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algebraic-stack_agda0000_doc_7876
module Impossible where {-# IMPOSSIBLE #-}
algebraic-stack_agda0000_doc_7877
module _ where open import Agda.Builtin.Equality open import Agda.Builtin.Bool open import Agda.Builtin.Unit open import Agda.Builtin.List open import Agda.Builtin.Nat open import Agda.Builtin.Reflection renaming (returnTC to return; bindTC to _>>=_) _>>_ : {A B : Set} → TC A → TC B → TC B m >> m' = m >>= λ _ → m' ...
algebraic-stack_agda0000_doc_7878
open import Agda.Builtin.Nat data Sing : Nat → Set where i : (k : Nat) → Sing k toSing : (n : Nat) → Sing n toSing n = i n fun : (n : Nat) → Nat fun n with toSing n fun .n | i n with toSing n fun .(n + n) | i .n | i n = {!!}
algebraic-stack_agda0000_doc_7879
module PrintNat where import PreludeShow open PreludeShow mainS = showNat 42
algebraic-stack_agda0000_doc_7880
------------------------------------------------------------------------ -- The Agda standard library -- -- The sublist relation over propositional equality. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.List.Relation.Binary.Subset.Propositiona...
algebraic-stack_agda0000_doc_7881
open import Common.Prelude renaming (Nat to ℕ; _+_ to _+ℕ_) open import Common.Product open import Common.Equality postulate _≤ℕ_ : (n m : ℕ) → Set maxℕ : (n m : ℕ) → ℕ When : (b : Bool) (P : Set) → Set When true P = P When false P = ⊤ infix 30 _⊕_ infix 20 _+_ infix 10 _≤_ infix 10 _<_ infixr 4 _,_ mutual ...
algebraic-stack_agda0000_doc_7882
open import Categories open import Functors open import RMonads module RMonads.RKleisli.Functors {a b c d}{C : Cat {a}{b}}{D : Cat {c}{d}} {J : Fun C D}(M : RMonad J) where open import Library open import RMonads.RKleisli M open import RAdjunctions open Cat open Fun open RMonad M RK...
algebraic-stack_agda0000_doc_7883
postulate B : Set module M where record ⊤ : Set where module P (A : Set) where open M public module PB = P B
algebraic-stack_agda0000_doc_7884
{-# OPTIONS --experimental-irrelevance #-} {-# OPTIONS --sized-types #-} open import Agda.Primitive public using (lzero; lsuc) open import Agda.Builtin.Size public using (Size; ↑_) renaming (∞ to oo) open import Agda.Builtin.Nat public using (suc) renaming (Nat to ℕ) _+_ : Size → ℕ → Size s + 0 = s s + suc n ...
algebraic-stack_agda0000_doc_7885
import Oscar.Class.Reflexivity.Function import Oscar.Class.Transextensionality.Proposequality -- FIXME why not use the instance here? open import Oscar.Class open import Oscar.Class.Category open import Oscar.Class.HasEquivalence open import Oscar.Class.IsCategory open import Oscar.Class.IsPrecategory open import Osca...
algebraic-stack_agda0000_doc_7886
open import MLib.Algebra.PropertyCode open import MLib.Algebra.PropertyCode.Structures module MLib.Matrix.SemiTensor.Core {c ℓ} (struct : Struct bimonoidCode c ℓ) where open import MLib.Prelude open import MLib.Matrix.Core open import MLib.Matrix.Equality struct open import MLib.Matrix.Mul struct open import MLib.Mat...
algebraic-stack_agda0000_doc_7887
{-# OPTIONS --safe #-} module Cubical.Data.Int.MoreInts.BiInvInt where open import Cubical.Data.Int.MoreInts.BiInvInt.Base public open import Cubical.Data.Int.MoreInts.BiInvInt.Properties public
algebraic-stack_agda0000_doc_9120
open import Agda.Primitive variable a : Level A : Set a x : A postulate P : ∀ {a b} {A : Set a} {B : Set b} → (A → B) → Set p : P x postulate H : ∀ a (A : Set a) (x : A) → Set Id : ∀ {a} (A : Set a) → A → A → Set a h : (i : H _ _ x) (j : H a _ _) → Id (H _ A _) i j
algebraic-stack_agda0000_doc_9121
{- The sheaf property of a presheaf on a distributive lattice or a basis thereof can be expressed as preservation of limits over diagrams defined in this file. -} {-# OPTIONS --safe #-} module Cubical.Categories.DistLatticeSheaf.Diagram where open import Cubical.Foundations.Prelude open import Cubical.Foundations.I...
algebraic-stack_agda0000_doc_9122
module list-thms where -- see list-thms2 for more open import bool open import bool-thms open import functions open import list open import nat open import nat-thms open import product-thms open import logic ++[] : ∀{ℓ}{A : Set ℓ} → (l : 𝕃 A) → l ++ [] ≡ l ++[] [] = refl ++[] (x :: xs) rewrite ++[] xs = refl ++-a...
algebraic-stack_agda0000_doc_9123
------------------------------------------------------------------------ -- The Agda standard library -- -- Pointwise lifting of relations to vectors ------------------------------------------------------------------------ module Relation.Binary.Vec.Pointwise where open import Category.Applicative.Indexed open import...
algebraic-stack_agda0000_doc_9124
-- Andreas, 2017-01-26. Testing the --no-eta-equality option. -- Records in files without the option (unless Agda runs with this -- option globally), should have eta. module HaveEtaForImportedRecords.EtaRecord where open import Agda.Builtin.Equality public record ⊤ : Set where private test : ∀{x y : ⊤} → x ≡ y ...
algebraic-stack_agda0000_doc_9125
module _ where open import Agda.Builtin.Nat module Postulates where infixl 5 _<*>_ postulate F : Set → Set pure : ∀ {A} → A → F A _<*>_ : ∀ {A B} → F (A → B) → F A → F B test₀ : F Nat → F Nat → F Nat test₀ a b = (| a + b |) test₁ : F Nat test₁ = (| 5 |) test₂ : F Nat → F Nat tes...
algebraic-stack_agda0000_doc_9126
open import Data.Boolean open import Type module Data.List.Sorting.HeapSort {ℓ} {T : Type{ℓ}} (_≤?_ : T → T → Bool) where import Lvl open import Data.List import Data.List.Functions as List open import Data.BinaryTree import Data.BinaryTree.Heap as Heap open import Functional using (_∘_) heapSort : Li...
algebraic-stack_agda0000_doc_9127
module Lemmachine.Default.Lemmas where open import Lemmachine import Lemmachine.Default import Lemmachine.Lemmas open Lemmachine.Lemmas Lemmachine.Default.resource open import Relation.Binary.PropositionalEquality open import Data.Empty open import Data.Maybe open import Data.Product hiding (map) open import Data.Funct...
algebraic-stack_agda0000_doc_9128
-- Andreas, 2020-03-27, issue #3684 -- Warn about duplicate fields instead of hard error. module DuplicateFields where postulate X : Set record D : Set where field x : X d : X → X → D d x y = record{ x = x; x = y }
algebraic-stack_agda0000_doc_9129
{-# OPTIONS --without-K --exact-split --allow-unsolved-metas #-} module 14-image where import 13-propositional-truncation open 13-propositional-truncation public {- We introduce the image inclusion of a map. -} precomp-emb : { l1 l2 l3 l4 : Level} {X : UU l1} {A : UU l2} (f : A → X) {B : UU l3} ( i : B ↪ X) (q ...
algebraic-stack_agda0000_doc_9130
module Builtin where data Bool : Set where false : Bool true : Bool not : Bool -> Bool not true = false not false = true _||_ : Bool -> Bool -> Bool true || _ = true false || x = x _&&_ : Bool -> Bool -> Bool true && x = x false && _ = false {-# BUILTIN BOOL Bool #-} {-# BUILTIN TRUE true #-} {-# BUILTI...
algebraic-stack_agda0000_doc_9131
{-# OPTIONS --without-K --safe #-} open import Categories.Category using (Category) -- 'Heterogeneous' identity morphism and some laws about them. module Categories.Morphism.HeterogeneousIdentity {o ℓ e} (C : Category o ℓ e) where open import Level open import Relation.Binary.PropositionalEquality import Categories...
algebraic-stack_agda0000_doc_9132
{-# OPTIONS --allow-unsolved-metas #-} open import Oscar.Class open import Oscar.Class.Smap open import Oscar.Class.Transitivity open import Oscar.Class.Reflexivity open import Oscar.Class.Transleftidentity open import Oscar.Class.Symmetry open import Oscar.Class.Hmap open import Oscar.Data.Proposequality open import ...
algebraic-stack_agda0000_doc_9133
open import Level open import Ordinals module VL {n : Level } (O : Ordinals {n}) where open import zf open import logic import OD open import Relation.Nullary open import Relation.Binary open import Data.Empty open import Relation.Binary open import Relation.Binary.Core open import Relation.Binary.PropositionalEqu...
algebraic-stack_agda0000_doc_9134
{-# OPTIONS --without-K --safe #-} module Categories.Category.Discrete where -- Discrete Category. -- https://ncatlab.org/nlab/show/discrete+category -- says: -- A category is discrete if it is both a groupoid and a preorder. That is, -- every morphism should be invertible, any two parallel morphisms should be equal. ...
algebraic-stack_agda0000_doc_9135
module Issue417 where data _≡_ (A : Set₁) : Set₁ → Set₂ where refl : A ≡ A abstract A : Set₁ A = Set unfold-A : A ≡ Set unfold-A = refl -- The result of inferring the type of unfold-A is the following: -- -- Set ≡ Set
algebraic-stack_agda0000_doc_11056
-- The debug output should include the text "Termination checking -- mutual block MutId 0" once, not three times. {-# OPTIONS -vterm.mutual.id:40 #-} record R : Set₁ where constructor c field A : Set _ : A → A _ = λ x → x _ : A → A _ = λ x → x _ : A → A _ = λ x → x -- Included in order to make...
algebraic-stack_agda0000_doc_11057
------------------------------------------------------------------------ -- The Agda standard library -- -- Decidable equality over lists parameterised by some setoid ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Relation.Binary module Data.Li...
algebraic-stack_agda0000_doc_11058
module Everything where import Relation.Ternary.Separation -- The syntax and interpreter of LTLC import Typed.LTLC -- The syntax and interpreter of LTLC with strong updatable references import Typed.LTLCRef -- The syntax of a session typed language import Sessions.Syntax -- ... and its semantics import Sessions.Se...
algebraic-stack_agda0000_doc_11059
{-# OPTIONS --safe --warning=error --without-K #-} open import LogicalFormulae open import Functions.Definition open import Lists.Definition open import Lists.Monad open import Boolean.Definition module Lists.Filter.AllTrue where allTrue : {a b : _} {A : Set a} (f : A → Set b) (l : List A) → Set b allTrue f [] = Tru...
algebraic-stack_agda0000_doc_11060
module _ (A : Set) where record R : Set where field f : A test : R → R test r = {!r!}
algebraic-stack_agda0000_doc_11061
module Text.Greek.SBLGNT.Rom where open import Data.List open import Text.Greek.Bible open import Text.Greek.Script open import Text.Greek.Script.Unicode ΠΡΟΣ-ΡΩΜΑΙΟΥΣ : List (Word) ΠΡΟΣ-ΡΩΜΑΙΟΥΣ = word (Π ∷ α ∷ ῦ ∷ ∙λ ∷ ο ∷ ς ∷ []) "Rom.1.1" ∷ word (δ ∷ ο ∷ ῦ ∷ ∙λ ∷ ο ∷ ς ∷ []) "Rom.1.1" ∷ word (Χ ∷ ρ ∷ ι ∷ ...
algebraic-stack_agda0000_doc_11062
------------------------------------------------------------------------ -- The Agda standard library -- -- Examples showing how the case expressions can be used ------------------------------------------------------------------------ module README.Case where open import Data.Fin hiding (pred) open import Data.Mayb...
algebraic-stack_agda0000_doc_11063
{-# OPTIONS --universe-polymorphism #-} module Categories.FunctorCategory where open import Data.Product open import Categories.Category import Categories.Functor as Cat open import Categories.Functor hiding (equiv; id; _∘_; _≡_) open import Categories.NaturalTransformation open import Categories.Product open import ...
algebraic-stack_agda0000_doc_11064
{-# OPTIONS --without-K #-} open import library.Basics hiding (Type ; Σ) open import library.types.Sigma open import Sec2preliminaries module Sec3hedberg where -- Lemma 3.2 discr→pathHasConst : {X : Type} → has-dec-eq X → pathHasConst X discr→pathHasConst dec x₁ x₂ with (dec x₁ x₂) discr→pathHasConst dec x₁ x₂ |...
algebraic-stack_agda0000_doc_11065
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Relation.Binary.Raw where open import Cubical.Relation.Binary.Base public open import Cubical.Relation.Binary.Raw.Definitions public open import Cubical.Relation.Binary.Raw.Structures public open import Cubical.Relation.Binary.Raw.Bundles public
algebraic-stack_agda0000_doc_11066
{-# OPTIONS --allow-unsolved-metas #-} postulate Nat : Set variable A : _ F : _ → _
algebraic-stack_agda0000_doc_11067
------------------------------------------------------------------------ -- The Agda standard library -- -- Properties related to Fin, and operations making use of these -- properties (or other properties not available in Data.Fin) ------------------------------------------------------------------------ {-# OPTIONS --...
algebraic-stack_agda0000_doc_11068
{-# OPTIONS --without-K --rewriting #-} open import HoTT open import homotopy.HSpace renaming (HSpaceStructure to HSS) open import homotopy.Freudenthal open import homotopy.IterSuspensionStable open import homotopy.Pi2HSusp open import homotopy.EM1HSpace open import homotopy.EilenbergMacLane1 module homotopy.Eilenber...
algebraic-stack_agda0000_doc_11069
------------------------------------------------------------------------ -- The Agda standard library -- -- Core definitions for Characters ------------------------------------------------------------------------ module Data.Char.Core where open import Data.Nat using (ℕ) open import Data.Bool using (Bool; true; false...
algebraic-stack_agda0000_doc_11070
module Imports.Bool where data Bool : Set where true false : Bool
algebraic-stack_agda0000_doc_11071
module AKS.Rational where open import AKS.Rational.Base public open import AKS.Rational.Properties public
algebraic-stack_agda0000_doc_10144
------------------------------------------------------------------------ -- Properties related to negation ------------------------------------------------------------------------ module Relation.Nullary.Negation where open import Relation.Nullary open import Relation.Unary open import Data.Empty open import Data.Fun...
algebraic-stack_agda0000_doc_10145
open import Common.Prelude open import Common.Reflection open import Common.Equality ` : Term → Term ` (def f []) = con (quote def) (vArg (lit (qname f)) ∷ vArg (con (quote []) []) ∷ []) ` _ = lit (string "other") macro primQNameType : QName → Tactic primQNameType f hole = bindTC (getType f) λ a → bindTC ...
algebraic-stack_agda0000_doc_10146
-- Andreas, 2017-11-01, issue #2824 -- allow built-in pragmas in parametrized modules {-# OPTIONS --rewriting #-} open import Agda.Builtin.Equality module _ (A : Set) where -- This is the top-level module header. {-# BUILTIN REWRITE _≡_ #-} postulate P : A → Set a b : A a→b : a ≡ b {-# REWRITE a→b #-} tes...
algebraic-stack_agda0000_doc_10147
-- Andreas, 2019-11-06 issue #4168, version with shape-irrelevance. -- Eta-contraction of records with all-irrelevant fields is unsound. -- In this case, it lead to a compilation error. {-# OPTIONS --irrelevant-projections #-} -- {-# OPTIONS -v tc.cc:20 #-} open import Agda.Builtin.Unit open import Common.IO using ...
algebraic-stack_agda0000_doc_10148
open import Agda.Builtin.Bool open import Agda.Builtin.Equality open import Agda.Builtin.List open import Agda.Builtin.Reflection renaming (bindTC to _>>=_) open import Agda.Builtin.Unit postulate @0 A : Set @0 _ : @0 Set → (Set → Set) → Set _ = λ @0 where A G → G A @0 _ : @0 Set → (Set → Set) → Set _ = λ @0 { A...
algebraic-stack_agda0000_doc_10149
-- Category of □-coalgebras module SOAS.Abstract.Coalgebra {T : Set} where open import SOAS.Common open import SOAS.Construction.Structure as Structure open import SOAS.Context open import SOAS.ContextMaps.Combinators open import SOAS.ContextMaps.CategoryOfRenamings {T} open import SOAS.Sorting open import SOAS.Famil...
algebraic-stack_agda0000_doc_10150
{-# OPTIONS --without-K --safe #-} -- The identity pseudofunctor module Categories.Pseudofunctor.Identity where open import Data.Product using (_,_) open import Categories.Bicategory using (Bicategory) import Categories.Bicategory.Extras as BicategoryExt open import Categories.Category using (Category) open import ...
algebraic-stack_agda0000_doc_10151
{-# OPTIONS --cubical --safe #-} module Data.Binary.Equatable where open import Prelude open import Data.Binary.Definition open import Data.Bits.Equatable public
algebraic-stack_agda0000_doc_10152
-- Andreas, 2012-02-14, issue reported by Wolfram Kahl -- {-# OPTIONS -v scope.top:10 #-} module Issue562 where data Bool : Set where true false : Bool f : Bool → Bool f b with b f true | _ = b -- WAS: panic unbound variable b -- should be: Not in scope: b
algebraic-stack_agda0000_doc_10153
-- 2010-11-21 -- testing correct implementation of eta for records with higher-order fields module Issue366 where data Bool : Set where true false : Bool record R (A : Set) : Set where constructor r field unR : A open R foo : Bool foo = unR (r (unR (r (λ (_ : Bool) → false)) true)) -- befor...
algebraic-stack_agda0000_doc_10154
module TerminationMixingTupledCurried where data Nat : Set where zero : Nat succ : Nat -> Nat data _×_ (A B : Set) : Set where _,_ : A -> B -> A × B good : Nat × Nat -> Nat -> Nat good (succ x , y) z = good (x , succ y) (succ z) good (x , succ y) z = good (x , y) x good xy (succ z) = good xy z good _ _ =...
algebraic-stack_agda0000_doc_10155
{-# OPTIONS --safe #-} module Cubical.Algebra.Group where open import Cubical.Algebra.Group.Base public open import Cubical.Algebra.Group.Properties public
algebraic-stack_agda0000_doc_10156
data Nat : Set where zero : Nat suc : Nat → Nat test : ∀{N M : Nat} → Nat → Nat → Nat test N M = {!.N N .M!} -- Andreas, 2016-07-10, issue 2088 -- Changed behavior: -- The hidden variables .N and .M are made visible -- only the visible N is split.
algebraic-stack_agda0000_doc_10157
postulate A : Set f : A → A mutual F : A → Set F x = D (f x) data D : A → Set where c : (x : A) → F x G : (x : A) → D x → Set₁ G _ (c _) = Set
algebraic-stack_agda0000_doc_10158
{-# OPTIONS --copatterns #-} module Issue950b where postulate A : Set record R : Set where field x : A record S : Set where field y : A open R f : ? x f = ? -- Good error: -- Cannot eliminate type ?0 with projection pattern x -- when checking that the clause x f = ? has type ?0
algebraic-stack_agda0000_doc_10159
{-# OPTIONS --without-K --rewriting #-} open import HoTT module groups.KernelSndImageInl {i j k} (G : Group i) {H : Group j} {K : Group k} -- the argument [φ-snd], which is intended to be [φ ∘ᴳ ×-snd], -- gives the possibility of making the second part -- (the proof of being a group homomorphism) abstract. ...
algebraic-stack_agda0000_doc_9936
module OldBasicILP.UntypedSyntax.Common where open import Common.UntypedContext public -- Types parametrised by closed, untyped representations. module ClosedSyntax (Proof : Set) where infixr 10 _⦂_ infixl 9 _∧_ infixr 7 _▻_ data Ty : Set where α_ : Atom → Ty _▻_ : Ty → Ty → Ty _⦂_ : Pro...
algebraic-stack_agda0000_doc_9937
open import Nat open import Prelude open import core open import disjointness module elaboration-generality where mutual elaboration-generality-synth : {Γ : tctx} {e : hexp} {τ : htyp} {d : ihexp} {Δ : hctx} → Γ ⊢ e ⇒ τ ~> d ⊣ Δ → Γ ⊢ e => τ elaboration...
algebraic-stack_agda0000_doc_9938
open import Functional using (id) import Structure.Logic.Constructive.NaturalDeduction module Structure.Logic.Constructive.Functions.Properties {ℓₗ} {Formula} {ℓₘₗ} {Proof} {ℓₒ} {Domain} ⦃ constructiveLogicSign : _ ⦄ where open Structure.Logic.Constructive.NaturalDeduction.ConstructiveLogicSignature {ℓₗ} {Formula...
algebraic-stack_agda0000_doc_9939
------------------------------------------------------------------------ -- The Agda standard library -- -- Finite maps with indexed keys and values, based on AVL trees ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Data.Product as Prod open imp...
algebraic-stack_agda0000_doc_9940
------------------------------------------------------------------------ -- The Agda standard library -- -- Showing booleans ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Bool.Show where open import Data.Bool.Base using (Bool; false; true) ope...
algebraic-stack_agda0000_doc_9941
{-# OPTIONS --cubical --safe #-} open import Algebra module Algebra.SemiringLiterals {r} (rng : Semiring r) where open Semiring rng open import Literals.Number open import Data.Nat.Literals open import Data.Unit import Data.Unit.UniversePolymorphic as Poly open import Data.Nat.DivMod open import Data.Nat using (ℕ; ...
algebraic-stack_agda0000_doc_9942
{-# OPTIONS --without-K --safe #-} module Util.Relation.Binary.PropositionalEquality where open import Relation.Binary.PropositionalEquality public open import Data.Product using (uncurry) open import Util.Prelude private variable α β γ γ′ δ : Level A B C A′ B′ C′ : Set α trans-unassoc : {a b c d : A} ...
algebraic-stack_agda0000_doc_9943
{-# OPTIONS --without-K #-} module MidiEvent where open import Data.Fin using (Fin; #_) open import Data.List using (List; _∷_; []; concat; map) open import Data.Nat using (ℕ; _+_; _⊔_) open import Data.Product using (_×_; _,_; proj₁) open import Data.String using (String) open import Data.Vec using (...
algebraic-stack_agda0000_doc_9944
{-# OPTIONS --without-K --safe #-} module TypeTheory.HoTT.Data.Empty.Properties where -- agda-stdlib open import Data.Empty -- agda-misc open import TypeTheory.HoTT.Base isProp-⊥ : isProp ⊥ isProp-⊥ x = ⊥-elim x
algebraic-stack_agda0000_doc_9945
{-# OPTIONS --without-K --safe #-} module Math.Combinatorics.Function.Properties.Lemma where open import Data.Unit using (tt) open import Data.Product open import Data.Sum open import Data.Nat open import Data.Nat.Properties open import Data.Nat.DivMod open import Data.Nat.Solver using (module +-*-Solver) open import...
algebraic-stack_agda0000_doc_9946
module Semantics where open import Syntax public -- Kripke models. record Model : Set₁ where infix 3 _⊩ᵅ_ field World : Set _≤_ : World → World → Set refl≤ : ∀ {w} → w ≤ w trans≤ : ∀ {w w′ w″} → w ≤ w′ → w′ ≤ w″ → w ≤ w″ idtrans≤ : ∀ {w w′} → (p : w ≤ w′) → trans≤ refl≤ p ≡...
algebraic-stack_agda0000_doc_9947
{- 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 -} {-# OPTIONS --allow-unsolved-metas #-} -- This module proves the two "V...
algebraic-stack_agda0000_doc_9948
-- Andreas, 2017-01-26 -- A hopefully exhaustive list of reasons why a function cannot -- be projection-like. The correctness is ensured by triggering -- a crash if any of the functions in this file is projection-like. {-# OPTIONS -v tc.proj.like.crash:1000 #-} data ⊥ : Set where record ⊤ : Set where data Bool : S...
algebraic-stack_agda0000_doc_9949
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Experiments.CohomologyGroups where open import Cubical.ZCohomology.Base open import Cubical.ZCohomology.Properties open import Cubical.ZCohomology.MayerVietorisUnreduced open import Cubical.ZCohomology.Groups.Unit open import Cubical.ZCohomology.KcompPr...
algebraic-stack_agda0000_doc_9950
module Sec2 where open import Sec4 data Bool : Set where T : Bool F : Bool _∣∣_ : Bool → Bool → Bool _ ∣∣ F = F _ ∣∣ T = T _&_ : Bool → Bool → Bool _ & F = F F & T = F T & T = T _==>_ : Bool → Bool → Bool F ==> _ = T T ==> F = F T ==> T = T not : Bool -> Bool not T = F not F = T data ℕ : Set where Z : ...
algebraic-stack_agda0000_doc_9951
{-# OPTIONS --without-K #-} module algebra.monoid where open import algebra.monoid.core public open import algebra.monoid.morphism public open import algebra.monoid.mset public
algebraic-stack_agda0000_doc_7520
module x02induction where -- prove properties of inductive naturals and operations on them via induction import Relation.Binary.PropositionalEquality as Eq open Eq using (_≡_; refl; cong; sym) open Eq.≡-Reasoning using (begin_; _≡⟨⟩_; step-≡; _∎) open import Data.Nat using (ℕ; zer...
algebraic-stack_agda0000_doc_7521
-- Helper operations to construct and build signatures module SOAS.Syntax.Build (T : Set) where open import SOAS.Common open import SOAS.Families.Build {T} open import SOAS.Context {T} open import Data.List.Base open import SOAS.Syntax.Signature T -- Syntactic sugar to construct arity - sort mappings ⟼₀_ : T → List...
algebraic-stack_agda0000_doc_7522
module ANF where open import Data.Nat open import Data.Vec open import Data.Fin open import Data.String open import Data.Rational open import Data.Sum open import Data.Unit open import Binders.Var record DataConApp (universe a : Set) : Set where constructor _#_◂_ -- theres probably room for a...
algebraic-stack_agda0000_doc_7523
{-# OPTIONS --postfix-projections #-} module StateSized.cellStateDependent where open import Data.Product open import Data.String.Base {- open import SizedIO.Object open import SizedIO.ConsoleObject -} open import SizedIO.Console hiding (main) open import SizedIO.Base open import NativeIO open import StateSizedI...
algebraic-stack_agda0000_doc_7524
module Logic.Propositional.Xor where open import Logic.Propositional open import Logic import Lvl -- TODO: Is it possible write a general construction for arbitrary number of xors? Probably by using rotate₃Fn₃Op₂? data _⊕₃_⊕₃_ {ℓ₁ ℓ₂ ℓ₃} (P : Stmt{ℓ₁}) (Q : Stmt{ℓ₂}) (R : Stmt{ℓ₃}) : Stmt{ℓ₁ Lvl.⊔ ℓ₂ Lvl.⊔ ℓ₃} w...
algebraic-stack_agda0000_doc_7525
module _ where open import Agda.Builtin.Bool postulate Eq : Set → Set it : {A : Set} → ⦃ A ⦄ → A it ⦃ x ⦄ = x module M1 (A : Set) ⦃ eqA : Eq A ⦄ where postulate B : Set variable n : B postulate P : B → Set module M2 (A : Set) ⦃ eqA : Eq A ⦄ where open M1 A postulate p₁ : P n p₂ : P ⦃ it ⦄ n ...
algebraic-stack_agda0000_doc_7526
record R : Set₁ where field A : Set module _ (r : R) where open R r data D : Set where c : A → D data P : D → Set where d : (x : A) → P (c x) postulate f : D → A g : (x : D) → P x → D g x (d y) with Set g x (d y) | _ = x
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postulate A : Set f : A → A → A → A → A → A → A → A → A → A → A test : A test = {!f!}
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{-# OPTIONS --without-K --safe #-} open import Level open import Categories.Category using (Category; _[_,_]) -- Various conclusions that can be drawn from Yoneda -- over a particular Category C module Categories.Yoneda.Properties {o ℓ e : Level} (C : Category o ℓ e) where open import Function using (_$_; Inverse) -...
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------------------------------------------------------------------------ -- A virtual machine ------------------------------------------------------------------------ open import Prelude import Lambda.Virtual-machine.Instructions module Lambda.Virtual-machine {Name : Type} (open Lambda.Virtual-machine.Instructio...
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module Rewrite where open import Common.Equality data _≈_ {A : Set}(x : A) : A → Set where refl : ∀ {y} → x ≈ y lem : ∀ {A} (x y : A) → x ≈ y lem x y = refl thm : {A : Set}(P : A → Set)(x y : A) → P x → P y thm P x y px rewrite lem x y = {!!}
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module Issue3818.M where
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{-# OPTIONS --safe --experimental-lossy-unification #-} module Cubical.Algebra.Polynomials.Multivariate.EquivCarac.An[Am[X]]-Anm[X] where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Isomorphism open import Cubical.Data.Nat renaming (_+_ to _+n_; _·_ to _·n_) open import Cubical.Data.Vec op...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Some defined operations (multiplication by natural number and -- exponentiation) ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Algebra ...
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{-# OPTIONS --cubical --safe --postfix-projections #-} open import Prelude open import Relation.Binary module Data.AVLTree.Internal {k} {K : Type k} {r₁ r₂} (totalOrder : TotalOrder K r₁ r₂) where open import Relation.Binary.Construct.Bounded totalOrder open import Data.Nat using (_+_) open TotalOrder totalOrder usi...
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{-# OPTIONS --guardedness #-} module Stream where import Lvl open import Data.Boolean open import Data.List as List using (List) import Data.List.Functions as List import Data.List.Proofs as List import Data.List.Equiv.Id as List open import Functional open import Function.Iteration open import Fu...
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{-# OPTIONS --without-K #-} module Lecture8 where import Lecture7 open Lecture7 public -- Section 8.1 Propositions is-prop : {i : Level} (A : UU i) → UU i is-prop A = (x y : A) → is-contr (Id x y) is-prop-empty : is-prop empty is-prop-empty () is-prop-unit : is-prop unit is-prop-unit = is-prop-is-contr is-contr-u...
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module MLib.Fin.Parts.Nat where open import MLib.Prelude open import MLib.Fin.Parts.Core open Nat using (_*_; _+_; _<_) open Fin using (fromℕ≤) open Table module Impl where tryLookup : ∀ {n} {a} {A : Set a} → A → Table A n → ℕ → A tryLookup {n = zero} z t _ = z tryLookup {n = suc n} z t zero = lookup t zero ...
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Type-of : {A : Set} → A → Set Type-of {A = A} _ = A module _ (A : Set) where Foo : A → Set Foo a with Type-of a ... | B = B
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module RecordPatternMatching where record _×_ (A B : Set) : Set where constructor _,_ field proj₁ : A proj₂ : B data Unit : Set where unit : Unit foo : Unit × Unit → Unit foo (x , y) = {!!} record Box (A : Set) : Set where constructor [_] field proj : A bar : Box Unit → Unit bar [ x ] = {!!}
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------------------------------------------------------------------------ -- The Agda standard library -- -- Unary relations ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Relation.Unary where open import Data.Empty open import Data.Unit.Base using (...
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-- Andreas, 2016-06-20, issue #1891 -- Computation of which variables are splittable was wrong -- in the presence of a where-module. -- {-# OPTIONS -v interaction.case:20 #-} data D : Set where c : D test : (x : D) → D test x = {!x!} -- C-c C-c where y = c -- WAS: -- Splitting on x reports: -- Not a (split...
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open import Data.Nat using (ℕ; _+_) renaming (_≤?_ to _≤?ₙ_) open import Data.Bool using (Bool; true; false; not; _∧_) open import Data.String using (String; _≟_) open import Data.Sum using (_⊎_; [_,_]′; inj₁; inj₂) open import Data.Product using (_×_; _,_) open import Relation.Nullary u...
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module Category.Monoidal where open import Category.NatIsomorphism