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module Not-named-according-to-the-Haskell-lexical-syntax where
postulate
IO : Set -> Set
{-# BUILTIN IO IO #-}
{-# COMPILE GHC IO = type IO #-}
postulate
return : {A : Set} -> A -> IO A
{-# COMPILE GHC return = \ _ -> return :: a -> IO a #-}
data Unit : Set where
unit : Unit
{-# COMPILE GHC Unit = data () (... | {
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{-# OPTIONS --without-K --rewriting #-}
module NotNot where
open import Basics
open import lib.NType2
{-
The definitions here follow Penon's paper "Infinitesimaux et Intuitionisme".
-}
-- Since double negation is always proposition valued, we just define it that way
-- for convenience.
¬¬ : ∀ {i} ... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Examples of pretty printing
------------------------------------------------------------------------
module README.Text.Pretty where
open import Size
open import Data.Bool.Base
open import Data.List.Base as Li... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Automatic solvers for equations over naturals
------------------------------------------------------------------------
-- See README.Nat for examples of how to use this solver
{-# OPTIONS --without-K --safe #-}... | {
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module Data.List.Categorical where
import Lvl
open import Functional
open import Function.Equals
open import Data.List
open import Data.List.Functions
open import Data.List.Proofs
open import Data.List.Equiv.Id
open import Lang.Instance
open import Logic
open import Logic.Propositional
open import Relator.Equals
open ... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import Util.Prelude
module LibraBFT.Impl.OBM.ECP-LBFT-OBM-Diff.ECP-LBFT... | {
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module DiscriminationRules where
open import Data.Bool.Base
open import Data.List
open import Data.Nat
open import Relation.Binary.PropositionalEq... | {
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module Everything where
import Prelude
import Stack
import Syntax
import Semantics
import Convertibility
import Correctness
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-- Axiomatic embedding of guarded recursion in Agda
module guarded-recursion.embedding where
open import guarded-recursion.prelude
renaming (O to zero; S to suc)
open Coe
module M
(▹_ : ∀ {a} → Type_ a → Type_ a)
(▸ : ∀ {a} → ▹ (Type_ a) → Type_ a)
(next : ∀ {a} {A : Type_ a} → A → ▹ A)
(▸-rule :... | {
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module Issue644 where
postulate
A : Set
record R : Set₁ where
field P : A → Set
module M₁ (r : R) where
postulate
Foo₁ : ((x : A) → R.P r x) → Set
module M₂ (r : R) where
open R r
postulate
Foo₂ : ((x : A) → P x) → Set
postulate r : R
open R r
open M₁ r
open M₂ r
foo₂ : Set
foo₂ = Foo₂ r
-... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Instance.Properties.Setoids.CCC where
open import Level
open import Data.Product using (Σ ; _,_)
open import Function.Equality as ⟶ using (Π; _⟶_)
open import Relation.Binary using (Setoid)
open import Categories.Category
open import Categories.Category.M... | {
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module Lec8 where
open import CS410-Prelude
open import CS410-Functor
open import CS410-Monoid
open import CS410-Nat
data Maybe (X : Set) : Set where
yes : X -> Maybe X
no : Maybe X
maybeFunctor : Functor Maybe
maybeFunctor = record
{ map = \ { f (yes x) -> yes (f x)
; f no -> no
... | {
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open import OutsideIn.Prelude
open import OutsideIn.X
module OutsideIn.Inference.Separator(x : X) where
import OutsideIn.Constraints as C
open C(x)
open X(x)
open import Data.List hiding (map)
mutual
data SeparatedConstraint (n : Set) : Shape → Set where
SC : ∀ {s} → QConstraint n → Implications n ... | {
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-- submitted by Nisse, 2011-06-21
module Issue423 where
------------------------------------------------------------------------
-- Prelude
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
record Σ (A : Set) (B : A → Set) : Set where
constructor _,_
field
proj₁ : A
proj₂ : B proj₁
-- Andreas: c... | {
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module Oscar.Category.Category where
open import Oscar.Category.Setoid
open import Oscar.Category.Semigroupoid
open import Oscar.Level
module _
{𝔬 𝔪 𝔮}
(semigroupoid : Semigroupoid 𝔬 𝔪 𝔮)
where
open Semigroupoid semigroupoid
record IsCategory (ε : ∀ {x} → x ↦ x) : Set (𝔬 ⊔ 𝔪 ⊔ 𝔮) where
instan... | {
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module Diff where
open import Data.Nat using (ℕ; zero; suc)
open import Data.Float
open import Function using (_∘_)
postulate
post : ∀ {a} {A : Set a} → A
-- Need to generalize for bilinear forms
data _Is_DiffAt_ (f : Float → Float) : ℕ → Float → Set where
continuous : ∀ x → f Is zero DiffAt x
d : ∀ f' {n} x ... | {
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-- New NO_POSITIVITY_CHECK pragma for data definitions and mutual
-- blocks
-- Skipping an old-style mutual block: Before the `mutual` keyword.
{-# NO_POSITIVITY_CHECK #-}
mutual
data Cheat : Set where
cheat : Oops → Cheat
data Oops : Set where
oops : (Cheat → Cheat) → Oops
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------------------------------------------------------------------------
-- The Agda standard library
--
-- The free monad construction on indexed containers
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe --guardedness #-}
module Data.Container.Indexed.FreeMona... | {
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module _ where
open import Agda.Builtin.Nat
postulate
T : Set
C₁ : Set
instance I₁ : C₁
C₂ : Nat → Set
instance I₂ : ∀ {n} → C₂ n
it : {A : Set} {{_ : A}} → A
it {{x}} = x
postulate
f₁ : {{_ : Nat → C₁}} → T
f₂ : {{_ : ∀ n → C₂ n}} → T
works₁ : T
works₁ = f₁ -- f₁ {{λ _ → I₁}}
fails₁ : T
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module UniDB.Subst.Pair where
open import UniDB.Subst.Core
open import UniDB.Morph.Pair
instance
iLkPair :
{T : STX} {{apTT : Ap T T}}
{Ξ : MOR} {{lkTΞ : Lk T Ξ}}
{Ζ : MOR} {{lkTΖ : Lk T Ζ}} {{upΖ : Up Ζ}} →
Lk T (Pair Ξ Ζ)
lk {{iLkPair {T}}} (ξ ⊗ ζ) i = ap {T} ζ (lk {T} ξ i)
iLkRenPair :
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-- This file is the source Agda file
-- Edit this file not Common.hs
-- The warning below will be written to Common.hs
{- Description : Property based testing Name Utilities
This file contains various naming related utilities used for
generating Zerepoch Core types and terms.
-}
module ZerepochCore.Generators.NEAT.... | {
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-- AIM XXXV, 2022-05-06, issue #5891:
-- SizeUniv : SizeUniv was causing non-termination and inhabitation of Size< 0.
-- This is inconsistent; proof by Jonathan Chan.
{-# OPTIONS --sized-types #-}
open import Agda.Primitive
open import Agda.Builtin.Size
data ⊥ : Set where
-- Original exploit:
-- data False : SizeUn... | {
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{-# OPTIONS --cubical #-}
module Demos.Live where
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module Issue784.RefAPI where
open import Issue784.Values public hiding (seq)
open import Issue784.Context -- that should be private
open import Issue784.Transformer public
open import Data.List public using (List; []; _∷_; [_])
open import Data.Nat
open import Relation.Binary.PropositionalEquality.TrustMe
private
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------------------------------------------------------------------------------
-- Properties for the bisimilarity relation
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polym... | {
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open import Prelude
module Implicits.Substitutions.Type where
open import Implicits.Syntax.Type
open import Data.Fin.Substitution
open import Data.Star as Star hiding (map)
open import Data.Star.Properties
open import Data.Vec
module TypeApp {T} (l : Lift T Type) where
open Lift l hiding (var)
infixl 8 _/_
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module Thesis.SIRelBigStep.FundamentalProperty where
open import Data.Product
open import Relation.Binary.PropositionalEquality
open import Thesis.SIRelBigStep.IlcSILR
rfundamentalV3v : ∀ {Γ τ} (x : Var Γ τ) → (n : ℕ) → ∀ ρ1 dρ ρ2 (ρρ : rrelρ3 Γ ρ1 dρ ρ2 n) → rrelV3 τ (⟦ x ⟧Var ρ1) (D.⟦ x ⟧Var dρ) (⟦ x ⟧Var ρ2) n
rf... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties satisfied by decidable total orders
------------------------------------------------------------------------
open import Relation.Binary
module Relation.Binary.Properties.DecTotalOrder
{d₁ d... | {
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open import IO
main = run (putStr "Hacktoberfest")
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{-# OPTIONS --show-implicit --show-irrelevant #-}
-- {-# OPTIONS -v tc.conv.irr:20 -v tc.constr.findInScope:20 -v tc.meta:20 -v tc.conv.type:50 -v tc.conv.term:30 -v tc.conv.atom:50 -v tc.inj.use:20 #-}
module Issue631 where
import Common.Level -- for debug messages
data Bool : Set where
false true : Bool
F : Boo... | {
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{-# OPTIONS --cubical --safe #-}
module Data.Vec where
open import Prelude
private
variable
n m : ℕ
infixr 5 _∷_
data Vec (A : Type a) : ℕ → Type a where
[] : Vec A zero
_∷_ : A → Vec A n → Vec A (suc n)
head : Vec A (suc n) → A
head (x ∷ _) = x
foldr : (A → B → B) → B → Vec A n → B
foldr f b [] = b
fol... | {
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module GUIgeneric.GUIFeaturesPart3 where
open import GUIgeneric.Prelude renaming (addButton to addButton')
open import GUIgeneric.GUIDefinitions renaming (add to add'; add' to add)
open import GUIgeneric.GUI
open import GUIgeneric.GUIExampleLib
open import StateSizedIO.GUI.WxGraphicsLibLevel3 renaming (addButton to a... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties satisfied by strict partial orders
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Relation.Binary
module Relation.Binary.Prop... | {
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module parse-tree where
open import lib
record ParseTreeRec : Set lone where
field
ParseTreeT : Set
isParseTree : ParseTreeT → 𝕃 char → string → Set
ParseTreeToString : ParseTreeT → string
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module List where
data Bool : Set where
true : Bool
false : Bool
if_then_else_ : {A : Set} -> Bool -> A -> A -> A
if true then x else y = x
if false then x else y = y
boolElim : (P : Bool -> Set) -> P true -> P false -> (b : Bool) -> P b
boolElim P t f true = t
boolElim P t f false = f
data False : Set where
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------------------------------------------------------------------------
-- The Agda standard library
--
-- This module is DEPRECATED. Please use
-- Data.List.Relation.Binary.Permutation.Inductive directly.
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
mod... | {
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------------------------------------------------------------------------
-- A variant of the development in "Internalizing Representation
-- Independence with Univalence" (by Angiuli, Cavallo, Mörtberg and
-- Zeuner) with support for erasure
------------------------------------------------------------------------
-- T... | {
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{-# OPTIONS --without-K #-}
module Leftovers.Leftovers where
open import Function using (_$_)
open import Data.Bool
import Data.String as String
open import Leftovers.TraverseTerm
open import Leftovers.Utils
import Level as Level
open import Reflection
open import Reflection.Term
open import Reflection.TypeChecking.... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.HITs.Pushout.Base where
open import Cubical.Core.Glue
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Data.Unit
open import Cubical.HITs.Susp
data Pushout {ℓ ℓ' ℓ''} {A : Ty... | {
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{-
Generic UARel, DUARel, and SubstRel: the path relation is always univalent
-}
{-# OPTIONS --safe #-}
module Cubical.Displayed.Generic where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Transport
open import Cubical.Displayed.Base
open import Cubi... | {
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{-# OPTIONS --copatterns #-}
mutual
data D : Set where
c : R → D
record R : Set where
coinductive
field
out : D
open R
mutual
d : D
d = c r
r : R
out r = d
f : D → {A : Set} → A
f (c x) = f (out x)
-- should not termination check
absurd : {A : Set} → A
absurd = f d
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module _ (A : Set) where
record R : Set where
data D : Set where
open R (record {})
F : D → Set₃
F _ with Set₁
F _ | _ = Set₂
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open import SOAS.Metatheory.Syntax
-- Second-order equational logic library
module SOAS.Metatheory.SecondOrder.Equality {T : Set} (Syn : Syntax {T}) where
open import SOAS.Common
open import SOAS.Families.Core {T}
open import SOAS.Context
open import SOAS.Variable
open import SOAS.Metatheory.FreeMonoid Syn
open im... | {
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open import Agda.Builtin.Reflection
open import Agda.Builtin.Equality
open import Agda.Builtin.Int
open import Agda.Builtin.String
open import Common.Prelude
getFixity = primQNameFixity
infixl -1729 _to_
_to_ : Set → Set → Set
A to B = A → B
data Check : Set₁ where
equal : {A : Set} (x y : A) → x ≡ y → Check
pat... | {
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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 Data.Rational as ℝ using () renaming (ℚ to ℝ)
module monotonic... | {
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-- Operations on natural number
{-# OPTIONS --without-K --safe #-}
-- agad-stdlib
open import Relation.Binary.PropositionalEquality
module TypeTheory.Nat.Operations
{a}
-- | Type of natural number
(N : Set a)
-- | Zero
(zero : N)
-- | Successor function
(suc : N → N)
-- | Induction principle
(ind :... | {
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{-# OPTIONS --without-K --rewriting #-}
open import PathInduction
open import Pushout
module JamesSecondComposite {i} (A : Type i) (⋆A : A) where
open import JamesTwoMaps A ⋆A public
-- Second composite
to-ε∞ : to ε∞ == εJ
to-ε∞ = idp
to-α∞-in∞ : (a : A) (n : ℕ) (x : J n) → to (α∞ a (in∞ n x)) == αJ a (inJ n x)
t... | {
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module Relation.Ternary.Separation.Bigstar where
open import Level
open import Data.Bool
open import Data.Product
open import Relation.Unary
open import Relation.Ternary.Separation
open import Relation.Ternary.Separation.Monad
open import Relation.Ternary.Separation.Monad.Error
open import Relation.Ternary.Separation.... | {
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------------------------------------------------------------------------
-- A partial order
------------------------------------------------------------------------
{-# OPTIONS --sized-types #-}
open import Prelude
module Delay-monad.Partial-order {a} {A : Type a} where
open import Equality.Propositional as E
open ... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
open import Cubical.Relation.Binary.Base
open import Cubical.Core.Everything
module Cubical.Relation.Binary.Structures
{a ℓ} {A : Type a} -- The underlying type
(_<>_ : Rel A ℓ) -- The relation
where
open import Cubical.Foundations.Prelude using (refl; sym; ... | {
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{- Formal verification of authenticated append-only skiplists in Agda, version 1.0.
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 Data.Unit.NonEta
open import Data.Empty
open import Data... | {
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import Oscar.Class.Transextensionality.Proposequality -- FIXME why not use the instance here?
open import Oscar.Class
open import Oscar.Class.IsPrecategory
open import Oscar.Class.Transextensionality
open import Oscar.Class.Transitivity
open import Oscar.Data.Proposequality
open import Oscar.Prelude
open import Oscar.... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Heterogeneous N-ary Functions
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Function.Nary.NonDependent where
-------------------------------... | {
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{-
Functions building UARels and DUARels on Σ-types
-}
{-# OPTIONS --safe #-}
module Cubical.Displayed.Sigma where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Data.Sigma
open import Cubical.Displayed.Base
open import Cubical.Displayed.Subst
open import Cubica... | {
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-- Martin-Löf identity type without the K axiom
-- (we do not assume uniqueness of identity proofs).
{-# OPTIONS --without-K --safe #-}
module Tools.PropositionalEquality where
-- We reexport Agda's builtin equality type.
open import Agda.Builtin.Equality public using (_≡_; refl)
open import Tools.Empty
-- Inequal... | {
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{-# OPTIONS --safe #-}
open import Cubical.Foundations.Everything renaming (Iso to _≅_)
open import Cubical.Data.List
open import Cubical.Data.Unit
open import Cubical.Data.Prod hiding (map)
open import Cubical.Data.Nat
module Cubical.Data.List.Dependent where
open _≅_
data ListP {ℓA ℓB} {A : Type ℓA} (B : A → Type... | {
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{-# OPTIONS --safe --cubical #-}
module Data.Unit.UniversePolymorphic where
open import Level
record ⊤ {ℓ} : Type ℓ where constructor tt
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{-# OPTIONS --without-K #-}
module Formalization where
open import Agda.Primitive using (lsuc)
open import Relation.Binary.PropositionalEquality
open Relation.Binary.PropositionalEquality.≡-Reasoning
open import Level
-- Recall Lemma 1.12
ind₌ : ∀{a b}{A : Set a} → (C : (x y : A) → (x ≡ y) → Set b) → ((x : A) → C... | {
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module UniDB.Morph.WeakenOne where
open import UniDB.Spec
--------------------------------------------------------------------------------
data Weaken₁ : MOR where
weaken₁ : {γ : Dom} → Weaken₁ γ (suc γ)
instance
iLkWeaken₁ : {T : STX} {{vrT : Vr T}} → Lk T Weaken₁
lk {{iLkWeaken₁ {T}}} weaken₁ i = vr {T} (s... | {
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------------------------------------------------------------------------
-- A type for values that should be erased at run-time
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Equality
import Erased.Basics
import Erased.Level-1
module Erased
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open import Common.Level
postulate
ℓ : Level
data D : Set (lsuc ℓ) where
c : (ℓ : Level) → Set ℓ → D
-- Bad error:
-- The type of the constructor does not fit in the sort of the
-- datatype, since Set (lsuc ℓ) is not less or equal than Set (lsuc ℓ)
-- when checking the constructor c in the declaration of D
-- J... | {
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open import Data.Bool using ( Bool ; true ; false ; if_then_else_ )
open import Data.Product using ( _×_ ; _,_ )
open import Data.Sum using ( inj₁ ; inj₂ )
open import Relation.Unary using ( _∈_ )
open import Web.Semantic.DL.Concept using ( Concept ; ⟨_⟩ ; ¬⟨_⟩ ; ⊤ ; ⊥ ; _⊓_ ; _⊔_ ; ∀[_]_ ; ∃⟨_⟩_ ; ≤1 ; >1 ; neg )
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{-# OPTIONS --allow-unsolved-metas #-}
module finiteSet where
open import Data.Nat hiding ( _≟_ )
open import Data.Fin renaming ( _<_ to _<<_ ) hiding (_≤_)
-- open import Data.Fin.Properties hiding ( ≤-refl )
open import Data.Empty
open import Relation.Nullary
open import Relation.Binary.Definitions
open import Rel... | {
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import cedille-options
open import general-util
module spans (options : cedille-options.options) {mF : Set → Set} {{mFm : monad mF}} where
open import cedille-types
open import constants
open import conversion
open import ctxt
open import free-vars
open import syntax-util
open import type-util
open import to-string op... | {
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{-# OPTIONS --rewriting --confluence-check #-}
-- Let us assume that extensionality of functions cannot be proved
-- inside "plain" Agda. In that case the code below shows that the
-- REWRITE functionality is not a conservative extension, even if we
-- only use propositional equality as the rewriting relation, and do... | {
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module #15 where
{-
Show that indiscernability of identicals follows from path induction
-}
open import Data.Product
open import Relation.Binary.PropositionalEquality
id : ∀{x}{A : Set x} → A → A
id x = x
ind₌ : ∀{a}{A : Set a} → (C : (x y : A) → (x ≡ y) → Set) → ((x : A) → C x x refl) → (x y : A) → (p : x ≡ y) →... | {
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{-# OPTIONS --safe #-}
module Cubical.Categories.Instances.CommRings where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Algebra.Ring
open import Cubical.Algebra.CommRing
open import Cubical.Categories.Category
open Category
open CommRingHoms
CommRingsCategory... | {
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open import Data.Bool as Bool using (Bool; false; true; if_then_else_; not)
open import Data.String using (String)
open import Data.Nat using (ℕ; _+_; _≟_; suc; _>_; _<_; _∸_)
open import Relation.Nullary.Decidable using (⌊_⌋)
open import Data.List as l using (List; filter; map; take; foldl; length)
open import Data.Li... | {
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{-# OPTIONS --no-termination-check #-}
module optionsPragma where
-- Only goes through with the termination checker turned off.
Foo : Set
Foo = Foo
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data ⊥ : Set where
data Bool : Set where
false true : Bool
data _≡_ (x : Bool) : Bool → Set where
refl : x ≡ x
true≠false : false ≡ true → ⊥
true≠false ()
data Maybe (A : Set) : Set where
nothing : Maybe A
just : A → Maybe A
data Eq {A : Set} (_≈_ : A → A → Set) : Maybe A → Maybe A → Set where
just :... | {
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module Control.Monad.Writer where
open import Prelude
open import Control.Monad.Zero
open import Control.Monad.Identity
open import Control.Monad.Transformer
record WriterT {a} (W : Set a) (M : Set a → Set a) (A : Set a) : Set a where
no-eta-equality
constructor writerT
field runWriterT : M (A × W)
open Write... | {
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------------------------------------------------------------------------------
-- A Peano arithmetic proof without using a where clause
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-u... | {
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module 747Decidable where
-- Library
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; sym) -- added sym
open Eq.≡-Reasoning
open import Data.Nat using (ℕ; zero; suc; _≤_; z≤n; s≤s)
open import Data.Product using (_×_) renaming (_,_ to ⟨_,_⟩)
open import Data.Sum using (_⊎_; inj₁; inj₂)
ope... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.SuspProduct
open import homotopy.SuspSmash
open import homotopy.JoinSusp
open import cohomology.Theory
module cohomology.SphereProduct {i} (CT : CohomologyTheory i)
(n : ℤ) (m : ℕ) (X : Ptd i) where
open CohomologyTheory CT
open impo... | {
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module Examples.Parity where
open import Relation.Nullary
open import Relation.Binary.PropositionalEquality
open import Data.Empty
open import Data.Bool hiding (not)
open import Data.Nat
open import Data.Fin hiding (_+_)
open import Data.Product hiding (map)
open import Data.List hiding (and; or; sum; map; [_])
open im... | {
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-- Andreas, 2017-02-20, issue #2467
-- Proper error on missing BUILTIN REWRITE
{-# OPTIONS --rewriting #-}
postulate A : Set
{-# REWRITE A #-}
-- Should fail with error like
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-- Andreas, 2019-05-29, issue #3818, reported by Matthew Daggitt
-- An external module name, i.e., the object of `import`,
-- should not be considered clashing with an internal module name.
module _ where
module Issue3818 where
module M where -- Internal module Issue3818.M.
open import Issue3818.M -- Nam... | {
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module rewriting where
open import cedille-types
open import constants
open import conversion
open import ctxt
open import general-util
open import free-vars
--open import lift
open import rename
open import subst
open import syntax-util
open import type-util
--open import erase
open import datatype-util
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open import Agda.Builtin.Nat
open import Agda.Builtin.Unit
open import Agda.Builtin.Reflection renaming (bindTC to _>>=_)
open import Agda.Builtin.List
open import Agda.Builtin.Sigma
open import Agda.Builtin.Equality
infix 0 case_of_
case_of_ : ∀ {a b}{A : Set a}{B : Set b} → A → (A → B) → B
case x of f = f x
map : ... | {
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module Pi.Invariants where
open import Data.Empty
open import Data.Unit
open import Data.Sum
open import Data.Product
open import Data.List as L hiding (_∷_)
open import Relation.Binary.PropositionalEquality
open import Pi.Syntax
open import Pi.Opsem
open import Pi.NoRepeat
-- Get the type of the deepest context
get𝕌... | {
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module Thesis.SIRelBigStep.ArithExtra where
open import Relation.Binary.PropositionalEquality
open import Data.Nat public
open import Data.Nat.Properties public
open import Relation.Binary hiding (_⇒_)
lt1 : ∀ {k n} → k < n → k ≤ n
lt1 (s≤s p) = ≤-step p
m∸n≤m : ∀ m n → m ∸ n ≤ m
m∸n≤m m zero = ≤-refl
m∸n≤m zero (su... | {
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------------------------------------------------------------------------
-- An implementation of the Fibonacci sequence using tail
------------------------------------------------------------------------
module SingletonChunks where
open import Codata.Musical.Notation
open import Codata.Musical.Stream as S using (Str... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.HITs.Sn.Base where
open import Cubical.HITs.Susp
open import Cubical.Foundations.Pointed
open import Cubical.Data.Nat
open import Cubical.Data.NatMinusOne
open import Cubical.Data.Empty
open import Cubical.Foundations.Prelude
S : ℕ₋₁ → Type₀
S neg1 = ⊥... | {
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module Function.Domains.Functions where
import Lvl
open import Function.Domains
open import Function.Domains.Id
open import Structure.Relator.Properties
open import Structure.Setoid
open import Type
open import Type.Dependent
private variable ℓₒ₁ ℓₒ₂ ℓₑ₁ ℓₑ₂ : Lvl.Level
module _ {X : Type{ℓₒ₁}} {Y : Type{ℓₒ₂}} ... | {
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-- {-# OPTIONS --show-implicit #-}
-- {-# OPTIONS -v tc.meta:50 -v tc.conv:20 -v tc.conv.type:50 #-}
module Issue659 where
postulate
Level : Set
lzero : Level
lsuc : Level → Level
_⊔_ : Level → Level → Level
{-# BUILTIN LEVEL Level #-}
{-# BUILTIN LEVELZERO lzero #-}
{-# BUILTIN LEVELSUC lsuc #-}
{-#... | {
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{-# OPTIONS --without-K --safe #-}
module Data.Binary.Proofs.Addition where
open import Relation.Binary.PropositionalEquality
open import Data.Binary.Operations.Unary
open import Data.Binary.Operations.Addition
open import Data.Binary.Proofs.Unary
open import Data.Binary.Proofs.Semantics
open import Data.Binary.Defin... | {
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open import Relation.Binary.Core
module BBHeap.Equality.Properties {A : Set}(_≤_ : A → A → Set) where
open import BBHeap _≤_
open import BBHeap.Equality _≤_
open import Bound.Lower A
refl≈ : {b : Bound}{h : BBHeap b} → h ≈ h
refl≈ {b} {leaf} = ≈leaf
refl≈ {b} {left b≤x l⋘r} = ≈left b≤x b≤x l⋘r l⋘r refl≈ refl≈
refl≈... | {
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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.Base.Types
import ... | {
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{-# OPTIONS --rewriting #-}
open import Array
open import Array.APL using (reduce-1d)
open import Data.Nat as N
open import Data.Nat.Properties
open import Data.Vec as V hiding (_>>=_; _++_)
open import Data.Fin using (Fin; zero; suc; raise; inject+; #_)
open import Relation.Binary.PropositionalEquality
open import ... | {
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-- Compiled things must be a postulate
module CompiledMustBePostulate where
postulate
A : Set
foo : Set
foo = A
{-# COMPILED foo bar #-}
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{-# OPTIONS --cubical --cumulativity #-}
module equalities where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Univalence
open import Cubical.Data.Equality
module _ {a ℓ} {A : Set a} where
≣-Type = A → A → S... | {
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import Issue4267.M using ()
-- foo : {!Issue4267.M.R!} -- cannot give, but this is the solution
foo = record { f = Set}
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{-# OPTIONS --safe #-}
module Cubical.Algebra.Group.Instances.Int where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Int renaming (ℤ to ℤType ; _+_ to _+ℤ_ ; _-_ to _-ℤ_; -_ to -ℤ_ ; _·_ to _·ℤ_)
open import Cubical.Algebra.Group.Base
open GroupStr
ℤ : Group₀
fst ℤ = ℤType
1g (snd ℤ) = 0
_·_ (snd... | {
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{- revised nomenclature -}
module Oscar.Data4 where
record ⊤ : Set where
constructor tt
Const_ : ∀ {a} {A : Set a} {b} {B : Set b} → B → A → B
Const_ x _ = x
infixr 20 _∷_
-- List
data ⟦_⟧ {a} (A : Set a) : Set a where
∅ : ⟦ A ⟧
_∷_ : A → ⟦ A ⟧ → ⟦ A ⟧
-- Nat
⟦⟧ = ⟦ ⊤ ⟧
infix 21 ¡_
pattern ¡_ ⟦A⟧ = tt ∷ ⟦A⟧... | {
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{-# OPTIONS --show-irrelevant --subtyping #-}
module Issue2170-unify-subtyping where
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
record Squash (A : Set) : Set where
constructor squash
field .unsquash : A
open Squash
record UnSquash (A : Set) (s : A → Squash A) : Set where
constructor inverse
f... | {
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------------------------------------------------------------------------
-- Normal and neutral terms
------------------------------------------------------------------------
open import Level using (zero)
open import Data.Universe
module README.DependentlyTyped.NormalForm
(Uni₀ : Universe zero zero) where
open imp... | {
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------------------------------------------------------------------------
-- Semantics of the parsers
------------------------------------------------------------------------
-- Currently it is only specified when a string is _accepted_ by a
-- parser; semantic actions are not included.
module RecursiveDescent.Inducti... | {
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{-# OPTIONS --without-K #-}
module algebra.group where
open import algebra.group.core public
open import algebra.group.morphism public
open import algebra.group.gset public
open import algebra.group.classifying public
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-- ----------------------------------------------------------------------
-- The Agda σ-library
--
-- Substitutions
-- ----------------------------------------------------------------------
module Sigma.Subst.Core where
open import Sigma.Renaming.Base
open import Data.Nat using (ℕ; _+_)
open import Data.Fin using (... | {
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{-# OPTIONS --without-K --safe #-}
module Util.Relation.Binary.Closure.SymmetricTransitive where
open import Relation.Binary using (Rel)
open import Util.Prelude
data SymTrans {α ρ} {A : Set α} (R : Rel A ρ) : Rel A (α ⊔ℓ ρ) where
`base : ∀ {x y} → R x y → SymTrans R x y
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