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|---|---|
module Natural where
open import Equality
open import Cubical.Data.Nat.Properties public
open import Data.Empty
open import Data.Nat as ℕ public hiding (_+_; _*_; _^_)
open import Data.Nat.Properties public hiding (+-assoc; +-suc)
open import Data.Unit
open import Function
open import Syntax
instance
ℕ-plus-syntax ... | {
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{-# OPTIONS --universe-polymorphism #-}
module Issue286 where
open import Common.Level
data Bool : Set where
true false : Bool
{-# BUILTIN BOOL Bool #-}
{-# BUILTIN TRUE true #-}
{-# BUILTIN FALSE false #-}
data _≡_ {ℓ : Level} {A : Set ℓ} : A → A → Set ℓ where
refl : {a : A} → a ≡ a
{-# BUILTIN EQUALITY ... | {
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{-# OPTIONS -v5 #-}
module Debug where
postulate Foo : Set
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{-# OPTIONS --cubical --no-exact-split --safe #-}
module Cubical.Data.Queue.Base where
open import Cubical.Foundations.Everything
open import Cubical.Foundations.SIP
open import Cubical.Structures.Queue
open import Cubical.Data.Unit
open import Cubical.Data.Sum
open import Cubical.Data.List
open import Cubical.Data.... | {
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open import Oscar.Prelude
open import Oscar.Class.IsPrecategory
open import Oscar.Class.Surjection
open import Oscar.Class.Smap
open import Oscar.Class.Surjtranscommutativity
open import Oscar.Class.Surjextensionality
open import Oscar.Class.Transitivity
module Oscar.Class.IsPrefunctor where
module _
{𝔬₁} {𝔒₁ : ... | {
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{-# OPTIONS --cubical #-}
module README where
------------------------------------------------------------------------
-- Chapter 2: Programming and Proving in Cubical Agda
------------------------------------------------------------------------
-- 2.1: Basic Functional Programming in Agda
import Snippets.Bool using... | {
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{-# OPTIONS --copatterns #-}
record U : Set where
coinductive
field out : U
u : {A : Set} → U
u = {!!}
record Wrap (A : Set) : Set where
field
wrapped : A
wrap : ∀{A}{a : A} → Wrap A
wrap = {!!}
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{-
Copyright (c) 2017 Diego Pedraza.
This is Free/Libre Open Source Software, released under the MIT License.
For the full copyright and license information, please view the LICENSE
file that was distributed with this source code.
-}
module R2 where
open import Data.List using (List; _∷_; _++_; [_]; [])... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.NatSolver.Solver where
open import Cubical.Foundations.Prelude
open import Cubical.Data.FinData
open import Cubical.Data.Nat
open import Cubical.Data.Nat.Order using (zero-≤)
open import Cubical.Data.Vec.Base
open import Cubical.Algebra.NatSolver.NatExpression
open import... | {
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open import Nat
open import Prelude
open import Hazelnut-core
module Hazelnut-deterministic where
-- theorem 2
-- the same action applied to the same type makes the same resultant
-- type.
actdet1 : {t t' t'' : τ̂} {α : action} →
(t + α +> t') →
(t + α +> t'') →
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module Text.Greek.SBLGNT-Query where
open import Data.Bool
open import Data.Nat hiding (_≟_)
open import Data.List
open import Data.Maybe
open import Data.Product hiding (map)
open import Function
open import Relation.Binary.PropositionalEquality
open import Text.Greek.Bible
open import Text.Greek.Script
open import T... | {
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{-# OPTIONS --without-K #-}
open import Type using (Type₀; Type_)
open import Type.Identities
open import Function.NP using (Π; _∘_; const)
open import Function.Extensionality using (FunExt)
open import Data.One using (0₁)
open import Data.Two.Base using (0₂; 1₂)
open import Data.Product.NP using (_,_; fst)
open import... | {
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open import FRP.JS.Bool using ( Bool ; true ; false ; not ; _∨_ )
open import FRP.JS.True using ( True )
open import FRP.JS.Maybe using ( Maybe ; just ; nothing )
open import FRP.JS.Primitive using ( ℤ ; String )
module FRP.JS.Float where
infixr 4 _≤_ _<_ _≟_ _≠_
infixl 6 _+_ _-_
infixl 7 _*_ _/_ _/?_
open import FR... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Some Vec-related properties
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Vec.Properties where
open import Algebra.FunctionProperties
o... | {
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-- ASR (2016-12-23). UHC and GHC have different behaviours. This test
-- only is disabled for the UHC backend.
-- Issue #1856: UHC prints doubles with lower precision than GHC
--
-- For example, printing √2
--
-- GHC (8.0.1): 1.4142135623730951
-- UHC (1.1.9.5): 1.414213562373095
module _ where
open import Common.... | {
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data A : Set₁ → Set where
C : (S : Set₁) → A S
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{- 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... | {
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open import Type
open import Structure.Relator
open import Structure.Setoid renaming (_≡_ to _≡ₑ_)
module Structure.Sets.ZFC.Classical {ℓₛ ℓₗ ℓₑ} {S : Type{ℓₛ}} ⦃ equiv : Equiv{ℓₑ}(S) ⦄ (_∈_ : S → S → Type{ℓₗ}) ⦃ [∈]-binaryRelator : BinaryRelator(_∈_) ⦄ where
open import Data.Either as Either using ()
open import Fun... | {
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------------------------------------------------------------------------------
-- Division program
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS ... | {
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{-# OPTIONS --without-K #-}
module Data.ByteString.Primitive.Lazy where
open import Data.Word8.Primitive using (Word8)
open import Agda.Builtin.Nat using (Nat)
open import Data.Colist using (Colist)
open import Agda.Builtin.String using (String)
open import Agda.Builtin.Bool using (Bool)
open import Agda.Builtin.IO u... | {
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module Oscar.Data.Permutation.Properties where
open import Data.Permutation.Properties public
open import Data.Nat
open import Oscar.Data.Vec renaming (delete to deleteV)
open import Oscar.Data.Vec.Properties
open import Oscar.Data.Permutation
∈-enum : ∀ {n m} (i : Inj n m) → i ∈ enum n m
∈-enum {zero} [] = here
∈-... | {
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module SubstTheory where
open import Prelude
open import T
-- I originally used postulated extensional equality to reason about
-- identical substitutions. As it turns out, it's actually somewhat
-- cleaner to appeal to a proof that using identically performing subst
-- functions produce the same outputs.
---- (Lots... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Half adjoint equivalences
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Function.HalfAdjointEquivalence where
open import Function
open impo... | {
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{-# OPTIONS --cubical #-}
open import Agda.Builtin.Cubical.Path
open import Agda.Primitive
open import Agda.Primitive.Cubical
open import Agda.Builtin.Bool
variable
a p : Level
A : Set a
P : A → Set p
x y : A
refl : x ≡ x
refl {x = x} = λ _ → x
data Interval : Set where
left ... | {
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{-# OPTIONS --sized-types #-}
module SList.Order {A : Set}(_≤_ : A → A → Set) where
open import List.Sorted _≤_
open import Size
open import SList
data _*≤_ : {ι : Size} → A → SList A {ι} → Set where
genx : {ι : Size}{b : A}
→ (_*≤_) {↑ ι} b snil
gecx : {ι : Size}{b x : A}{xs : SList A {ι}}
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{-# OPTIONS --copatterns #-}
module examplesPaperJFP.IOGraphicsLib where
open import Data.Bool.Base
open import Data.Char.Base
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 import Data.Maybe.Base
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{-# OPTIONS --cubical --safe #-}
module Cubical.HITs.Modulo.Base where
open import Cubical.Foundations.Function
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Prelude
open import Cubical.Data.Empty
open import Cubical.Data.Fin
open import Cubical.D... | {
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------------------------------------------------------------------------
-- The list container
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Equality
module Container.List
{c⁺} (eq : ∀ {a p} → Equality-with-J a p c⁺) where
open Derived-defi... | {
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{-# OPTIONS --erased-cubical --safe #-}
module Music where
open import Data.Nat using (ℕ; zero; suc; _+_; _*_; _≤_; _≤?_)
open import Data.Integer using (ℤ; +_)
open import Data.List using (List; foldr; []; _∷_; reverse; sum; map)
open import Data.Product using (_×_; _,_)
open import Data.Sum using (_⊎_; i... | {
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module tests.String where
open import Prelude.IO
open import Prelude.List
open import Prelude.String
open import Prelude.Unit
testString : String
testString = "To boldly go where no man gone before"
printList : forall {A} -> (A -> IO Unit) -> List A -> IO Unit
printList p [] = return unit
printList p (x :: xs) =
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{-# OPTIONS --safe --without-K #-}
open import Relation.Binary
module Data.List.Membership.Setoid.Trans {a p} (S : Setoid a p) where
open Setoid S
open import Data.List.Membership.Setoid (S)
open import Data.List.Any
≈-trans-∈ : ∀ {x y xs} → x ≈ y → y ∈ xs → x ∈ xs
≈-trans-∈ x≈y (here px) = here (trans x≈y px)
≈-trans... | {
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-- {-# OPTIONS --no-coverage-check #-}
-- {-# OPTIONS -v tc.lhs:40 #-}
module FlexibleFunArity where
open import Common.Equality
data Bool : Set where true false : Bool
data Maybe (A : Set) : Set where
nothing : Maybe A
just : A → Maybe A
Case : {A : Set} → Maybe A → Set → Set → Set
Case nothing B C = B
Case (... | {
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-- Andreas, 2019-02-23, issue #3578.
-- Preserve types as much as possible during pattern matching.
-- New unifier (from Agda 2.5.1) was normalizing too much.
-- {-# OPTIONS -v tc.lhs.unify:45 #-}
data Nat : Set where
zero : Nat
postulate
MustNotBeNamed : Set
A = MustNotBeNamed
data P : Nat → Set where
z : A... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.HITs.SetTruncation where
open import Cubical.HITs.SetTruncation.Base public
open import Cubical.HITs.SetTruncation.Properties public
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-- Testing termination using subpatterns
module TerminationSubpattern where
-- a list with two different conses
data EOList (A : Set) : Set where
Nil : EOList A
ECons : A -> EOList A -> EOList A
OCons : A -> EOList A -> EOList A
butLastWithDefault : {A : Set} -> A -> EOList A -> A
butLastWithDefault a Ni... | {
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module Lemmachine.Runner where
{-# IMPORT Lemmachine.FFI #-}
open import Lemmachine.Resource
open import Lemmachine.Resource.Configure
open import Lemmachine.Request
open import Lemmachine.Response
open import Lemmachine.Utils
open import Lemmachine.Resolve
open import Data.Unit
open import Data.Nat
open import Data.St... | {
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module Common.MAlonzo where
open import Common.Prelude hiding (putStrLn)
open import Common.Coinduction
{-# IMPORT Data.Text.IO #-}
postulate
putStrLn : ∞ String → IO Unit
{-# COMPILED putStrLn Data.Text.IO.putStrLn #-}
main = putStrLn (♯ "This is a dummy main routine.")
mainPrint : String → _
mainPrint s = pu... | {
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import cedille-options
open import general-util
open import lib
module process-cmd
(options : cedille-options.options)
{mF : Set → Set}
{{_ : monad mF}}
(progress-update : string → 𝔹 → mF ⊤) where
--open import cedille-find
open import cedille-types
open import classify options {mF}
open import constants
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------------------------------------------------------------------------------
-- All the distributive laws modules
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism... | {
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module FOT.FOTC.Program.McCarthy91.WF-Relation.Induction.NonAcc.TerminationCheckIssue
where
data ℕ : Set where
zero : ℕ
succ : ℕ → ℕ
{-# BU... | {
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-- Andreas, 2016-12-20, issue #2349
{-# OPTIONS --show-implicit #-}
open import Agda.Primitive
open import Agda.Builtin.Equality
data D {{a}} (A : Set a) : Set a where
c : {{a : A}} (b : A) → D A
test : ∀ ℓ (A : Set ℓ) (x : D A) (a : A) → x ≡ c {{ℓ}} {{a = a}} a
test ℓ A x a = refl
-- ERROR:
-- x != c {{a}} of t... | {
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-- Andreas, 2012-09-15
-- Positive effects of making Agda recognize constant functions.
-- Arguments to constant functions are ignored in definitional equality.
{-# OPTIONS --copatterns #-}
module NonvariantPolarity where
open import Common.Equality
data ⊥ : Set where
record ⊤ : Set where
constructor trivial
data ... | {
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{-
This file contains:
- Pushout-products of two maps;
- The connectivity of pushout-product maps.
-}
{-# OPTIONS --safe #-}
module Cubical.HITs.Pushout.PushoutProduct where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Equiv.Properties
open import ... | {
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module SystemF.SmallStep where
open import Prelude
open import Data.Sum
open import Data.Product
open import Data.Vec hiding ([_])
open import SystemF.WellTyped
open import SystemF.Substitutions
open import SystemF.Substitutions.Lemmas
infixl 4 _≻_
-- irreducible System F terms
data Value {ν n} : Term ν n → Set wh... | {
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------------------------------------------------------------------------
-- Properties of non-empty lists
------------------------------------------------------------------------
module Data.List.NonEmpty.Properties where
open import Algebra
open import Category.Monad
open import Data.Function
open import Data.Produc... | {
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module Thesis.SIRelBigStep.DLang where
open import Thesis.SIRelBigStep.DSyntax public
open import Thesis.SIRelBigStep.DOpSem public
open import Thesis.SIRelBigStep.DLangDerive public
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Universes
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Universe where
open import Data.Product
open import Level
--------------------... | {
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------------------------------------------------------------------------------
-- First-order logic theorems
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-... | {
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open import Logic
open import Structure.Setoid
open import Structure.Operator.Ring
open import Structure.OrderedField
open import Type
module Structure.OrderedField.AbsoluteValue
{ℓ ℓₗ ℓₑ}
{F : Type{ℓ}}
⦃ equiv : Equiv{ℓₑ}(F) ⦄
(_+_ _⋅_ : F → F → F)
(_≤_ : F → F → Stmt{ℓₗ})
⦃ ring : Ring(_+_)(_⋅_) ⦄ -- TOD... | {
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open import Data.Product using (∃; ∃-syntax; _×_; _,_)
open import DeBruijn
open import Parallel
open import Beta
par-diamond : ∀ {n} {M N N′ : Term n}
→ M ⇉ N → M ⇉ N′
-----------------------
→ ∃[ L ] (N ⇉ L × N′ ⇉ L)
par-diamond (⇉-c {x = x}) ⇉-c = # x , ⇉-c , ⇉-c
par-diamond (⇉-ƛ p1) (⇉-ƛ p2)
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------------------------------------------------------------------------------
-- Mendelson's substitution
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# ... | {
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------------------------------------------------------------------------
-- Code related to the delay monad
--
-- Nils Anders Danielsson
------------------------------------------------------------------------
{-# OPTIONS --cubical --sized-types #-}
module README where
-- The concept referred to as the delay monad h... | {
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{-
This file contains:
- Definition of type quotients (i.e. non-truncated quotients)
-}
{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.HITs.TypeQuotients.Base where
open import Cubical.Core.Primitives
-- Type quotients as a higher inductive type:
data _/ₜ_ {ℓ ℓ'} (A : Type ℓ) (R : A → A → Type ℓ... | {
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------------------------------------------------------------------------
-- Code related to the abstract "Type Theory with Weak J" by Thorsten
-- Altenkirch, Paolo Capriotti, Thierry Coquand, Nils Anders
-- Danielsson, Simon Huber and Nicolai Kraus
--
-- The code is written by Nils Anders Danielsson
-------------------... | {
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open import Data.Nat
open import Data.Fin using (Fin; #_; suc; zero)
open import Data.List as List hiding (null)
open import Data.List.Membership.Propositional
open import Data.List.Relation.Unary.Any
open import Data.List.Relation.Unary.All
open import Data.Integer hiding (suc)
open import Data.Product hiding (map)
op... | {
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module Misc.PosBinary where -- Positive Binary Numbers
open import Data.Nat
open import Data.List
open import Relation.Binary.PropositionalEquality
using (_≡_; refl; sym)
open import Induction.WellFounded
open import Induction.Nat using (<-well-founded)
data Bin+ : Set where
[] : Bin+
1∷_ : Bin+ → Bin+
2∷_ ... | {
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module Tactic.Nat.Simpl where
open import Prelude hiding (abs)
open import Builtin.Reflection
open import Tactic.Reflection.Quote
open import Tactic.Reflection
open import Tactic.Nat.Reflect
open import Tactic.Nat.NF
open import Tactic.Nat.Exp
open import Tactic.Nat.Auto
open import Tactic.Nat.Auto.Lemmas
open impor... | {
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module Celeste where
open import Data.Nat using (ℕ; _⊔_; zero)
open import Data.String using (String)
open import Data.Vec using (Vec)
open import Data.Unsigned using (Unsigned)
open import Data.Signed using (Signed)
open import Data.Float using (Float)
private
variable
word-size : ℕ
mutual
data Type : ℕ → S... | {
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------------------------------------------------------------------------
-- The parser equivalence proof language is sound
------------------------------------------------------------------------
module TotalParserCombinators.Congruence.Sound where
open import Category.Monad
open import Codata.Musical.Notation
open i... | {
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module _ where
open import Agda.Builtin.Equality
open import Agda.Builtin.Nat
variable
f : Nat → Nat
-- Drops the argument to f!
foo : (n : Nat) → f n ≡ n → f (f n) ≡ n
foo n eq rewrite eq = eq
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{-# OPTIONS --without-K #-}
module algebra.monoid.mset where
open import level
open import algebra.monoid.core
open import algebra.monoid.morphism
open import algebra.semigroup
open import equality.core
open import hott.level
module _ {i}(M : Set i) ⦃ mM : IsMonoid M ⦄ where
open IsMonoid ⦃ ... ⦄
record IsMSet {... | {
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-- Andreas, 2013-10-27
{-# OPTIONS --copatterns #-}
module Issue907a where
import Common.Level
open import Common.Prelude
open import Common.Product
data Vec (A : Set) : Nat → Set where
[] : Vec A zero
test : ∀ {A} → Σ Nat λ n → Vec A n
proj₁ test = zero
proj₂ test = []
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{-# OPTIONS --without-K #-}
open import HoTT
open import homotopy.SuspAdjointLoop
open import cohomology.WithCoefficients
module cohomology.SuspAdjointLoopIso where
module SuspAdjointLoopIso {i j} (X : Ptd i) (Y : Ptd j) where
module ΣAΩ = SuspAdjointLoop X (⊙Ω Y)
GSΣ = →Ω-group-structure (⊙Susp X) Y
GSΩ = →Ω... | {
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{-
This second-order equational theory was created from the following second-order syntax description:
syntax Unit | U
type
𝟙 : 0-ary
term
unit : 𝟙
theory
(𝟙η) u : 𝟙 |> u = unit
-}
module Unit.Equality where
open import SOAS.Common
open import SOAS.Context
open import SOAS.Variable
open import SOAS.Fami... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.CoHSpace
open import cohomology.Theory
module cohomology.CoHSpace {i} (CT : CohomologyTheory i) (n : ℤ)
{X : Ptd i} (CHSS : CoHSpaceStructure X) where
open CohomologyTheory CT
open CoHSpaceStructure CHSS
open import cohomology.Wedge CT n... | {
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{-# OPTIONS --without-K #-}
--open import HoTT
open import homotopy.3x3.PushoutPushout
open import homotopy.3x3.Transpose
import homotopy.3x3.To as To
import homotopy.3x3.From as From
open import homotopy.3x3.Common
module homotopy.3x3.ToFrom {i} (d : Span^2 {i}) where
open Span^2 d
open M d hiding (Pushout^2)
open ... | {
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module SubstantiveDischargeIsConsistent where
open import HasNegation
open import HasSubstantiveDischarge
record SubstantiveDischargeIsConsistent (+ : Set) (- : Set) ⦃ _ : HasNegation (-) ⦄ ⦃ _ : HasSubstantiveDischarge (+) (-) ⦄ : Set₁
where
field
≽-consistent : {+ : +} → { - : - } → + ≽ - → + ⋡ ~ -
open Su... | {
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------------------------------------------------------------------------
-- Closure properties for h-levels
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
-- Partly based on Voevodsky's work on so-called univalent
-- foundations.
open import Equality
modu... | {
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open import Coinduction using ( ∞ ; ♭ ; ♯_ )
open import Data.Bool using ( Bool ; true ; false )
open import Data.Empty using ( ⊥ ; ⊥-elim )
open import Data.Unit using ( ⊤ ; tt )
open import System.IO.Transducers.Lazy using
( _⇒_ ; inp ; out ; done ; choice ) renaming
( ⟦_⟧ to ⟦_⟧' ; _⟫_ to _⟫'_
; _[&]_ to _[&... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import stash.modalities.gbm.GbmUtil
module stash.modalities.gbm.PullbackSplit where
-- L --> B K = A ×_D C / (f,h) d₁ = A -> D <- C
-- | |g L = B ×_A K / (g,left) d₂ = B -> A <- K
-- v v d =... | {
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{-
Closure properties of FinSet under several type constructors.
-}
{-# OPTIONS --safe #-}
module Cubical.Data.FinSet.Constructors where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Equiv
open import Cubical.HITs.PropositionalTruncation renaming (r... | {
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{-# OPTIONS --cubical --safe #-}
module Data.Sigma.Unique where
open import Data.Sigma.Base
open import Level
open import Path
∃! : ∀ {a b} {A : Type a} → (A → Type b) → Type (a ℓ⊔ b)
∃! B = ∃ x × B x × (∀ {y} → B y → x ≡ y)
infixr 4.5 ∃!-syntax
∃!-syntax : ∀ {a b} {A : Type a} (B : A → Type b) → Type (a ℓ⊔ b)
∃!-s... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- An inductive definition of the heterogeneous prefix relation
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.List.Relation.Binary.Prefix.H... | {
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module Structure.Category.Action where
open import Structure.Category.Functor
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{-# OPTIONS --without-K #-}
open import lib.Basics
open import lib.types.Coproduct
open import lib.types.Sigma
open import lib.types.Pi
open import lib.types.Fin
open import lib.types.Nat
open import lib.types.Empty
open import lib.NType2
open import lib.Equivalence2
open import Util.Misc
open import Util.Coproducts
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{-# OPTIONS --without-K --type-in-type #-}
module UnbiasedCategory where
open import Agda.Builtin.Equality
module TypedLists where
data TypedList (index : Set) (type : index -> index -> Set) : index -> index -> Set where
empty : {a : index} -> TypedList index type a a
fby : {a b c : index} -> type a b -> T... | {
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module L.Data.Bool.Properties where
open import L.Data.Bool.Core
open import L.Base.Id.Core
open import L.Base.Coproduct.Core
!∃tt∧!∃ff : (x : Bool) → (x ≡ ff) + (x ≡ tt)
!∃tt∧!∃ff = if (λ b → (b ≡ ff) + (b ≡ tt)) (inr refl) (inl refl)
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{-# OPTIONS --without-K --safe #-}
module Tools.Fin where
open import Tools.Nat
open import Tools.Nullary
open import Tools.PropositionalEquality
open import Data.Fin.Properties using (suc-injective)
open import Data.Fin public using (Fin) renaming (zero to x0 ; suc to _+1)
-- Decidability of equality
_≟ⱽ_ : {n ... | {
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{-
- Automatically generate UARel and DUARel instances
-}
{-# OPTIONS --no-exact-split --safe #-}
module Cubical.Displayed.Auto where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Function
open import Cubical.Foundations.Isomorphism
open import Cubica... | {
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{-# OPTIONS --cubical --safe #-}
module Diatonic where
open import Data.Bool using (Bool; false; true; if_then_else_; _∧_)
open import Data.Empty using (⊥)
open import Data.Fin using (Fin; toℕ; #_; _≟_) renaming (zero to fz; suc to fs)
open import Data.Integer using (ℤ; +_; -[1+_]... | {
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module MJSF.Examples.DynamicDispatch where
open import Prelude
open import Data.Star
open import Data.Bool
open import Data.List
open import Data.Integer
open import Data.List.Membership.Propositional
open import Data.List.Relation.Unary.Any
open import Data.List.Relation.Unary.All hiding (lookup)
open import Data.Pro... | {
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-- Andreas, 2016-12-31, issue #2374
-- Use hiding info to disambiguate overloaded projections.
-- {-# OPTIONS -v tc.lhs.split:40 #-}
postulate A B : Set
module M where
record R : Set₂ where
field
F : Set₁
module Order1 where
open M.R
open M.R {{...}}
test : M.R
F test = Set
inst : M.R
F {... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- This module is DEPRECATED. Please use
-- Data.Vec.Relation.Binary.Equality.Setoid directly.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open impor... | {
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{-# OPTIONS --without-K #-}
--open import HoTT
open import homotopy.3x3.PushoutPushout
open import homotopy.3x3.Transpose
import homotopy.3x3.To as To
import homotopy.3x3.From as From
open import homotopy.3x3.Common
module homotopy.3x3.ToFrom3 {i} (d : Span^2 {i}) where
open Span^2 d
open M d hiding (Pushout^2)
open... | {
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module calculus.properties where
open import utility
open import Esterel.Lang
open import Esterel.Lang.Binding
open import Esterel.Lang.Properties
open import Esterel.Lang.CanFunction
using (Canθₛ ; Canθₛₕ ; [S]-env)
open import Esterel.Environment as Env
using (Env ; Θ ; _←_ ; sig ; []env ; module SigMap ; modul... | {
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------------------------------------------------------------------------
-- Groupoids
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Equality
module Groupoid
{reflexive} (eq : ∀ {a p} → Equality-with-J a p reflexive) where
open import Prelud... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties connecting left-scaling and right-scaling
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Relation.Binary
-- The properties ar... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Complete where
open import Level
open import Categories.Category
open import Categories.Category.Construction.Cones
open import Categories.Functor
open import Categories.Diagram.Cone.Properties
open import Categories.Diagram.Limit using (Limit)
Complete ... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.EilenbergMacLane
open import homotopy.EilenbergMacLane1
open import homotopy.EilenbergMacLaneFunctor
open import homotopy.SmashFmapConn
open import homotopy.IterSuspSmash
open import cohomology.CupProduct.OnEM.InLowDegrees2
module cohomolog... | {
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open import Level using (_⊔_)
open import Function using (_$_)
open import Algebra using (CommutativeRing)
module AKS.Modular.Equivalence {c ℓ} (R : CommutativeRing c ℓ) where
open CommutativeRing R using (0#; 1#; _+_; _*_; -_; _-_)
renaming (Carrier to C)
open CommutativeRing R using (+-cong; +-congˡ; +-congʳ; +-i... | {
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{-# OPTIONS --prop --rewriting --confluence-check #-}
open import Agda.Primitive
open import Agda.Builtin.Equality
open import Agda.Builtin.Nat renaming (Nat to ℕ; _+_ to _+ℕ_)
infix 4 _≐_
data _≐_ {ℓ} {A : Set ℓ} (x : A) : A → Prop ℓ where
refl : x ≐ x
{-# BUILTIN REWRITE _≐_ #-}
variable
ℓ : Level
A B C : S... | {
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open import Nat
open import Prelude
open import core
module judgemental-inconsistency where
data incon : τ̇ → τ̇ → Set where
ICNumArr1 : {t1 t2 : τ̇} → incon num (t1 ==> t2)
ICNumArr2 : {t1 t2 : τ̇} → incon (t1 ==> t2) num
ICArr1 : {t1 t2 t3 t4 : τ̇} →
incon t1 t3 →
incon (t... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import stash.modalities.Orthogonality
module stash.modalities.NullifyFamily where
module _ {ℓ} {I : Type ℓ} (X : I → Type ℓ) (A : Type ℓ) where
private
data #NullifyAll : Type ℓ where
#inj : A → #NullifyAll
#apex : (i : I) →... | {
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open import Data.Bool using ( Bool ; true ; false ; if_then_else_ )
open import Data.Empty using ( ⊥-elim )
open import Data.Product using ( _×_ ; _,_ )
open import Data.Sum using ( inj₁ ; inj₂ )
open import Relation.Unary using ( _∈_ ; _∉_ )
open import Web.Semantic.DL.Concept using ( neg )
open import Web.Semantic.DL... | {
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module examplesPaperJFP.CatTerm where
open import examplesPaperJFP.BasicIO hiding (main)
open import examplesPaperJFP.Console hiding (main)
open import examplesPaperJFP.NativeIOSafe
cat : IO ConsoleInterface Unit
force cat =
exec′ getLine λ{ nothing → return unit ; (just line) → delay (
exec′ (putStrLn l... | {
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open import Prelude
open import Nat
open import core
open import contexts
open import disjointness
-- this module contains lemmas and properties about the holes-disjoint
-- judgement that double check that it acts as we would expect
module holes-disjoint-checks where
-- these lemmas are all structurally recursive ... | {
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{-# OPTIONS --universe-polymorphism #-}
module Categories.Agda.ISetoids.Cocomplete.Helpers where
open import Level
open import Relation.Binary using (Setoid; module Setoid; Preorder; module Preorder; Rel; _=[_]⇒_)
open import Data.Product using (Σ; _,_; Σ-syntax)
-- import Relation.Binary.EqReasoning as EqReasoning
o... | {
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{-# OPTIONS --without-K #-}
open import HoTT
open import homotopy.JoinComm
open import homotopy.JoinAssocCubical
module homotopy.JoinSusp where
module _ {i} {A : Type i} where
private
module Into = JoinRec {A = Bool} {B = A}
{D = Suspension A}
(if_then north else south)
(λ _ → south... | {
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{-# 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.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Lem... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category
module Categories.Morphism.Duality {o ℓ e} (C : Category o ℓ e) where
open Category C
import Categories.Morphism as M
private
module Op = M op
open M C
open import Categories.Morphism.Properties C
private
variable
A B X Y : Obj
f g h :... | {
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