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{-# OPTIONS --without-K #-}
module FinEquivTypeEquiv where
-- The goal is to establish that finite sets and equivalences form a
-- commutative semiring.
import Level using (zero)
open import Data.Nat using (ℕ; _+_; _*_)
open import Data.Fin using (Fin)
open import Relation.Binary using (IsEquivalence)
open import... | {
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{-# OPTIONS --cubical #-}
module Erased-cubical-Module-application.Cubical (_ : Set₁) where
open import Agda.Builtin.Cubical.Path
data ∥_∥ (A : Set) : Set where
∣_∣ : A → ∥ A ∥
trivial : (x y : ∥ A ∥) → x ≡ y
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.RingSolver.AlmostRing where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Sigma
open import Cubical.Algebra.Semigroup
open import Cubical.Algebra.Monoid
open import Cubical.Algebra.AbGroup
private
variable
ℓ : Level
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module Issue326 where
open import Common.Prelude
postulate
QName : Set
Unit : Set
IO : Set → Set
printBool : Bool → IO Unit
{-# BUILTIN QNAME QName #-}
{-# BUILTIN IO IO #-}
{-# COMPILED_TYPE IO IO #-}
{-# COMPILED_TYPE Unit () #-}
{-# COMPILED printBool print #-}
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module REMatch where
open import Data.Char
import Data.Nat
--open import Data.List
open import Data.Bool
open import Data.Product
import Algebra
import Algebra.FunctionProperties
open import Relation.Nullary
open import Relation.Binary
open import Relation.Binary.PropositionalEquality
open import Data.List
open im... | {
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-- Define the integers as a HIT by identifying +0 and -0
{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.HITs.Ints.QuoInt.Base where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Transport
open import... | {
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module Oscar.Data.Term.internal.SubstituteAndSubstitution {𝔣} (FunctionName : Set 𝔣) where
open import Oscar.Category.Action
open import Oscar.Category.Category
open import Oscar.Category.CategoryAction
open import Oscar.Category.Functor
open import Oscar.Category.Morphism
open import Oscar.Category.Semifunctor
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module Lemmachine.Default where
open import Lemmachine
resource : Hooks
resource = []
main = runResolve (toApp resource)
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import Lvl
-- TODO: Just testing how it goes with creating an axiomatic system
module Geometry.Test2 (Point : Set(Lvl.𝟎)) where
open import Functional
open import Logic.Propositional{Lvl.𝟎}
open import Logic.Predicate{Lvl.𝟎}{Lvl.𝟎}
open import Relator.Equals{Lvl.𝟎}{Lvl.𝟎}
-- open import Structure.Setoid.Uniquen... | {
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{-# OPTIONS --rewriting #-}
-- Interface to the standard library.
-- Place to add own auxiliary definitions.
module Library where
open import Size public
open import Level public using () renaming (zero to lzero)
open import Data.Unit public using (⊤)
open import Data.Empty public using (⊥; ⊥-el... | {
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------------------------------------------------------------------------
-- INCREMENTAL λ-CALCULUS
--
-- The syntax of types with the Nehemiah plugin.
------------------------------------------------------------------------
module Nehemiah.Syntax.Type where
import Parametric.Syntax.Type as Type
data Base : Type.Stru... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Relations between properties of scaling and other operations
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Algebra.Module.Consequences where
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module Module where
data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
_+_ : ℕ → ℕ → ℕ
zero + n = zero
suc m + n = suc (m + n)
import Data.Nat using (ℕ; zero; suc; _+_)
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-- Andreas, 2015-05-10 Report wrong hiding for copattern
{-# OPTIONS --copatterns #-}
record ⊤ : Set where
record Foo (A : Set) : Set where
field
foo : A
bar : Foo ⊤
Foo.foo {bar} = _
-- Error WAS: Unexpected implicit argument
-- Better error:
-- Wrong hiding used for projection Foo.foo
-- when checking t... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Basic definitions for Characters
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Char.Base where
open import Level using (zero)
import Da... | {
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{-# OPTIONS --without-K --safe #-}
private
variable
A : Set
a : A
variable
A : Set
private
A = B
where
B = Set
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Instance.Properties.Setoids.Choice where
open import Categories.Category using (Category)
open import Categories.Category.Exact using (Exact)
open import Categories.Category.Instance.Setoids using (Setoids)
open import Data.Product using (∃; proj₁; proj₂;... | {
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------------------------------------------------------------------------
-- Properties of functions
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe --exact-split #-}
module Math.Combinatorics.ListFunction.Properties where
-- agda-stdlib
open import Data.List hi... | {
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-- Andreas, 2017-11-01, issue #2824
-- allow built-in pragmas in parametrized modules
data Nat : Set where
zero : Nat
suc : Nat → Nat
module M (A : Set) where
{-# BUILTIN NATURAL Nat #-}
test = 5
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open import Common.Prelude
open import Common.Reflection
id : {A : Set} → A → A
id x = x
idTerm : Term
idTerm = lam visible (abs "x" (def (quote id) (arg₁ ∷ arg₂ ∷ [])))
where
arg₁ = arg (argInfo hidden relevant) (def (quote Nat) [])
arg₂ = arg (argInfo visible relevant) (var 0 [])
-- Should fail since id... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Categories.Adjoint where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Sigma
open import Cubical.Categories.Category
open import Cubical.Categories.Functor
open import Cubical.Categories.NaturalTransformation
open import Cubical.Foun... | {
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module my-integer where
open import bool
open import bool-thms2
open import eq
open import nat
open import nat-thms
open import product
--open import product-thms
open import sum
-- open import unit
data ⊤ : Set where
triv : ⊤
ℤ-pos-t : ℕ → Set
ℤ-pos-t 0 = ⊤
ℤ-pos-t (suc _) = 𝔹
data ℤ : Set where
mkℤ : (n : ℕ)... | {
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{-
This files contains:
- Lots of useful properties about (this) decidable predicates on finite sets.
(P.S. We use the alternative definition of decidability for computational effectivity.)
-}
{-# OPTIONS --safe #-}
module Cubical.Data.FinSet.DecidablePredicate where
open import Cubical.Foundations.Prelude
open i... | {
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open import Relation.Ternary.Separation
module Relation.Ternary.Separation.Construct.ListOf
{a} (A : Set a)
{{ r : RawSep A }}
{{ _ : IsSep r }}
where
open import Level
open import Data.Product
open import Data.List
open import Data.List.Properties using (++-isMonoid)
open import Data.List.Relation.Binary.E... | {
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module drawingProgram where
open import Unit
open import Data.Bool.Base
open import Data.Char.Base renaming (primCharEquality to charEquality)
open import Data.Nat.Base hiding (_≟_;_⊓_; _+_; _*_)
open import Data.List.Base hiding (_++_)
open import Data.Integer.Base hiding (suc)
open import Data.String.Base
open imp... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category
-- Lifts a 1-Category into a bicategory
module Categories.Bicategory.Construction.1-Category
{o ℓ e} b (C : Category o ℓ e) where
open import Level using (Lift; lift)
open import Data.Unit using (⊤; tt)
open import Data.Product using (uncurry)
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------------------------------------------------------------------------
-- Lexicographic products of binary relations
------------------------------------------------------------------------
-- The definition of lexicographic product used here is suitable if
-- the left-hand relation is a strict partial order.
modul... | {
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module Issue556 (A : Set) (x : A) where
y : A
y = x
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{-# OPTIONS --cubical-compatible #-}
module Issue1025 where
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
postulate mySpace : Set
postulate myPoint : mySpace
data Foo : myPoint ≡ myPoint → Set where
foo : Foo refl
test : {e : myPoint ≡ myPoint} → (a : Foo e) → (i : a ≡ a) → i ≡ refl
test foo refl = {... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Non empty trie, basic type and operations
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe --sized-types #-}
open import Relation.Binary using (StrictTotal... | {
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module Basic where
open import Prelude
data List (A : Set) : Set
data List A where
nil : List A
cons : A -> List A -> List A
append : {A : Set} -> List A -> List A -> List A
append nil ys = ys
append (cons x xs) ys = cons x (append xs ys)
record Equiv {A : Set} (R : A -> A -> Set) : Set
record Equiv {A} R wh... | {
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{-
This file contains:
- An implementation of the free groupoid (a free group that has no limitiations
over the high dimensional path structure). An intermediate construction used
to calculate the fundamental group of a Bouquet.
-}
{-# OPTIONS --safe #-}
module Cubical.HITs.FreeGroupoid.Base where
open import ... | {
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{-# OPTIONS --without-K --exact-split #-}
module encode-decode where
import 05-identity-types
open 05-identity-types public
record Lift {i j : Level} (A : UU i) : UU (i ⊔ j) where
field
raise : A
module Coprod where
code-left : {i j : Level} {A : UU i} {B : UU j} → A → (coprod A B) → (UU i)
code-left a₀ (... | {
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------------------------------------------------------------------------------
-- Properties of the mirror function
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism... | {
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module UnequalTerms where
data Zero : Set where
data One : Set where one : One
err1 : Zero
err1 = one
err2 : One -> One
err2 = \(x : Zero) -> one
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-- Andreas, 2015-02-26
-- {-# OPTIONS -v interaction:100 #-}
data D : Set where
c : D
goal : D
goal = {! !} -- C-c C-r gave a parse error here, as there was a (single) space.
g1 : D
g1 = {! !}
g2 : D
g2 = {! !}
-- works now
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Code related to vector equality over propositional equality that
-- makes use of heterogeneous equality
------------------------------------------------------------------------
{-# OPTIONS --with-K --safe #-}
m... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Relation.Binary.Construct.Constant where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels using (hProp)
open import Cubical.Relation.Binary
open import Cubical.Structures.Carrier
-----... | {
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{-# OPTIONS --cubical --save-metas #-}
module Erased-cubical-Pattern-matching-Cubical where
data D : Set where
c₁ c₂ : D
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{-# OPTIONS --cubical #-}
module Numeral.Natural.Equiv.Path where
open import Data.Boolean.Equiv.Path
open import Functional
open import Logic.Propositional
open import Numeral.Natural.Oper.Comparisons
open import Numeral.Natural
open import Relator.Equals.Proofs.Equivalence using () renaming ([≡]-equiv to Id-equiv ;... | {
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module List.Order.Bounded {A : Set}(_≤_ : A → A → Set) where
open import Bound.Total A
open import Bound.Total.Order _≤_
open import Data.List
data _≤*_ : List A → Bound → Set where
lenx : {t : Bound} → [] ≤* t
lecx : {t : Bound}{x : A}{xs : List A} → LeB (val x) t → xs ≤* t → (x ∷ xs) ≤* t
data _*≤_ : Bound → ... | {
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{-# OPTIONS --safe --without-K #-}
module Source.Size.Substitution.Theory where
open import Source.Size
open import Source.Size.Substitution.Canonical as SC using (Sub⊢)
open import Source.Size.Substitution.Universe as SU using (⟨_⟩ ; Sub⊢ᵤ)
open import Util.Prelude
record SubTheory (A : Ctx → Set) : Set where
inf... | {
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{-# OPTIONS --allow-unsolved-metas #-}
module LateExpansionOfRecordMeta where
postulate
I : Set
i : I
A : I → Set
a : A i
data D : Set₁ where
d : (P : A i → Set) → P a → D
record R (P : A i → Set) : Set where
field
p : P a
record ID : Set₁ where
field
P : (i : I) → A i → Set
isR : R (P ... | {
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module lib.libraryString where
open import Data.String
open import Data.Bool
open import Agda.Builtin.String using ( primStringEquality )
open import Data.String public using ()
renaming (toList to primStringToList;
_++_ to _++Str_)
_==Str_ : Str... | {
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-}
module Light.Variable.Levels where
open import Light.Level using (Level)
variable ℓ aℓ bℓ cℓ dℓ eℓ fℓ gℓ hℓ : Level
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module ReasoningEx where
open import Prelude
open import T
open import Contexts
open import Eq
open import Eq.Theory
open import Eq.ObsTheory
---- some example programs
-- boy, de bruijn indexes are unreadable
w = weaken-closed
plus-rec : ∀{Γ} → TExp Γ nat → TExp Γ nat → TExp Γ nat
plus-rec n m = rec n m (suc (var Z... | {
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{-# OPTIONS --rewriting --confluence-check #-}
module Issue4333.N where
open import Issue4333.M
open import Issue4333.N0
open import Issue4333.N1
postulate
of-type : (X : Set) (x : X) → Set
-- Subject reduction violated for b₁' = b.
_ = of-type (B a₁') b₁'
_ = of-type (B a₀') b
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{-# OPTIONS --without-K #-}
open import HoTT
module homotopy.ConstantToSetFactorization
{i j} {A : Type i} {B : Type j} (B-is-set : is-set B)
(f : A → B) (f-is-const : ∀ a₁ a₂ → f a₁ == f a₂) where
private
Skel = SetQuotient {A = A} (λ _ _ → Unit)
abstract
Skel-has-all-paths : has-all-paths Skel... | {
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module Cats.Functor.Representable where
open import Data.Product using (_×_ ; _,_)
open import Relation.Binary using (Setoid)
open import Cats.Bifunctor using (Bifunctor)
open import Cats.Category
open import Cats.Category.Op using (_ᵒᵖ)
open import Cats.Category.Setoids as Setoids using (Setoids ; ≈-intro)
open impo... | {
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{-# OPTIONS --without-K #-}
module Computability.Prelude where
open import Data.Bool public using (Bool; false; true)
open import Data.Empty public using (⊥; ⊥-elim)
open import Data.Nat public using (ℕ; zero; suc; _+_; _*_)
open import Data.Product public using (Σ; Σ-syntax; _×_; _,_; proj₁; proj₂)
open import Data.S... | {
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module UniDB.Morph.Bla where
open import UniDB.Spec
open import UniDB.Morph.WeakenOne
open import UniDB.Morph.Sub
open import UniDB.Morph.ShiftsPrime
open import UniDB.Morph.Subs
-- mutual
-- data BlaSubst (T : STX) : MOR where
-- blasubst : {γ₁ γ₂ : Dom} → BlaSubst T γ₁ γ₂
mutual
data BlaWeak* (T : STX) : ... | {
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open import Categories.Category using (Category)
import Categories.Category.CartesianClosed
open import Data.Fin using (Fin) renaming (zero to fzero; suc to fsuc)
open import Data.List using (List; []; _∷_)
open import Data.Product using (Σ; Σ-syntax; proj₁; proj₂)
open import Syntax
open import Level using (_⊔_; su... | {
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{-# OPTIONS --without-K #-}
module Util.Induction.WellFounded where
open import Induction.WellFounded public using
( Acc ; acc ; WellFounded ; module Subrelation ; module InverseImage
; module TransitiveClosure ; module Lexicographic )
open import Relation.Binary using (Rel)
open import Util.HoTT.FunctionalExten... | {
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-- WARNING: This file was generated automatically by Vehicle
-- and should not be modified manually!
-- Metadata
-- - Agda version: 2.6.2
-- - AISEC version: 0.1.0.1
-- - Time generated: ???
{-# OPTIONS --allow-exec #-}
open import Vehicle
open import Vehicle.Data.Tensor
open import Data.Rational as ℚ using (ℚ)
op... | {
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{-# OPTIONS --without-K --rewriting #-}
{-
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.
favonia:
On 2017/05/08, I further partition... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.NConnected
open import lib.NType2
open import lib.types.Paths
open import lib.types.Pi
open import lib.types.Truncation
open import lib.types.Unit
open import lib.types.Bool
open import lib.types.Suspension
open import lib.types.IteratedSus... | {
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module _ where
open import Common.Prelude
open import Common.Reflection
postulate
stuck : TC ⊤
macro
not-so-good : Tactic
not-so-good hole = stuck
fail : Nat
fail = not-so-good
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import Issue2447.Type-error
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-- Monoidal categories
{-# OPTIONS --safe #-}
module Cubical.Categories.Monoidal.Base where
open import Cubical.Categories.Category.Base
open import Cubical.Categories.Constructions.BinProduct
open import Cubical.Categories.Functor.Base
open import Cubical.Categories.Functor.BinProduct
open import Cubical.Categories.... | {
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{-# OPTIONS --copatterns #-}
module SplitResult where
open import Common.Product
test : {A B : Set} (a : A) (b : B) → A × B
test a b = {!!}
testFun : {A B : Set} (a : A) (b : B) → A × B
testFun = {!!}
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-- | NOTE: This module can only represent file paths which are valid strings.
-- On Linux, a file path may be an arbitrary sequence of bytes, but using anything
-- except utf8 for file paths is a terrible idea.
--
-- What should happen if we come across a non utf8 path from an untrusted source?
-- crash -> denial-of-se... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.CommRing.Integers where
open import Cubical.Foundations.Prelude
open import Cubical.Algebra.CommRing
open import Cubical.HITs.Ints.BiInvInt
renaming (
_+_ to _+ℤ_;
-_ to _-ℤ_;
+-assoc to +ℤ-assoc;
+-comm to +ℤ-comm
)
BiInvI... | {
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{- 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.B... | {
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module Issue3080 where
open import Agda.Builtin.Nat
open import Agda.Builtin.Equality
data Fin (m : Nat) : Set where
fzero' : (n : Nat) (p : m ≡ suc n) → Fin m
fsuc' : (n : Nat) (p : m ≡ suc n) (i : Fin n) → Fin m
lift : (m : Nat) (i : Fin m) → Fin (suc m)
lift m (fzero' n p) = {!p!}
lift m (fsuc' n p i) = {!... | {
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open import Relation.Binary.Core
module InsertSort.Impl1.Correctness.Order {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_) where
open import Data.List
open import Data.Sum
open import InsertSort.Impl1 _≤_ tot≤
open import List.Sorted _≤_
lemma-insert-sorted : {xs : List A}(x : A... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Natural numbers represented in binary natively in Agda.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Nat.Binary where
open import Data... | {
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open import Common.Prelude
open import Common.Reflection
module TermSplicingLooping where
mutual
f : Set -> Set
f = unquote (give (def (quote f) []))
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Instance.Properties.Setoids.Complete where
open import Level
open import Data.Product using (Σ; proj₁; proj₂; _,_; Σ-syntax; _×_; -,_)
open import Function.Equality using (Π)
open import Relation.Binary using (Setoid; Rel)
open import Categories.Category ... | {
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module Ints.Add.Assoc where
open import Ints
open import Nats renaming (suc to nsuc; _+_ to _:+:_)
open import Nats.Add.Assoc
open import Nats.Add.Comm
open import Ints.Add.Comm
open import Equality
open import Function
------------------------------------------------------------------------
-- internal stuffs
pr... | {
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mutual
data D : Set where
c : R → D
record R : Set where
inductive
field
out : D
open R
f : D → {A : Set} → A
f (c x) = f (out x)
-- should termination check
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{-
Functions building DUARels on constant families
-}
{-# OPTIONS --safe #-}
module Cubical.Displayed.Constant where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Displayed.Base
open import Cubical.Displayed.Subst
private
variable
ℓ ℓA ℓA' ℓP ℓ≅A ℓ≅A' ℓB ... | {
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{-# OPTIONS --without-K #-}
module sets.finite where
open import sets.finite.core public
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-- A Typed version of a subset of Landin's ISWIM from "The Next 700 Programming
-- Languages"
module ISWIM where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
_+_ : Nat -> Nat -> Nat
zero + m = m
suc n + m = suc (n + m)
{-# BUILTIN NATURAL Nat #-}
{-# BUILTIN ZERO zero #-}
{-# BUILTIN SUC suc #-}... | {
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postulate
P : {A : Set} → A → A → Set
p : {A : Set} {x : A} → P x x
q : {A : Set} (x : A) {y : A} → P x y → P x y
A : Set
record R (F : Set → Set) : Set₁ where
field
f₁ : (A → A) → F A → F A
f₂ : P (f₁ (λ x → x)) (λ (x : F A) → x)
open R ⦃ … ⦄ public
instance
r : R (λ O → O → O)
r = record
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{-
Reflection-based tools for converting between iterated record types, particularly between
record types and iterated Σ-types.
See end of file for examples.
-}
{-# OPTIONS --cubical --no-exact-split --safe #-}
module Cubical.Reflection.RecordEquiv where
open import Cubical.Foundations.Prelude
open import Cub... | {
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module Oscar.Builtin.Nat where
open import Agda.Builtin.Nat public
using ()
renaming (Nat to ℕ; zero to ∅; suc to ↑_)
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--
-- Created by Dependently-Typed Lambda Calculus on 2020-10-07
-- Isomorphism
-- Author: dplaindoux
--
{-# OPTIONS --without-K --no-sized-types --no-guardedness bbbbb#-}
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; cong; cong-app)
open Eq.≡-Reasoning
open import Data.Nat using (ℕ; ze... | {
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------------------------------------------------------------------------------
-- Logical Theory of Constructions for PCF (LTC-PCF)
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-unive... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category
open import Categories.Functor.Bifunctor
module Categories.Diagram.Coend {o ℓ e o′ ℓ′ e′} {C : Category o ℓ e} {D : Category o′ ℓ′ e′}
(F : Bifunctor (Category.op C) C D) where
private
module C = Category C
module D = Category D
open D
open... | {
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module Plus where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
infixr 40 _+_
infix 10 _==_
_+_ : Nat -> Nat -> Nat
zero + m = m
suc n + m = suc (n + m)
data _==_ (x, y : Nat) : Set where
-- ...
postulate
refl : {n : Nat} -> n == n
cong : (f : Nat -> Nat){n, m : Nat} -> n == m -> f n == f m
plusZ... | {
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open import Common.Prelude renaming (return to foo)
main : IO Unit
main = foo unit
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-- There's something very strange going on with mutual and parameterised
-- modules. Can't reproduce the bug... :(
module Mutual where
data True : Set where
tt : True
data False : Set where
data _\/_ (A B : Set) : Set where
inl : A -> A \/ B
inr : B -> A \/ B
swap : {A B : Set} -> A \/ B -> B \/ A
swap (inl... | {
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open import Agda.Builtin.Bool
F : Bool → Set
F true = Bool
F _ = Bool
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open import Relation.Binary.Core
module BHeap.Height {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_) where
open import Bound.Lower A
open import Bound.Lower.Order _≤_
open import BHeap _≤_
open import BHeap.Properties _≤_
open import Data.Nat renaming (_≤_ to _≤ₙ_)
open import Da... | {
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module Cats.Category.Constructions.Iso where
open import Relation.Binary using (IsEquivalence ; Setoid)
open import Level
open import Cats.Category.Base
open import Cats.Util.Conv
import Relation.Binary.EqReasoning as EqReasoning
import Cats.Category.Constructions.Epi as Epi
import Cats.Category.Constructions.Mono ... | {
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{-# OPTIONS --type-in-type #-}
module Fusion where
open import Data.Product renaming (proj₁ to ₁; proj₂ to ₂) hiding (map; zip)
open import Relation.Binary.PropositionalEquality
open import Data.Sum hiding (map)
open import Data.Bool
open import Data.Nat
open import Data.Unit
open import Data.Empty
open import Funct... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Results concerning uniqueness of identity proofs, with axiom K
------------------------------------------------------------------------
{-# OPTIONS --with-K --safe #-}
module Axiom.UniquenessOfIdentityProofs.Wi... | {
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-- examples for termination checking mutual recursion
module Mutual where
data Odd : Set
data Even : Set where
zeroE : Even
succE : Odd -> Even
data Odd where
succO : Even -> Odd
addEO : Even -> Odd -> Odd
addOO : Odd -> Odd -> Even
addOO (succO x) y = succE (addEO x y)
addEO zeroE y = y
addEO (succE x) y ... | {
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--{-# OPTIONS -v tc.pos:100 #-}
open import Agda.Builtin.Equality
data ⊥ : Set where
postulate
A : Set
R : A → Set
magic : ⊥ → A
magic ()
test : (a : ⊥) → magic a ≡ magic _
test a = refl
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module Main where
{-# IMPORT System.IO #-}
{-# IMPORT System.Environment #-}
open import Base
open import IO
open import IO.File
postulate
getArgs : IO (List String)
{-# COMPILED getArgs getArgs #-}
_`bindIO`_ : {A B : Set} -> IO A -> (A -> IO B) -> IO B
_`bindIO`_ = bindIO
main : IO Unit
main = getArgs `bindIO... | {
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-- A term model à la Beth
open import Library hiding (_∈_)
module TermModel (Base : Set) where
import Formulas ; open module Form = Formulas Base
import Derivations; open module Der = Derivations Base
-- Beth model
data Cover (Δ : Cxt) : Set where
idc : Cover Δ
bot : (t : Δ ⊢ False) → Cover Δ
node : ... | {
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------------------------------------------------------------------------
-- Decoding types and subtypes into SK terms and equality
------------------------------------------------------------------------
{-# OPTIONS --safe --exact-split --without-K #-}
module FOmegaInt.Undecidable.Decoding where
open import Data.Lis... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.ZCohomology.Groups.WedgeOfSpheres where
open import Cubical.ZCohomology.Base
open import Cubical.ZCohomology.Properties
open import Cubical.ZCohomology.Groups.Unit
open import Cubical.ZCohomology.Groups.Sn
open import Cubical.ZCohomology.Groups.Wedge
op... | {
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open import Agda.Builtin.Size
mutual
data Unit (i : Size) : Set where
c : Unit′ i → Unit i
record Unit′ (i : Size) : Set where
coinductive
field
force : {j : Size< i} → Unit j
open Unit′ public
tail : Unit ∞ → Unit ∞
tail (c x) = force x
u : (∀ {i} → Unit′ i → Unit i) →
∀ {i} → Unit i
u ... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
-- custom pushout for Blakers-Massey
module homotopy.blakersmassey.Pushout {i j k}
{A : Type i} {B : Type j} (Q : A → B → Type k) where
bmspan : Span {i} {j} {lmax i (lmax j k)}
bmspan = span A B (Σ A λ a → Σ B λ b → Q a b) fst (fst ∘ snd)
BMPushout : Type... | {
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{-# OPTIONS --without-K --safe #-}
-- The category build from ObjectRestriction can be done so Functorially
module Categories.Functor.Construction.ObjectRestriction where
open import Level
open import Data.Product using (proj₁)
open import Relation.Unary using (Pred)
open import Function using () renaming (id to id→... | {
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open import Data.Nat using (_+_; _*_; zero; suc; ℕ)
open import Relation.Binary.PropositionalEquality as PropEq
using (_≡_; _≢_; refl; cong)
import Data.Nat.Properties
open Data.Nat.Properties.SemiringSolver
using (solve; _:=_; con; var; _:+_; _:*_; :-_; _:-_)
open PropEq.≡-Reasoning
lem1 : (4 + 6 ≡ 10)
lem1 = ref... | {
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-- test for pattern matching on Strings
module StringPattern where
open import Common.IO
open import Common.Unit
open import Common.String
f : String → String
f "bla" = "found-bla"
f x = x
-- expected:
-- no-bla
-- found-bla
main : IO Unit
main =
putStrLn (f "no-bla") ,,
putStrLn (f "bla")
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module Issue183 where
postulate A : Set
T : Set
T = A → A
data L (A : Set) : Set where
data E (x : T) : T → Set where
e : E x x
foo : (f : A → A) → L (E f (λ x → f x))
foo = λ _ → e
-- Previously:
-- An internal error has occurred. Please report this as a bug.
-- Location of the error: src/full/Agda/Syntax/Tra... | {
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module Type.Proofs where
open import Logic
import Lvl
open import Type
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