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algebraic-stack_agda0000_doc_13652
------------------------------------------------------------------------ -- Parsers containing non-terminals, and grammars using such parsers ------------------------------------------------------------------------ module StructurallyRecursiveDescentParsing.Grammar where open import Data.Bool open import Data.Empty o...
algebraic-stack_agda0000_doc_13653
{-# OPTIONS --universe-polymorphism #-} module Categories.Square where open import Level open import Function renaming (id to idᶠ; _∘_ to _©_) open import Categories.Support.PropositionalEquality open import Categories.Category import Categories.Morphisms as Mor open import Relation.Binary hiding (_⇒_) module Glue...
algebraic-stack_agda0000_doc_13654
-- Andreas, 2016-06-09 issue during refactoring for #1963 -- Shrunk this issue with projection-like functions from std-lib -- {-# OPTIONS --show-implicit #-} -- {-# OPTIONS -v tc.proj.like:10 #-} open import Common.Level open import Common.Nat renaming ( Nat to ℕ ) data ⊥ : Set where record ⊤ : Set where construc...
algebraic-stack_agda0000_doc_13655
open import Level using (_⊔_; suc; Lift; lift) open import Function using (_$_; _∘_; _⤖_) open import Relation.Nullary using (¬_) open import Relation.Nullary.Decidable using (False) open import Relation.Binary using (Rel; Decidable; Setoid; DecSetoid; IsEquivalence; IsDecEquivalence) open import Data.Empty using (⊥) ...
algebraic-stack_agda0000_doc_13656
open import Agda.Builtin.Nat open import Agda.Builtin.Equality record Eq (A : Set) : Set₁ where field _≈_ : A → A → Set open Eq {{...}} public record Setoid : Set₁ where field ∣_∣ : Set {{eq}} : Eq ∣_∣ open Setoid public -- instance -- EqNat : Eq Nat -- _≈_ {{EqNat}} = _≡_ NatSetoid : Seto...
algebraic-stack_agda0000_doc_13657
open import Data.Bool module GUIgeneric.GUIExample where open import GUIgeneric.Prelude renaming (inj₁ to secondBtn; inj₂ to firstBtn; WxColor to Color) hiding (addButton; _>>_) open import GUIgeneric.GUIDefinitions renaming (add to add'; add' to add) open import GUIgeneric.GUI open import GUIgeneric.GUIExampleLi...
algebraic-stack_agda0000_doc_13658
-- {-# OPTIONS -v tc.conv.level:60 #-} -- {-# OPTIONS -v tc.conv:30 #-} {- Agda development version: Wed Oct 30 16:30:06 GMT 2013 The last line of code triggers the following error, but replacing '_' with 'a' typechecks just fine. Bug.agda:32,8-11 tt != a of type ⊤ when checking that the expression s ...
algebraic-stack_agda0000_doc_13659
module x01-842Naturals where -- This is a comment. {- This is a multi-line comment -} -- Definition of datatype representing natural numbers. ♭ data ℕ : Set where zero : ℕ suc : ℕ → ℕ -- A couple of definitions using this datatype. one : ℕ one = suc zero two : ℕ two = suc (suc zero) -- I could have also...
algebraic-stack_agda0000_doc_13660
-- Andreas, 2018-05-28, issue #3095, fail on attempt to make hidden parent variable visible data Nat : Set where suc : {n : Nat} → Nat data IsSuc : Nat → Set where isSuc : ∀{n} → IsSuc (suc {n}) test : ∀{m} → IsSuc m → Set test p = aux p where aux : ∀{n} → IsSuc n → Set aux isSuc = {!.m!} -- Split on .m h...
algebraic-stack_agda0000_doc_13661
{-# OPTIONS --without-K --safe #-} module Categories.Minus2-Category.Properties where -- All -2-Categories are equivalent to One open import Level open import Data.Product using (Σ; _,_; proj₁; proj₂) open import Data.Unit using (⊤; tt) open import Categories.Minus2-Category open import Categories.Category import C...
algebraic-stack_agda0000_doc_13662
module gc where open import lib -- we will model addresses in memory as just natural numbers Address : Set Address = ℕ -- a value of type (Bounded n) is an address a together with a proof that a is less than n Bounded : Address → Set Bounded n = Σ Address (λ a → a < n ≡ tt) -- a (Cell a) models an addre...
algebraic-stack_agda0000_doc_13663
{- In this file we apply the cubical machinery to Martin Hötzel-Escardó's structure identity principle: https://www.cs.bham.ac.uk/~mhe/HoTT-UF-in-Agda-Lecture-Notes/HoTT-UF-Agda.html#sns -} {-# OPTIONS --cubical --safe #-} module Cubical.Foundations.SIP where open import Cubical.Foundations.Prelude open import Cubi...
algebraic-stack_agda0000_doc_3936
module Record where module M where record A : Set where constructor a open M record B : Set where record C : Set where constructor c x : A x = a y : C y = record {} record D (E : Set) : Set where record F : Set₁ where field G : Set ...
algebraic-stack_agda0000_doc_3937
{-# OPTIONS --cubical --safe #-} module JustBeInjective where open import Cubical.Core.Everything open import Cubical.Data.Unit data maybe (A : Set) : Set where just : A -> maybe A nothing : maybe A variable A : Set unwrap : A → (a : maybe A) → A unwrap _ (just x) = x unwrap a nothing = a just-injective : ∀ {A ...
algebraic-stack_agda0000_doc_3938
{-# OPTIONS --cubical #-} module LaterPrims where open import Agda.Primitive open import Agda.Primitive.Cubical renaming (itIsOne to 1=1) open import Agda.Builtin.Cubical.Path open import Agda.Builtin.Cubical.Sub renaming (Sub to _[_↦_]; primSubOut to outS) module Prims where primitive primLockUniv : Set₁ open...
algebraic-stack_agda0000_doc_3939
module 120-natural-induction-necessary where open import 010-false-true open import 020-equivalence open import 100-natural -- We prove that the induction axiom is necessary. -- Peano axioms without induction. record NaturalWithoutInduction {M : Set} (zero : M) (suc : M -> M) (_==_ : M -> M -> Set) : Set1...
algebraic-stack_agda0000_doc_3940
module Issue468 where data Unit : Set where nothing : Unit data Maybe (A : Set) : Set where nothing : Maybe A just : A → Maybe A data P : (R : Set) → Maybe R → Set₁ where p : (R : Set) (x : R) → P R (just x) works : P Unit (just _) works = p _ nothing fails : Unit → P Unit (just _) fails x = p _ nothing
algebraic-stack_agda0000_doc_3941
{-# OPTIONS --safe --warning=error --without-K #-} open import Setoids.Setoids open import Agda.Primitive using (Level; lzero; lsuc; _⊔_) open import Groups.Definition open import Groups.Homomorphisms.Definition module Groups.Isomorphisms.Definition where record GroupIso {m n o p : _} {A : Set m} {S : Setoid {m} {o}...
algebraic-stack_agda0000_doc_3942
module Lib.Vec where open import Lib.Prelude open import Lib.Nat open import Lib.Fin infixr 40 _::_ _++_ data Vec (A : Set) : Nat -> Set where [] : Vec A 0 _::_ : forall {n} -> A -> Vec A n -> Vec A (suc n) _++_ : {A : Set}{n m : Nat} -> Vec A n -> Vec A m -> Vec A (n + m) [] ++ ys = ys (x :: xs) ++ y...
algebraic-stack_agda0000_doc_3943
{-# OPTIONS --safe #-} module Cubical.Algebra.CommRing.Instances.Unit where open import Cubical.Foundations.Prelude open import Cubical.Data.Unit open import Cubical.Algebra.Ring open import Cubical.Algebra.CommRing private variable ℓ : Level open CommRingStr UnitCommRing : ∀ {ℓ} → CommRing ℓ fst UnitCommRi...
algebraic-stack_agda0000_doc_3944
module Prelude.String where open import Prelude.Bool open import Prelude.Char open import Prelude.List open import Prelude.Nat postulate String : Set nil : String primStringToNat : String → Nat charToString : Char -> String {-# BUILTIN STRING String #-} primitive primStringAppend : String → String → Str...
algebraic-stack_agda0000_doc_3945
module Everything where import Library import Syntax import RenamingAndSubstitution import EquationalTheory
algebraic-stack_agda0000_doc_3946
-- TODO: Unfinished open import Logic open import Type open import Structure.Relator open import Structure.Setoid module Geometry.HilbertAxioms {ℓₚ ℓₗ ℓₚₑ ℓₗₑ ℓₚₗ ℓₚₚₚ} (Point : Type{ℓₚ}) ⦃ equiv-point : Equiv{ℓₚₑ}(Point) ⦄ -- The type of points on a plane. (Line : Type{ℓₗ}) ⦃ equiv-line : Equiv{ℓₗₑ}(Line) ⦄ ...
algebraic-stack_agda0000_doc_3947
{-# OPTIONS --sized-types #-} module GiveSize where postulate Size : Set {-# BUILTIN SIZE Size #-} id : Size → Size id i = {!i!}
algebraic-stack_agda0000_doc_3948
open import Formalization.PredicateLogic.Signature module Formalization.PredicateLogic.Syntax.NegativeTranslations (𝔏 : Signature) where open Signature(𝔏) open import Data.ListSized import Lvl open import Formalization.PredicateLogic.Syntax (𝔏) open import Functional using (_∘_ ; _∘₂_ ; swap) open import Nume...
algebraic-stack_agda0000_doc_3949
module Lawvere where open import Library open import Data.Sum open import Categories open import Categories.Sets open import Categories.Initial open import Categories.PushOuts open import Categories.Products hiding (_×_) open import Categories.CoProducts open import Categories.Terminal open import Functors open impor...
algebraic-stack_agda0000_doc_3950
module UniDB.Subst.Core where open import UniDB.Spec public open import UniDB.Morph.Unit record Ap (T X : STX) : Set₁ where field ap : {Ξ : MOR} {{lkTΞ : Lk T Ξ}} {{upΞ : Up Ξ}} {γ₁ γ₂ : Dom} (ξ : Ξ γ₁ γ₂) (x : X γ₁) → X γ₂ open Ap {{...}} public record ApVr (T : STX) {{vrT : Vr T}} {{apTT : Ap T T}} : ...
algebraic-stack_agda0000_doc_3951
{-# OPTIONS --allow-unsolved-metas #-} infixr 6 _∷_ data List (A : Set) : Set where [] : List A _∷_ : A -> List A -> List A postulate Bool : Set t : Bool long : List Bool long = t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ t ∷ ...
algebraic-stack_agda0000_doc_5280
------------------------------------------------------------------------ -- A definitional interpreter ------------------------------------------------------------------------ {-# OPTIONS --cubical --safe #-} module Lambda.Simplified.Partiality-monad.Inductive.Interpreter where open import Equality.Propositional.Cub...
algebraic-stack_agda0000_doc_5281
module Elements where open import OscarPrelude open import Arity open import Vector open import Element record Elements : Set where constructor ⟨_⟩ field {arity} : Arity elements : Vector Element arity open Elements public instance EqElements : Eq Elements Eq._==_ EqElements (⟨_⟩ {𝑎₁} εs₁) (⟨_⟩ {𝑎₂}...
algebraic-stack_agda0000_doc_5282
{-# OPTIONS --safe --experimental-lossy-unification #-} module Cubical.Categories.DistLatticeSheaf.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Structure open import Cubical.Foundations.HLevels open import Cubical.Foundations.Powerset open import Cubical.Data.Sigma open import Cub...
algebraic-stack_agda0000_doc_5283
{- 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 -} -- This is a selection of useful functions and definitions -- from the s...
algebraic-stack_agda0000_doc_5284
{-# OPTIONS --without-K --safe #-} module Math.NumberTheory.Product.Generic where -- agda-stdlib open import Algebra -- agda-misc open import Math.NumberTheory.Summation.Generic -- TODO add syntax module MonoidProduct {c e} (M : Monoid c e) = MonoidSummation M renaming ( Σ< to Π< ; Σ≤ to Π≤ ; Σ<range to Π...
algebraic-stack_agda0000_doc_5285
postulate C : Set anything : C record I : Set where constructor c field f : C data Wrap : (j : I) → Set where wrap : ∀ {j} → Wrap j -- The following should not pass. -- It did before the fix of #142. issue142 : ∀ {j} → Wrap j → C issue142 {c _} (wrap {c _}) with anything issue142 {c _} (wrap .{c anyth...
algebraic-stack_agda0000_doc_5286
open import Relation.Unary using ( ∅ ; _∪_ ) open import Web.Semantic.DL.Signature using ( Signature ; CN ; RN ) open import Web.Semantic.Util using ( Subset ; ⁅_⁆ ) module Web.Semantic.DL.Role where data Role (Σ : Signature) : Set where ⟨_⟩ : (r : RN Σ) → Role Σ ⟨_⟩⁻¹ : (r : RN Σ) → Role Σ inv : ∀ {Σ} → Role Σ ...
algebraic-stack_agda0000_doc_5287
{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9. Copyright (c) 2020, 2021 Oracle and/or its affiliates. Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl -} open import LibraBFT.Prelude open import LibraBFT.Lemmas open import Libr...
algebraic-stack_agda0000_doc_5288
module Issue252 where data I : Set where zero : I data D : I → Set where c : ∀ i → D i → D i id : I → I id i = i index : ∀ i → D i → I index i _ = i foo : ∀ i → D i → D zero foo .i (c i d) with id i foo ._ (c i d) | zero = d bar : ∀ i → D i → D zero bar .i (c i d) with index i d bar ._ (c i d) | zero = d -- ...
algebraic-stack_agda0000_doc_5289
module Thesis.SIRelBigStep.Normalization where open import Thesis.SIRelBigStep.Lang open import Data.Unit.Base hiding (_≤_) open import Data.Product open import Relation.Binary.PropositionalEquality -- Define logical relation for normalization. Adapted from TAPL Ch. 12. mutual normT : ∀ {Γ} τ (t : Term Γ τ) (ρ : ⟦...
algebraic-stack_agda0000_doc_5290
module Esterel.Environment where open import utility open import Data.Empty open import Esterel.Variable.Signal as Signal using (Signal ; _ₛ) open import Esterel.Variable.Shared as SharedVar using (SharedVar ; _ₛₕ) open import Esterel.Variable.Sequential as SeqVar using (SeqVar ; _ᵥ) open import Data.Product i...
algebraic-stack_agda0000_doc_5291
{-# OPTIONS --safe #-} module Cubical.Algebra.DistLattice.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.Equiv.HalfAdjoint open import Cubical.Foundations.HLevels open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Unival...
algebraic-stack_agda0000_doc_5292
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Relation.Binary.Raw.Construct.Intersection where open import Cubical.Core.Everything open import Cubical.Foundations.Function using (_∘_) open import Cubical.Data.Prod open import Cubical.Data.Sum.Base using (_⊎_; inl; inr; rec) open import Cubical.Re...
algebraic-stack_agda0000_doc_5293
-- Andreas & Jesper, 2018-05-11, issue #3052 reported by identicalsnowflake -- -- The problem here was that free variable collection had the standard -- monoid instance of IntMap, which is just "randomly" picking one variant. -- Thus, if we have both irrelevant and relevant occurrences of a variable, -- we get whatever...
algebraic-stack_agda0000_doc_5294
module Ex3Lec where ---------------------------------------------------------------------------- -- EXERCISE 3 -- MONADS FOR HUTTON'S RAZOR -- -- VALUE: 15% -- DEADLINE: 5pm, Friday 20 November (week 9) -- -- DON'T SUBMIT, COMMIT! -- -- The purpose of this exercise is to introduce you to some useful -- mathematic...
algebraic-stack_agda0000_doc_5295
{-# OPTIONS --type-in-type #-} open import Data.Product data ⊥ : Set where -- f doesn't type check unless we put the equality type in Set data _≡_ {ℓ} {A : Set ℓ} (a : A) : A → Set where refl : a ≡ a subst : ∀ {ℓ ℓ′} {A : Set ℓ} {a b : A} → (P : A → Set ℓ′) → (p : a ≡ b) → P a → P b subst _ refl pa = pa ¬_ : ∀ {...
algebraic-stack_agda0000_doc_4288
{-# OPTIONS --cubical --safe #-} -- Counterpoint Exercises module Exercises where open import MidiEvent open import Note open import Pitch open import Data.Fin open import Data.List open import Data.Nat -- Exercise 5.4 cantusFirmus : List Pitch cantusFirmus = a 4 ∷ c 5 ∷ b 4 ∷ c 5 ∷ d 5 ∷ e 5 ∷ c 5 ∷ b 4 ∷ a 4 ∷ ...
algebraic-stack_agda0000_doc_4289
module examplesPaperJFP.SpaceShipSimpleVar where open import SizedIO.Base open import StateSizedIO.GUI.BaseStateDependent open import Data.Bool.Base open import Data.List.Base open import Data.Integer open import Data.Product hiding (map) open import SizedIO.Object open import SizedIO.IOObject open import NativeIO ...
algebraic-stack_agda0000_doc_4290
-- {-# OPTIONS --no-coverage #-} -- {-# OPTIONS -v tc.cover:20 #-} open import Common.Bool open import Common.Equality _∨_ : Bool → Bool → Bool a ∨ b = if a then true else b module Works where data Term : Bool → Set where I : Term false App : ∀ a b c → a ∨ b ≡ c → Term a → Term b → Term c -- The follo...
algebraic-stack_agda0000_doc_4291
{-# OPTIONS --without-K --safe #-} open import Algebra module Data.FingerTree.View {r m} (ℳ : Monoid r m) where open import Level using (_⊔_) open import Data.Product open import Function open import Data.List as List using (List; _∷_; []) open import Data.FingerTree.Structures ℳ open import Data.FingerTree....
algebraic-stack_agda0000_doc_4292
module Logic.Predicate.Multi where open import Data.Tuple.RaiseTypeᵣ open import Function.Multi open import Function.Multi.Functions open import Numeral.Natural open import Logic.Predicate open import Logic -- Universal quantification of multiple variables. -- Example: -- ∀₊(3) P = ∀{x}{y}{z} → P(x)(y)(z) ∀₊ : (n :...
algebraic-stack_agda0000_doc_4293
{-# OPTIONS --cubical --safe --no-sized-types --no-guardedness --no-subtyping #-} module Agda.Builtin.Cubical.Glue where open import Agda.Primitive open import Agda.Builtin.Sigma open import Agda.Primitive.Cubical renaming (primINeg to ~_; primIMax to _∨_; primIMin to _∧_; ...
algebraic-stack_agda0000_doc_4294
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Algebra.RingSolver.NatAsAlmostRing where open import Cubical.Foundations.Prelude open import Cubical.Data.Nat open import Cubical.Algebra.RingSolver.AlmostRing open import Cubical.Algebra.Semigroup open import Cubical.Algebra.Monoid open import Cubical....
algebraic-stack_agda0000_doc_4295
open import Nat open import Prelude open import core open import contexts open import lemmas-consistency open import type-assignment-unicity open import binders-disjoint-checks open import lemmas-subst-ta module preservation where -- if d and d' both result from filling the hole in ε with terms of the -- same ty...
algebraic-stack_agda0000_doc_4296
{-# OPTIONS --without-K --safe #-} module Categories.NaturalTransformation.NaturalIsomorphism.Properties where open import Level open import Categories.Category open import Categories.Category.Instance.Setoids open import Categories.Functor renaming (id to idF) open import Categories.Functor.Construction.LiftSetoids...
algebraic-stack_agda0000_doc_4297
{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-} module Light.Implementation.Standard where module Data where module Empty where open import Light.Implementation.Standard.Data.Empty public module Unit where open import Light.Implementation.Standard.Data.Unit public mod...
algebraic-stack_agda0000_doc_4298
module Oscar.Data where open import Agda.Builtin.Unit open import Oscar.Function open import Oscar.Level infixr 20 ∷_ infixr 20 _∷_ data NAT : Set where ∅ : NAT ∷_ : NAT → NAT testNAT : NAT testNAT = ∷ ∷ ∷ ∅ -- List data ⟦_⟧ {a} (A : Set a) : Set a where ∅ : ⟦ A ⟧ _∷_ : A → ⟦ A ⟧ → ⟦ A ⟧ -- Nat ⟦⟧ = ⟦ ⊤ ...
algebraic-stack_agda0000_doc_4299
open import Agda.Builtin.Nat record R : Set where field x : Nat open R {{...}} f₁ f₂ : R -- This is fine. x ⦃ f₁ ⦄ = 0 -- THIS WORKS BUT MAKES NO SENSE!!! f₂ ⦃ .x ⦄ = 0
algebraic-stack_agda0000_doc_4300
{-# POLARITY F #-}
algebraic-stack_agda0000_doc_4301
module Imports.Issue1913-M where data D : Set where d : D
algebraic-stack_agda0000_doc_4302
{- 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 -} open import LibraBFT.Prelude open import LibraBFT.Base.PKCS open import LibraBF...
algebraic-stack_agda0000_doc_4303
module Vehicle.Data.Tensor where open import Level using (Level) open import Data.Empty.Polymorphic using (⊥) open import Data.Nat.Base using (ℕ; zero; suc) open import Data.List.Base using (List; []; _∷_) open import Data.Vec.Functional using (Vector) private variable a : Level A : Set a n : ℕ Tensor...
algebraic-stack_agda0000_doc_5360
module GUIgeneric.GUIExampleBankAccount where open import GUIgeneric.Prelude renaming (inj₁ to firstBtn; inj₂ to secondBtn; WxColor to Color;_∸_ to _-_) hiding (addButton; _>>_ ; show) open import GUIgeneric.GUIDefinitions renaming (add to add'; add' to add) open import GUIgeneric.GUI open import GUIgeneric.GUIExa...
algebraic-stack_agda0000_doc_5361
-- {-# OPTIONS -v 100 -v tc.meta.name:100 -v interactive.meta:10 #-} module Issue526 where -- Don't just write _49, -- include the corresponding implicit variable name as well (if any) postulate f : {A : Set} → {a : A} → Set1 → {B : Set} → Set test : Set test = f Set test₁ : Set test₁ = f {A = _} Set postulate ...
algebraic-stack_agda0000_doc_5362
module MLib.Prelude.RelProps where open import MLib.Prelude.FromStdlib import Relation.Binary.Indexed as I open FE using (cong) import Data.Product.Relation.SigmaPropositional as OverΣ Σ-bij : ∀ {a b c} {A : Set a} {B : A → Set b} {C : A → Set c} → (∀ x → B x ↔ C x) → Σ A B ↔ Σ A C Σ-bij pw = record { to = ≡.→-to-...
algebraic-stack_agda0000_doc_5363
module Imports.A where postulate A : Set
algebraic-stack_agda0000_doc_5364
module _ where import Issue1168 ; module I = Issue1168 import PrettyInterface ; module P = PrettyInterface id : {A : Set} → A → A id {A = A} a = a
algebraic-stack_agda0000_doc_5365
module Dot where postulate h : Set f : Set -> Set -> Set f .n n = h
algebraic-stack_agda0000_doc_5366
{-# OPTIONS --cubical --no-exact-split --safe #-} module Cubical.Data.Nat.Properties where open import Cubical.Core.Everything open import Cubical.Foundations.Prelude open import Cubical.Data.Nat.Base open import Cubical.Data.Empty open import Cubical.Data.Prod.Base open import Cubical.Relation.Nullary open import ...
algebraic-stack_agda0000_doc_5367
{- 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 -} open import Haskell.Modules.RWS.RustAnyHow import LibraBFT.Impl.Consensu...
algebraic-stack_agda0000_doc_5368
module Data.BitVector.ContainmentOrder where open import Data.Empty open import Data.Sum open import Data.Vec open import Relation.Nullary open import Relation.Binary open import Relation.Binary.PropositionalEquality open import Data.Nat hiding (_≟_; _≤_; _≤?_) renaming (zero to Nzero; suc to Nsuc) open import Data...
algebraic-stack_agda0000_doc_5369
------------------------------------------------------------------------ -- The Agda standard library -- -- Properties of sums (disjoint unions) ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Sum.Properties where open import Level open import D...
algebraic-stack_agda0000_doc_5370
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Displayed.Properties where open import Cubical.Foundations.Prelude open import Cubical.Foundations.HLevels open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Equiv open import Cubical.Foundations.Univalence using (pathToEquiv) ...
algebraic-stack_agda0000_doc_5371
{- This file contains: - the abelianization of groups as a coequalizer of sets as performed in https://1lab.dev/Algebra.Group.Ab.Free.html - the proof that this way of defining the abelianization of groups is equivalent to defining it as a HIT, more precisely that there is a unique isomorphism betw...
algebraic-stack_agda0000_doc_5372
module list-to-string where open import list open import string 𝕃-to-string : ∀ {ℓ} {A : Set ℓ} → (f : A → string) → (separator : string) → 𝕃 A → string 𝕃-to-string f sep [] = "" 𝕃-to-string f sep (x1 :: (x2 :: xs)) = (f x1) ^ sep ^ (𝕃-to-string f sep (x2 :: xs)) 𝕃-to-string f sep (x1 :: []) = (f x1)
algebraic-stack_agda0000_doc_5373
module AbstractRationals where open import Algebra open import Data.Integer.Base using (+0) open import Data.Maybe.Base using (just; nothing; decToMaybe) open import Data.Rational.Base as ℚ public hiding (_+_; _*_; _-_) open import Data.Rational.Properties as ℚ public using (module ≤-Reasoning; <⇒≤) open import Re...
algebraic-stack_agda0000_doc_5374
module Issue461 where data D : Set where data D : Set where
algebraic-stack_agda0000_doc_5375
{-# OPTIONS --no-auto-inline #-} module Where where open import Haskell.Prelude hiding (_+_; _*_; _-_) open import Agda.Builtin.Nat postulate bool2nat : Bool → Nat -- no outer arguments ex1 : Nat ex1 = mult num + bool2nat true where num : Nat num = 42 mult : Nat → Nat mult = _* 100 -- nested wh...
algebraic-stack_agda0000_doc_5296
open import System.IO using ( _>>_ ; putStr ; commit ) open import Data.Natural using ( show ) open import System.IO.Examples.Four using ( four ) module System.IO.Examples.HelloFour where main = putStr "Hello, " >> putStr (show four) >> putStr ".\n" >> commit
algebraic-stack_agda0000_doc_5297
{-# OPTIONS --safe --warning=error --without-K #-} open import LogicalFormulae open import Monoids.Definition module Semirings.Definition where record Semiring {a : _} {A : Set a} (Zero One : A) (_+_ : A → A → A) (_*_ : A → A → A) : Set a where field monoid : Monoid Zero _+_ commutative : (a b : A) → a + b...
algebraic-stack_agda0000_doc_5298
{-# OPTIONS --type-in-type --rewriting #-} open import Agda.Builtin.Sigma open import Agda.Builtin.Equality coe : {A B : Set} → A ≡ B → A → B coe refl x = x {-# BUILTIN REWRITE _≡_ #-} Tel = Set U = Set variable Δ : Tel A B : Δ → U δ₀ δ₁ : Δ postulate IdTel : (Δ : Tel)(δ₀ δ₁ : Δ) → Tel Id : (A : Δ → U){...
algebraic-stack_agda0000_doc_5299
{-# OPTIONS --cubical-compatible --rewriting --confluence-check #-} module Issue1719.Spans where open import Issue1719.Common record Span : Set₁ where constructor span field A B C : Set f : C → A g : C → B open Span public
algebraic-stack_agda0000_doc_5300
------------------------------------------------------------------------ -- Products ------------------------------------------------------------------------ module Data.Product where open import Data.Function open import Relation.Nullary.Core infixr 4 _,_ infix 4 ,_ infixr 2 _×_ _-×-_ _-,-_ ----------------------...
algebraic-stack_agda0000_doc_5301
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Foundations.Equiv.Base where open import Cubical.Foundations.Function open import Cubical.Foundations.Prelude open import Cubical.Core.Glue public using ( isEquiv ; equiv-proof ; _≃_ ; equivFun ; equivProof ) fiber : ∀ {ℓ ℓ'} {A : Type ℓ} {B : Type ...
algebraic-stack_agda0000_doc_5302
module Prelude.List.Base where open import Prelude.Nat open import Prelude.Bool open import Prelude.Maybe open import Prelude.Product open import Prelude.Empty open import Prelude.Function open import Prelude.Functor open import Prelude.Applicative open import Prelude.Monad open import Prelude.Decidable open import Pr...
algebraic-stack_agda0000_doc_5303
import Relation.Binary.PropositionalEquality as Eq open Eq using (_≡_; refl; sym; trans; cong; cong-app) open Eq.≡-Reasoning open import Data.Nat using (ℕ; zero; suc; _+_; _*_) open import Data.Product using (∃; _,_) +-assoc : ∀ (m n p : ℕ) → m + (n + p) ≡ (m + n) + p +-assoc zero n p = begin zero + (n + p) ≡⟨...
algebraic-stack_agda0000_doc_5304
module ExportTestAgda where open import Common.Prelude itWorksText : String itWorksText = "It works!" {-# COMPILED_EXPORT itWorksText itWorksText #-}
algebraic-stack_agda0000_doc_5305
-- There was a bug when unifying things of function type during pattern matching -- (the T argument to P is unified with D below) module Issue199 where data D (A : Set) : Set where data P {A : Set} : {T : Set → Set} → T A → Set where p : ∀ d → P {_} {D} d foo : ∀ {A} {l : D A} → P l → Set₁ foo (p _) = Set
algebraic-stack_agda0000_doc_5306
open import Type module Relator.Converse {ℓ₁ ℓ₂} {T : Type{ℓ₁}} (_▫_ : T → T → Type{ℓ₂}) where import Lvl open import Functional Converse : T → T → Type{ℓ₂} Converse = swap(_▫_)
algebraic-stack_agda0000_doc_5307
module Issue4954 where open import Issue4954.M Set
algebraic-stack_agda0000_doc_5308
module Relator.Ordering.Proofs where open import Data import Lvl open import Functional open import Lang.Instance open import Logic open import Logic.Classical open import Logic.Propositional open import Logic.Propositional.Theorems open import Type import Relator.Ordering open import Structure.Relator.Order...
algebraic-stack_agda0000_doc_5309
module HasSatisfaction where open import OscarPrelude open import Interpretation record HasSatisfaction (A : Set) : Set₁ where field _⊨_ : Interpretation → A → Set _⊭_ : Interpretation → A → Set _⊭_ I = ¬_ ∘ I ⊨_ open HasSatisfaction ⦃ … ⦄ public {-# DISPLAY HasSatisfaction._⊨_ _ = _⊨_ #-} {-# DISPLAY ...
algebraic-stack_agda0000_doc_5310
{-# OPTIONS --without-K --safe #-} open import Algebra open import Relation.Unary open import Relation.Binary hiding (Decidable) module Data.FingerTree.Split.Intermediate {r m} (ℳ : Monoid r m) {s} {ℙ : Pred (Monoid.Carrier ℳ) s} (ℙ-resp : ℙ Respects (Monoid._≈_ ℳ)) (ℙ? : Decidable ℙ) where open import...
algebraic-stack_agda0000_doc_5311
{-# OPTIONS --safe #-} module Cubical.Algebra.AbGroup.Instances.Unit where open import Cubical.Foundations.Prelude open import Cubical.Foundations.HLevels open import Cubical.Data.Unit renaming (Unit* to UnitType) open import Cubical.Algebra.AbGroup open import Cubical.Algebra.Group.Instances.Unit using (UnitGroup) ...
algebraic-stack_agda0000_doc_5248
{-# OPTIONS --universe-polymorphism #-} module Categories.Profunctor where open import Level hiding (lift) open import Categories.Category open import Categories.Agda open import Categories.Bifunctor using (Functor; Bifunctor; _∘_) open import Categories.Functor.Hom open import Categories.Lan open import Categories.Y...
algebraic-stack_agda0000_doc_5249
{-# OPTIONS --safe #-} open import Definition.Typed.EqualityRelation module Definition.LogicalRelation.Properties.Reduction {{eqrel : EqRelSet}} where open EqRelSet {{...}} open import Definition.Untyped open import Definition.Typed open import Definition.Typed.Properties open import Definition.Typed.RedSteps open i...
algebraic-stack_agda0000_doc_5250
open import Data.String using ( String ) open import Data.List.Primitive using ( #List ) open import Data.Maybe.Primitive using ( #Maybe ) open import Web.URI.Port.Primitive using ( Port? ) open import Web.URI.Scheme.Primitive using ( Scheme? ) module Web.URI.Primitive where {-# IMPORT Data.Maybe #-} {-# IMPORT Web.UR...
algebraic-stack_agda0000_doc_5251
open import Oscar.Prelude open import Oscar.Class.IsPrefunctor open import Oscar.Class.Smap open import Oscar.Class.Surjection open import Oscar.Class.Transitivity module Oscar.Class.Prefunctor where record Prefunctor 𝔬₁ 𝔯₁ ℓ₁ 𝔬₂ 𝔯₂ ℓ₂ : Ø ↑̂ (𝔬₁ ∙̂ 𝔯₁ ∙̂ ℓ₁ ∙̂ 𝔬₂ ∙̂ 𝔯₂ ∙̂ ℓ₂) where constructor ∁ field ...
algebraic-stack_agda0000_doc_5252
module Negative5 where data Funny (A : Set) : Set where funny : A -> Funny (Funny A -> A) -> Funny A
algebraic-stack_agda0000_doc_5253
module _ where -- Check that previous clauses reduce in later ones open import Agda.Builtin.Nat hiding (_==_) record Σ (A : Set) (B : A → Set) : Set where field fst : A snd : B fst open Σ postulate T : Nat → Set mkT : ∀ n → T n t5 : Σ Nat T fst t5 = 5 snd t5 = mkT 5 -- Also with instance projectio...
algebraic-stack_agda0000_doc_5254
------------------------------------------------------------------------ -- The Agda standard library -- -- Natural numbers represented in binary. ------------------------------------------------------------------------ -- This module aims to create an alternative formulation of ℕ that is -- still reasonably computati...
algebraic-stack_agda0000_doc_5255
------------------------------------------------------------------------ -- The Agda standard library -- -- Convenient syntax for reasoning with a setoid ------------------------------------------------------------------------ -- Example use: -- n*0≡0 : ∀ n → n * 0 ≡ 0 -- n*0≡0 zero = refl -- n*0≡0 (suc n) = begin...