Syntax.LNMetaType open import Implicits.Substitutions.LNMetaType open import Data.Fin.Substitution open import Data.Fin.Substitution.Lemmas open import Data.Vec.Properties o...
algebraic-stack_agda0000_doc_14048
{-# OPTIONS --universe-polymorphism #-} module Categories.Enriched where open import Categories.Category open import Categories.Monoidal -- moar
algebraic-stack_agda0000_doc_14049
{-# OPTIONS --without-K --rewriting #-} open import lib.Basics open import lib.cubical.Square open import lib.types.Bool open import lib.types.Coproduct open import lib.types.FunctionSeq open import lib.types.Paths open import lib.types.Pointed open import lib.types.Span open import lib.types.Pushout open import lib.t...
algebraic-stack_agda0000_doc_14050
-- Testing parameterised records in parameterised modules module Exist (X : Set) where data [_] (a : Set) : Set where [] : [ a ] _∷_ : a -> [ a ] -> [ a ] map : forall {a b} -> (a -> b) -> [ a ] -> [ b ] map f [] = [] map f (x ∷ xs) = f x ∷ map f xs record ∃ (a : Set) (P : a -> Set) : Set where field ...
algebraic-stack_agda0000_doc_14051
{-# OPTIONS --without-K --safe #-} open import Relation.Binary using (Rel; Setoid; IsEquivalence) module Structures {a ℓ} {A : Set a} -- The underlying set (_≈_ : Rel A ℓ) -- The underlying equality relation where open import Algebra.Core open import Level using (_⊔_) open import Data.Product using (_,_; pr...
algebraic-stack_agda0000_doc_14052
-- Andreas, 2016-10-04, issue #2236 -- Result splitting should not insert hidden arguments visibly -- {-# OPTIONS -v interaction.case:100 #-} -- {-# OPTIONS -v tc.cover:100 #-} -- {-# OPTIONS -v reify.clause:100 #-} -- {-# OPTIONS -v reify.implicit:100 #-} splitMe : (A : Set) {B : Set} → Set splitMe = {!!} -- C-c C-...
algebraic-stack_agda0000_doc_14053
{-# OPTIONS --without-K --exact-split --safe #-} open import Fragment.Algebra.Signature module Fragment.Algebra.Free.Base (Σ : Signature) where open import Fragment.Algebra.Algebra Σ open import Fragment.Algebra.Free.Atoms public open import Level using (Level; _⊔_) open import Function using (_∘_) open import Dat...
algebraic-stack_agda0000_doc_14054
-- 2011-09-14 posted by Nisse -- Andreas: this failed since SubstHH for Telescopes was wrong. -- {-# OPTIONS --show-implicit -v tc.lhs.unify:15 #-} module Issue292-14 where data D : Set where d : D postulate T : D → D → Set data T′ (x y : D) : Set where c : T x y → T′ x y F : D → D → Set F x d = T′ x d -- bloc...
algebraic-stack_agda0000_doc_14055
{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-} {-# OPTIONS --type-in-type #-} -- Note: Using this module is discouraged unless absolutely necessary. -- Use `Data.Product` or `Data.Both` instead. module Light.Indexed where open import Light.Level using (Level) postulate ℓ : Level rec...
algebraic-stack_agda0000_doc_14056
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Algebra.Group.Action where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.HLevels open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Structure open import Cubical.A...
algebraic-stack_agda0000_doc_14057
{- This file contains: - Properties of set truncations -} {-# OPTIONS --cubical --safe #-} module Cubical.HITs.SetTruncation.Properties where open import Cubical.HITs.SetTruncation.Base open import Cubical.Foundations.Prelude open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Equiv open im...
algebraic-stack_agda0000_doc_14058
{-# OPTIONS --without-K #-} open import Base open import Homotopy.TruncatedHIT open import Spaces.Spheres open import Integers module Sets.Quotient {i j} (A : Set i) ⦃ p : is-set A ⦄ (R : A → A → Set j) ⦃ q : (x y : A) → is-prop (R x y) ⦄ where private data _#/_ : Set (max i j) where #proj : A → _#/_ #t...
algebraic-stack_agda0000_doc_14059
{-# OPTIONS --allow-unsolved-metas #-} -- When instantiating metas, we can't ignore variables occurring in -- irrelevant terms. If we do the irrelevant terms will become illformed -- (and we get __IMPOSSIBLE__s) -- For instance -- _42 := DontCare (Just (Var 0 [])) -- is a bad thing to do. In the example below we hit ...
algebraic-stack_agda0000_doc_14060
module Categories.Support.Experimental where open import Relation.Binary.PropositionalEquality.TrustMe open import Categories.Support.PropositionalEquality ≣-relevant : ∀ {l} {A : Set l} {X Y : A} -> .(X ≣ Y) -> X ≣ Y ≣-relevant _ = trustMe private ≣-coe : ∀ {a} {A B : Set a} → (A ≣ B) -> A -> B ≣-coe ≣-refl a ...
algebraic-stack_agda0000_doc_14061
{-# OPTIONS --without-K --safe #-} open import Polynomial.Parameters module Polynomial.NormalForm.Construction {a ℓ} (coeffs : RawCoeff a ℓ) where open import Relation.Nullary using (Dec; yes; no) open import Level using (lift; lower; _⊔_) open import Data.Unit using (...
algebraic-stack_agda0000_doc_14062
-- Andreas, 2011-04-14 module UnificationUndecidedForNonStronglyRigidOccurrence where data Nat : Set where zero : Nat suc : Nat -> Nat data _≡_ {A : Set}(a : A) : A -> Set where refl : a ≡ a i : (f : Nat -> Nat)(n : Nat) -> n ≡ f n -> Nat i f n () -- this should fail, since n ≡ f n is not always empty, only i...
algebraic-stack_agda0000_doc_14063
{-# OPTIONS --safe #-} module JVM.Compiler where open import JVM.Types open import JVM.Syntax.Instructions module _ 𝑭 where open import JVM.Compiler.Monad StackTy ⟨ 𝑭 ∣_↝_⟩ noop using (Compiler) public module _ {𝑭} where open import JVM.Compiler.Monad StackTy ⟨ 𝑭 ∣_↝_⟩ noop hiding (Compiler) public
algebraic-stack_agda0000_doc_13648
-- The purpose of this universe construction is to get some definitional -- equalities in the model. Specifically, if we define ⟦σ⟧ : ⟦Δ⟧ → ⟦Ω⟧ -- (a functor) for the "canonical" notion of subsitution, then we have -- ⟦Wk⟧ (δ , m) ≡ δ propositionally, but *not* definitionally. This then -- complicates proofs involving ...
algebraic-stack_agda0000_doc_13649
{-# OPTIONS --safe #-} module Cubical.Algebra.DirectSum.DirectSumHIT.Properties where open import Cubical.Foundations.Prelude open import Cubical.Data.Empty as ⊥ open import Cubical.Data.Sigma open import Cubical.Relation.Nullary open import Cubical.Algebra.Group open import Cubical.Algebra.AbGroup open import Cubi...
algebraic-stack_agda0000_doc_13650
-- Check that unquoted functions are termination checked. module _ where open import Common.Prelude hiding (_>>=_) open import Common.Reflection `⊥ : Type `⊥ = def (quote ⊥) [] {- Generate aux : ⊥ aux = aux loop : ⊥ loop = aux -} makeLoop : QName → TC ⊤ makeLoop loop = freshName "aux" >>= λ aux → declar...
algebraic-stack_agda0000_doc_13651
------------------------------------------------------------------------ -- The Agda standard library -- -- Definitions for types of functions that only require an equality -- relation over the domain. ------------------------------------------------------------------------ -- The contents of this file should usually ...