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{-# OPTIONS --sized-types #-} open import Relation.Binary.Core module BubbleSort.Correctness.Order {A : Set} (_≤_ : A → A → Set) (tot≤ : Total _≤_) (trans≤ : Transitive _≤_) where open import BubbleSort _≤_ tot≤ open import Data.Product open import Data.List ope...
module nix-emacs-agda where
{-# OPTIONS --without-K #-} open import lib.Base open import lib.PathGroupoid open import lib.PathFunctor open import lib.Equivalences module lib.Univalence where {- The map [coe-equiv] is the map which is supposed to be an equivalence according to the univalence axiom. We do not define it directly by path induction...
module Data.List.Relation.Binary.Subset.Propositional.Instances where open import Data.List using (List; _∷_; []) open import Data.List.Relation.Unary.Any using (here; there) open import Data.List.Membership.Propositional using (_∈_; _∉_) open import Data.List.Membership.Setoid.Properties using (∈-resp-≈) open import ...
module Pin where -- N-dimensional version of Pi -- open import Data.Fin open import Data.Nat open import Data.Empty open import Data.Unit open import Data.Sum open import Data.Product open import Function renaming (_∘_ to _○_) open import Relation.Binary.PropositionalEquality using (module ≡-Reasoning) open ≡-Reas...
{-# OPTIONS --allow-unsolved-metas #-} module Issue442 where postulate A : Set f : (P : A → A → Set) → (∀ {x} → P x x) → (∀ {x y z} → P y z → P x y → A) → A P : A → A → Set reflP : ∀ {x} → P x x g : ∀ {x y z} → P y z → P x y → A a : A a = f _ reflP g
------------------------------------------------------------------------------ -- First-order logic theorems ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} {-...
open import Mockingbird.Forest using (Forest) -- Birds Galore module Mockingbird.Problems.Chapter11 {b ℓ} (forest : Forest {b} {ℓ}) where open import Data.Product using (_×_; _,_; proj₁; proj₂; ∃-syntax) open import Data.Unit using (⊤; tt) open import Function using (_$_) import Mockingbird.Problems.Chapter09 forest...
{-# OPTIONS --safe --experimental-lossy-unification #-} module Cubical.ZCohomology.Properties where {- This module contains: 1. direct proofs of connectedness of Kn and ΩKn 2. Induction principles for cohomology groups of pointed types 3. Equivalence between cohomology of A and reduced cohomology of (A + 1) 4. Equival...
module PatternSynonymImports where open import PatternSynonyms renaming (z to zzz) pattern myzero = zzz two = ss zzz list : List ℕ list = 1 ∷ []
{-# OPTIONS --cubical #-} module Issue2799 where open import Agda.Primitive.Cubical postulate PathP : ∀ {ℓ} (A : I → Set ℓ) → A i0 → A i1 → Set ℓ {-# BUILTIN PATHP PathP #-} _≡_ : ∀ {ℓ} {A : Set ℓ} → A → A → Set ℓ _≡_ {A = A} = PathP (λ _ → A) record Stream (A : Set) : Set where coinductive const...
postulate A : Set record Overlap : Set where constructor mk field overlap {{a}} : A record NoOverlap : Set where constructor mk field {{a}} : A ok : A → NoOverlap ok a = mk {{a}} bad : A → Overlap bad a = mk {{a}} -- Function does not accept argument {{a}} -- when checking that {{a}} is a valid argument to...
{-# OPTIONS --without-K --safe #-} open import Categories.Category module Categories.Morphism.IsoEquiv {o ℓ e} (𝒞 : Category o ℓ e) where open import Level open import Function using (flip; _on_) open import Relation.Binary hiding (_⇒_) import Relation.Binary.Construct.On as On open import Categories.Morphism 𝒞 ...
open import OutsideIn.Prelude open import OutsideIn.X module OutsideIn.Expressions(x : X) where import OutsideIn.TypeSchema as TS open TS(x) open X(x) {- SYNTAX -} data Name (n : Set) : NameType → Set where N : n → Name n Regular DC : ∀ {x} → dc x → Name n (Datacon x) mutual data Alternativ...
{-# OPTIONS --cubical #-} module Type.Cubical.Path.Equality where open import Functional open import Function.Axioms import Lvl open import Type open import Type.Cubical open import Type.Cubical.Path open import Type.Cubical.Path.Proofs as Path open import Structure.Function open import Structure.Operator open i...
module PureLambda where data D : Set where lam : (D -> D) -> D _·_ : D -> D -> D lam f · x = f x δ : D δ = lam (\x -> x · x) loop : D loop = δ · δ
-- 2010-09-07 Andreas module IrrelevantRecordMatching where record Prod (A B : Set) : Set where constructor _,_ field fst : A snd : B wrongElim : {A : Set} -> .(Prod A A) -> A wrongElim (a , a') = a -- needs to fail because a is irrelevant
module _ where open import Common.Prelude hiding (_>>=_) open import Common.Reflection pattern `Nat = def (quote Nat) [] unquoteDecl f = declareDef (vArg f) `Nat >>= λ _ → freshName "aux" >>= λ aux → declareDef (vArg aux) `Nat >>= λ _ → defineFun f (clause [] (def aux []) ∷ [])
module Structure.LinearAlgebra where import Lvl open import Data open import Data.Tuple open import Functional hiding (id) open import Function.Equals open import Function.Proofs open import Logic open import Logic.Propositional open import Logic.Propositional.Theorems open import Logic.Predicate open import Nume...
{-# OPTIONS --universe-polymorphism #-} open import Categories.Category module Categories.Pullback {o ℓ e} (C : Category o ℓ e) where open Category C open import Level record Pullback {X Y Z}(f : X ⇒ Z)(g : Y ⇒ Z) : Set (o ⊔ ℓ ⊔ e) where field P : Obj p₁ : P ⇒ X p₂ : P ⇒ Y field .commutes : f ...
module Issue2641.Import where open import Agda.Builtin.Nat five : Nat five = 5
{-# OPTIONS --safe --warning=error #-} open import Sets.EquivalenceRelations open import Functions.Definition open import Agda.Primitive using (Level; lzero; lsuc; _⊔_; Setω) open import Setoids.Setoids open import Groups.Definition open import LogicalFormulae open import Orders.WellFounded.Definition open import Numb...
{-# OPTIONS --safe -WnoSafeFlagNoCoverageCheck #-} open import Agda.Builtin.Bool open import Agda.Builtin.Equality data ⊥ : Set where {-# NON_COVERING #-} f : ∀ b → b ≡ true → ⊥ f false () bad : ⊥ bad = f true refl
{-# OPTIONS --without-K --safe #-} module Categories.Yoneda where -- Yoneda Lemma. In total, provides: -- * the Yoneda Embedding (called embed here) from any Category C into Presheaves C -- Worth noticing that there is no 'locally small' condition here; however, if one looks at -- the levels involved, there is in...
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.ZCohomology.MayerVietorisUnreduced where open import Cubical.ZCohomology.Base open import Cubical.ZCohomology.Properties open import Cubical.ZCohomology.KcompPrelims open import Cubical.Foundations.HLevels open import Cubical.Foundations.Function open ...
------------------------------------------------------------------------ -- The Agda standard library -- -- The basic code for equational reasoning with three relations: -- equality, strict ordering and non-strict ordering. ------------------------------------------------------------------------ -- -- See `Data.Nat.Pro...
open import Everything module Test.Test0 where test-functor-surjidentity : ∀ {𝔬₁ 𝔯₁ ℓ₁ 𝔬₂ 𝔯₂ ℓ₂} ⦃ functor : Functor 𝔬₁ 𝔯₁ ℓ₁ 𝔬₂ 𝔯₂ ℓ₂ ⦄ (open Functor functor) → Surjidentity.type _∼₁_ _∼₂_ _∼̇₂_ functor-smap ε₁ ε₂ test-functor-surjidentity = surjidentity -- test-functor-transextension...
module tree where open import bool open import eq open import level open import list open import list-to-string open import nat open import nat-thms open import string ---------------------------------------------------------------------- -- datatype -----------------------------------------------------------------...
{-# OPTIONS --safe #-} module Cubical.Categories.Monad.Base where open import Cubical.Foundations.Prelude open import Cubical.Categories.Category open import Cubical.Categories.Functor renaming (𝟙⟨_⟩ to funcId) open import Cubical.Categories.NaturalTransformation.Base open import Cubical.Categories.NaturalTransformat...
-- Non-deterministic insert and permutation with choose oracle -- The oracle is passed through the individual functions. open import bool module even-double-eo (Choice : Set) (choose : Choice → 𝔹) (lchoice : Choice → Choice) (rchoice : Choice → Choice) where open import eq open import bool-thms open import...
module _ where module G where module H where module A where module B where module C where open G public module I = A.B.C.H
{-# OPTIONS --without-K --rewriting #-} open import HoTT -- This file contains a helper module for FinSet, -- proving the finite pigeonhole principle module homotopy.Pigeonhole where {- loosely based on code by copumpkin and xplat via byorgey -} incl : ∀ {m n} (m<n : m < n) → Fin m → Fin n incl m<n (k , k<m) = k ...
open import Data.Unit using ( ⊤ ) open import FRP.LTL.RSet.Core using ( RSet ) module FRP.LTL.RSet.Unit where T : RSet T t = ⊤
-- Andreas, 2017-07-13, issue #2642 record R : Set₁ where field F : Set F : Set -- duplicate field, should be rejected -- Otherwise, this gives an internal error: test : Set → R test A = record{ F = A }
------------------------------------------------------------------------ -- The Agda standard library -- -- Vectors defined in terms of the reflexive-transitive closure, Star ------------------------------------------------------------------------ {-# OPTIONS --with-K --safe #-} module Data.Star.Vec where open impor...
-- Andreas, 2017-04-11, Issue 2543 -- Printing of second non-trivial with-pattern -- {-# OPTIONS -v interaction.case:100 #-} data D : Set where c : D → D f : D → D f y with c y ... | c z with c y ... | q = {!q!} -- C-c C-c q -- Was: -- f y | c z | (c q) = ? -- Expected: -- f y | c z | c q = ?
------------------------------------------------------------------------ -- The Agda standard library -- -- Showing natural numbers ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Nat.Show where open import Data.Char as Char using (Char) open im...
module Issue892b where record R : Set₁ where field A : Set B : A → Set -- The type of R.B should print as (r : R) → R.A r → Set -- rather than ( : R) → R.A → Set. bad : R.B bad = ?
------------------------------------------------------------------------ -- Programs used to define and specify breadth-first manipulations of -- trees ------------------------------------------------------------------------ module BreadthFirst.Programs where open import Codata.Musical.Notation open import Codata.Mus...
{-# OPTIONS --allow-unsolved-metas #-} module Real-Backup where open import Data.Float hiding (_-_; _≈_) open import Level using (0ℓ) open import Algebra.Bundles using (CommutativeRing) open import Algebra.Module.Bundles using (Module) open import Relation.Binary.Structures using (IsStrictTotalOrder) open import Rela...
-- Andreas, 2012-05-04 -- Occurs check when unifying indices in patterns {-# OPTIONS --allow-unsolved-metas #-} -- The option is supplied to force a real error to pass the regression test. module OccursCheck1 where data Nat : Set where zero : Nat suc : Nat -> Nat data _==_ {A : Set}(x : A) : A -> Set where ref...
{-# OPTIONS --safe --warning=error --without-K --guardedness #-} open import Agda.Primitive using (Level; lzero; lsuc; _⊔_) open import Setoids.Setoids open import Rings.Definition open import Rings.Lemmas open import Rings.Orders.Partial.Definition open import Rings.Orders.Total.Definition open import Groups.Definiti...
module Day4 where open import Prelude.String as String open import Data.Maybe open import Foreign.Haskell using (Unit) open import Prelude.List as List open import Data.Nat open import Data.Nat.DivMod open import Data.Nat.Properties import Data.Nat.Show as ℕs open import Prelude.Char open import Data.Vec as Vec rena...
module Basics where id : {A : Set} -> A -> A id a = a _o_ : {A : Set}{B : A -> Set}{C : (a : A)(b : B a) -> Set} -> ({a : A}(b : B a) -> C a b) -> (g : (a : A) -> B a) -> (a : A) -> C a (g a) _o_ f g a = f (g a)
{-# OPTIONS --without-K --safe #-} module Definition.Conversion.Whnf where open import Definition.Untyped open import Definition.Typed open import Definition.Conversion open import Tools.Product mutual -- Extraction of neutrality from algorithmic equality of neutrals. ne~↑ : ∀ {t u A Γ} → Γ ⊢ t ~ u ↑ A ...
postulate A : Set B : A → Set @0 T : _ T = (@0 x : A) → B x
------------------------------------------------------------------------ -- Types used to make recursive arguments coinductive ------------------------------------------------------------------------ -- See Data.Colist for examples of how this type is used, or -- http://article.gmane.org/gmane.comp.lang.agda/633 for a...
open import Prelude open import Data.List.Properties open import Data.List.Any hiding (map) open import Extensions.Vec open import Data.Vec open import Data.List.All as All hiding (map; lookup) module Implicits.Resolution.Infinite.Semantics where open import Implicits.Syntax open import Implicits.Resolution.Infinite....
module Issue846.DivModUtils where open import Data.Nat open import Data.Bool open import Issue846.OldDivMod open import Relation.Nullary open import Data.Nat.Properties hiding (≤-antisym) open import Data.Nat.Solver open import Data.Fin using (Fin; toℕ; zero; suc; fromℕ≤) open import Data.Fin.Properties using ( bound...
module Oscar.Property.IsReflexive where open import Oscar.Level record IsReflexive {𝔬} (⋆ : Set 𝔬) {ℓ} (_≣_ : ⋆ → ⋆ → Set ℓ) : Set (𝔬 ⊔ ℓ) where field reflexivity : ∀ x → x ≣ x
module Impure.LFRef.Welltyped where open import Prelude open import Data.List hiding ([_]) open import Data.List.All hiding (map) open import Data.Vec as Vec hiding ([_]; map) open import Data.Star hiding (_▻▻_; map) open import Data.Sum hiding (map) open import Extensions.List as L using () open import Impure.LFRef...
------------------------------------------------------------------------ -- Lemmas related to application of substitutions ------------------------------------------------------------------------ open import Data.Universe.Indexed module deBruijn.Substitution.Data.Application.Application221 {i u e} {Uni : IndexedUni...
module OverloadedConInParamModule where data A : Set where module M (X : Set) where data B : Set where c : B data C : Set where c : C open M A f : B f = c
-- Copyright: (c) 2016 Ertugrul Söylemez -- License: BSD3 -- Maintainer: Ertugrul Söylemez <esz@posteo.de> module Data.Mod where open import Core open import Data.Int.Core hiding (module Props) import Data.Int.Core as ℤ open import Data.Nat.Core using (ℕ) import Data.Nat.Core as ℕ private module ℤP = ℤ.Props ...
module L.Base.Sigma where -- Reexport definitions open import L.Base.Sigma.Core public
open import Prelude renaming (_++_ to _++-List_) open import Data.Maybe using (Maybe; just; nothing; maybe; From-just) open import Data.Fin using (Fin; toℕ) renaming (inject+ to finject; raise to fraise; zero to fzero; suc to fsuc) open import Data.List.All as A open import Data.Vec using (Vec; _∷_; []) open import Da...
{- ℚ is a Field -} {-# OPTIONS --safe #-} module Cubical.Algebra.Field.Instances.QuoQ where open import Cubical.Foundations.Prelude open import Cubical.Foundations.HLevels open import Cubical.Data.Sigma open import Cubical.Data.Empty as Empty open import Cubical.Data.Nat using (ℕ ; zero ; suc) open import Cubical.D...
module Absurd where open import Prelude absurd : {A : Set} -> Empty -> A absurd x = {!!}
module Ethambda.Common where open import Eth.Prelude infixr 3 _<<_ infixr 3 _<d>_ export _<d>_ : String -> String -> String v <d> w = if isNullStr v then v else v ++ " " ++ " " ++ w export ShowS : Type ShowS = String -> String export _<d_ : String -> ShowS -> ShowS s <d c = (s <.>) . c
{- The James Construction, also known as James Reduced Product A very fundamental and useful construction in classical homotopy theory. It can be seen as the free A∞-monoid constructed out of a given type, namely the "correct higher version" of free monoid that is meaningful for all types, instead of only h-Sets. ...
{-# OPTIONS --type-in-type #-} module Compilation.Data where open import Context open import Type.Core open import Function open import Data.Product open import Data.List.Base infixr 6 _⇒ᶜ_ {- Note [Type denotations] The denotation of a System Fωμ type is an Agda type that somehow corresponds to the original type....
-- Issue reported by Christian Sattler on 2019-12-02 postulate M : Set m₀ : M D : Set d : D Y : (m : M) (a : D) → Set y : Y m₀ d R' : M → Set data X : M → Set where conX : X m₀ R : M → Set R = R' postulate felt : (m : M) (f : X m → D) (g : (x : X m) → Y m (f x)) → R m -- No e...
-- Functions used in googology {-# OPTIONS --without-K --safe --exact-split #-} module Math.Googology.Function where -- agda-stdlib open import Data.Nat open import Data.Nat.GeneralisedArithmetic open import Function -- Ackermann function. -- ack m n = Ack(m, n) ack : ℕ → ℕ → ℕ ack 0 n = 1 + n ack (suc ...
------------------------------------------------------------------------ -- The Agda standard library -- -- Pointwise equality for containers ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.Container.Relation.Binary.Pointwise where open import D...
{-# OPTIONS --cubical #-} F : Set → Set F A = A record R : Set₁ where field A : Set r : Set → R r A = λ where .R.A → A
module CF.Examples.Ex1 where open import Function open import Data.Bool open import Data.Product open import Data.List open import Data.List.Relation.Unary.All open import Data.Nat open import Data.String open import Relation.Binary.PropositionalEquality using (refl) open import Relation.Ternary.Core open import Rela...
{-# OPTIONS --prop --allow-unsolved-metas #-} data _≡_ {α}{A : Set α}(a : A) : A → Prop where refl : a ≡ a data _≃_ {α}{A : Set α}(a : A) : ∀ {B} → B → Prop where refl̃ : a ≃ a data ⊥ : Set where data Con : Set data Con~ : Con → Con → Prop data Ty : Con → Set data Ty~ : ∀ {Γ₀ Γ₁} → Con~ Γ₀ Γ₁ → Ty Γ₀ → Ty Γ...
module PushArgument where open import ScopeState open import Data.List.NonEmpty open import Data.List open import ParseTree open import Data.Nat open import AgdaHelperFunctions open import Data.Unit open import Data.String hiding (toVec) open import Data.Bool open import Data.Product open import Data.Maybe open import ...
-- {-# OPTIONS -v tc.cover.splittree:10 -v tc.cc.splittree:10 #-} module Issue106 where data ℕ : Set where zero : ℕ suc : ℕ -> ℕ {-# BUILTIN NATURAL ℕ #-} {-# BUILTIN ZERO zero #-} {-# BUILTIN SUC suc #-} _+_ : ℕ -> ℕ -> ℕ zero + m = m suc n + m = suc (n + m) record ⊤ : Set where data C : ℕ -> Set where c ...
module Data where data D (A : Set) : Set data D A where c : D A data E (B : Set) : Set where
{-# OPTIONS --without-K --show-implicit #-} module WithoutK10 where data Unit : Set where unit : Unit data D {A : Set} (f : Unit → A) : A → Set where d : ∀ {x} → D f x Foo : ∀ {A} {x : A} → D (let f = λ { unit → x } in f) x → Set₁ Foo d = Set
{- Index a structure S by the type variable: X ↦ X → S X -} {-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Structures.Relational.UnaryOp where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Equiv open import Cubical.Foundations.F...
module Bound.Total.Order {A : Set}(_≤_ : A → A → Set) where open import Bound.Total A data LeB : Bound → Bound → Set where lebx : {b : Bound} → LeB bot b lexy : {x y : A} → x ≤ y → LeB (val x) (val y) lext : {b : Bound} → LeB b top...
{-# OPTIONS --safe --warning=error --without-K #-} open import LogicalFormulae open import Groups.Homomorphisms.Definition open import Groups.Definition open import Rings.Definition open import Rings.Homomorphisms.Definition open import Rings.IntegralDomains.Definition open import Setoids.Setoids open import Sets.Equi...
{- This file contains: - Properties of 2-groupoid truncations -} {-# OPTIONS --cubical --safe #-} module Cubical.HITs.2GroupoidTruncation.Properties where open import Cubical.Foundations.Prelude open import Cubical.HITs.2GroupoidTruncation.Base rec2GroupoidTrunc : ∀ {ℓ ℓ'} {A : Type ℓ} {B : Type ℓ'} (gB : is2Group...
{-# OPTIONS --safe --warning=error --without-K #-} open import LogicalFormulae module Decidable.Sets {a : _} (A : Set a) where DecidableSet : Set a DecidableSet = (a b : A) → ((a ≡ b) || ((a ≡ b) → False))
{-# OPTIONS --without-K #-} open import Axiom.Extensionality.Propositional module FLA.Axiom.Extensionality.Propositional where -- Since (dependent) extensionality is not allowed in standard Agda, we -- postulate it here. In the standard library, the Extensionality term is -- given in the type, which is then often na...
------------------------------------------------------------------------ -- Some derivable properties ------------------------------------------------------------------------ open import Algebra module Algebra.Props.DistributiveLattice (dl : DistributiveLattice) where open DistributiveLattice dl im...
even : ℕ → Bool odd : ℕ → Bool even zero = true even (suc n) = odd n odd zero = false odd (suc n) = even n
{- Please do not move this file. Changes should only be made if necessary. This file contains pointers to the code examples and main results from the paper: Internalizing Representation Independence with Univalence Carlo Angiuli, Evan Cavallo, Anders Mörtberg, Max Zeuner Preprint: https://arxiv.org/abs/2009.05547 ...
open import Nat open import Prelude open import Hazelnut-core module Hazelnut-sensible where -- theorem 1: action sensibility synthmovelem : {Γ : ·ctx} {e e' : ê} {t : τ̇} {δ : direction} → (e + move δ +>e e') → (Γ ⊢ e ◆e => t) → (Γ ⊢ e' ◆e => t) synthmovelem E...
--{-# OPTIONS --allow-unsolved-metas #-} module StateSizedIO.GUI.Prelude where open import Size public renaming (Size to AgdaSize) open import Data.Nat.Base public open import Data.Bool.Base hiding (_≟_) public open import Data.List.Base public open import Function public open import Data.Integer.Base public hiding...
-- Andreas, 2019-08-20, issue #4012 -- unquoteDef and unquoteDecl should respect `private` open import Agda.Builtin.Reflection renaming (bindTC to _>>=_) open import Agda.Builtin.List data D : Set where c : D module M where private unquoteDecl g = do ty ← quoteTC D _ ← declareDef (arg (arg-inf...
{-# OPTIONS --without-K #-} {- Imports everything that is not imported by something else. This is not supposed to be used anywhere, this is just a simple way to do `make all' This file is intentionally named index.agda so that Agda will generate index.html. -} module index where -- import Spaces.IntervalProps -- im...
open import Data.List using (List; _∷_; []) open import Data.Product using (_×_; _,_; Σ) open import Data.Unit using (⊤; tt) open import Relation.Binary.PropositionalEquality using (_≡_) module SystemT where data _∈_ {A : Set} : (x : A) (l : List A) → Set where -- type \in i0 : {x : A} {xs : List A} → x ∈...
{-# OPTIONS --universe-polymorphism #-} -- {-# OPTIONS --verbose tc.records.ifs:15 #-} -- {-# OPTIONS --verbose tc.constr.findInScope:15 #-} -- {-# OPTIONS --verbose tc.term.args.ifs:15 #-} module 05-equality-std1 where open import Relation.Binary using (IsDecEquivalence; module IsDecEquivalence; Reflexive; module De...
module Thesis.SIRelBigStep.DenSem where open import Data.Nat open import Data.Product open import Thesis.SIRelBigStep.Syntax open import Data.Nat ⟦_⟧Type : Type → Set ⟦ σ ⇒ τ ⟧Type = ⟦ σ ⟧Type → ⟦ τ ⟧Type ⟦ nat ⟧Type = ℕ ⟦ pair τ1 τ2 ⟧Type = ⟦ τ1 ⟧Type × ⟦ τ2 ⟧Type import Base.Denotation.Environment module Den = Ba...
-- Subtyping is no longer supported for irrelevance. f : {A B : Set} → (.A → B) → A → B f g = λ .x → g x
open import Agda.Builtin.Equality open import Agda.Builtin.Sigma postulate X : Set variable x : X data C : Σ X (λ x → x ≡ x) → Set where mkC : let eq : x ≡ x -- don't generalize over x at eq eq = refl {x = x} in C (x , eq)
module Sets.IterativeUSet where open import Data renaming (Empty to EmptyType) open import Functional import Lvl import Lvl.Decidable as Lvl open import Structure.Setoid renaming (_≡_ to _≡ₛ_) open import Syntax.Function open import Type open import Type.Dependent private variable ℓ ℓₒ ℓₑ ℓ₁ ℓ₂ : Lvl.Level ...
module treeThms where open import lib -- simple Tree type storing natural numbers data Tree : Set where Node : ℕ → Tree → Tree → Tree Leaf : Tree mirror : Tree → Tree mirror (Node x t1 t2) = Node x (mirror t2) (mirror t1) mirror Leaf = Leaf mirror-mirror : ∀ (t : Tree) → mirror (mirror t) ≡ t mirr...
open import Agda.Builtin.Unit open import Agda.Builtin.Bool open import Agda.Builtin.Sigma open import Agda.Builtin.List open import Agda.Builtin.Equality open import Agda.Builtin.Reflection renaming (returnTC to return; bindTC to _>>=_) _>>_ : ∀ {a} {b} {A : Set a} {B : Set b} → TC A → TC B → TC B x >> y = x >>...
{-# OPTIONS --without-K --rewriting --termination-depth=2 #-} open import HoTT open import cohomology.ChainComplex open import cohomology.Theory open import groups.KernelImage open import cw.CW module cw.cohomology.ReconstructedHigherCohomologyGroups {i : ULevel} (OT : OrdinaryTheory i) where open OrdinaryTheory O...
module Verifier (down : Set₁ -> Set) (up : Set → Set₁) (iso : ∀ {A} → down (up A) -> A) (osi : ∀ {A} → up (down A) -> A) where import UniverseCollapse as UC open UC down up iso osi using (anything) check : (A : Set) -> A check = anything
module Data.Bin.DivMod where import Data.Fin import Data.Product import Data.Bin import Data.Nat import Relation.Binary.PropositionalEquality import Data.Digit hiding (0b; 1b) import Data.List import Algebra import Algebra.Structures import Data.Bin.NatHelpers open Data.Bin using (Bin; toℕ; toBits; fromB...
{-# OPTIONS --safe --experimental-lossy-unification #-} module Cubical.Algebra.ZariskiLattice.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Function open import Cubical.Foundations.Equiv open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Univalence open im...
------------------------------------------------------------------------------ -- Agda-Prop Library. -- Theorems with different connectives. ------------------------------------------------------------------------------ open import Data.Nat using ( ℕ ) module Data.PropFormula.Theorems.Mixies ( n : ℕ ) where --------...
------------------------------------------------------------------------ -- The Agda standard library -- -- Properties of non-empty lists ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.List.NonEmpty.Properties where open import Category.Monad o...
{-# OPTIONS --without-K --safe #-} module Categories.Bicategory where open import Level open import Data.Product using (_,_) open import Relation.Binary using (Rel) open import Categories.Category using (Category; module Commutation) open import Categories.Category.Monoidal.Instance.Cats using (module Product) open ...
{- Pointed structure: X ↦ X -} {-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Structures.Pointed where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.Univalence open import Cubical.Foundations.SIP open import Cubical.Foundations.Point...