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|---|---|
{-# OPTIONS --without-K #-}
module CPermCat where
open import Level using (zero)
open import Data.Nat using (ℕ; _+_; _*_)
open import Data.Fin using () renaming (zero to 0F)
open import Data.Product using (_,_; uncurry)
import Relation.Binary.PropositionalEquality as P
using (_≡_; refl; sym; cong₂; isEquivalence)
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open import Common.Prelude hiding (_>>=_)
open import Common.Reflection
open import Common.Equality
record Functor (F : Set → Set) : Set₁ where
field
fmap : ∀ {A B} → (A → B) → F A → F B
IdF : Functor (λ A → A)
unquoteDef IdF =
defineFun IdF (clause (vArg (projP (quote Functor.fmap)) ∷ vArg (var "f") ∷ vArg ... | {
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category.Core
module Categories.Morphism.Regular.Properties {o ℓ e} (𝒞 : Category o ℓ e) where
open import Categories.Morphism 𝒞
open import Categories.Morphism.Regular 𝒞
open import Categories.Diagram.Equalizer 𝒞
open import Categories.Diagram.Equalizer.... | {
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module Categories.Monad.Algebra where
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.PtdAdjoint
open import groups.FromSusp
open import groups.ToOmega
module groups.SuspAdjointLoop {i} where
import homotopy.SuspAdjointLoop {i} as A
module _ (X Y : Ptd i) where
private
pres-comp : preserves-comp
(Gro... | {
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open import Relation.Binary.Core
module BHeap.Everything {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_) where
open import BHeap.Heap _≤_
open import BHeap.Height _≤_ tot≤
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{-# OPTIONS --cubical-compatible --show-implicit #-}
module WithoutK3 where
-- Homogeneous equality.
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
-- The J rule.
J : {A : Set} (P : {x y : A} → x ≡ y → Set) →
(∀ x → P (refl {x = x})) →
∀ {x y} (x≡y : x ≡ y) → P x≡y
J P p refl = p _
-- Heterogen... | {
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{-# OPTIONS --without-K #-}
module Data.ByteString where
import Data.ByteString.Primitive as Prim
import Data.ByteString.Utf8 as Utf8
open import Data.Word8 using (Word8)
open import Data.Nat using (ℕ)
open import Data.Colist using (Colist)
open import Data.List using (List)
open import Data.String using (String)
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module Base.Free where
-- Reexport definitions from Agda's standard library that are needed by the
-- generated code.
open import Function using (case_of_) public
open import Data.Bool using (if_then_else_) public
open import Size using (Size; ↑_) public
-- The `Free` mon... | {
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{-# OPTIONS --without-K --safe #-}
module Cats.Category.Presheaves.Facts where
open import Cats.Category.Presheaves.Facts.Exponential public using
( hasExponentials )
open import Cats.Category
open import Cats.Category.Presheaves
import Cats.Category.Fun.Facts as Fun
import Cats.Category.Setoids.Facts
module _ {... | {
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open import Relation.Binary.Core
module PLRTree.Drop.Heap {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_)
(trans≤ : Transitive _≤_) where
open import PLRTree {A}
open import PLRTree.Compound {A}
open import PLRTree.Drop _≤_ tot≤
open import PLRTree.D... | {
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module explore where
import Explore.BigDistr
import Explore.BinTree
import Explore.Core
import Explore.Dice
import Explore.Examples
import Explore.Explorable
import Explore.Fin
import Explore.Group
import Explore.GuessingGameFlipping
import Explore.Isomorphism
import Explore.Monad
import Explore.One
import Explore.Prod... | {
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module Bool where
data Bool : Set where
false : Bool
true : Bool
data IsTrue : Bool -> Set where
isTrue : IsTrue true
open import Vec
open import All
allEnvs : {n : Nat} -> List (Vec Bool n)
allEnvs {zero } = ε :: []
allEnvs {suc n} = map (_►_ false) allEnvs ++ map (_►_ true) allEnvs
∈++left : {A : Set}{x ... | {
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open import Nat
open import Prelude
open import dynamics-core
open import contexts
open import lemmas-consistency
open import lemmas-disjointness
open import lemmas-matching
open import weakening
module typed-elaboration where
mutual
typed-elaboration-synth : {Γ : tctx} {e : hexp} {τ : htyp} {d : ihexp} {Δ : hct... | {
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{-# OPTIONS --without-K --safe #-}
-- Adjoint Functor Theorem
module Categories.Adjoint.AFT where
open import Level
open import Data.Product
open import Data.Product using (Σ)
open import Categories.Category
open import Categories.Category.Complete
open import Categories.Category.Complete.Properties
open import Cate... | {
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{-# OPTIONS --cubical --safe #-}
module Equiv where
open import Agda.Builtin.Cubical.Glue public
using ( isEquiv
; equiv-proof
; _≃_)
open import Cubical.Foundations.Everything public using (ua)
open import Cubical.Foundations.Equiv public
using (equivToIso; isPropIsEquiv)
renaming (compEquiv t... | {
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open import Agda.Builtin.Equality
open import Agda.Builtin.Nat
data ⊥ : Set where
data Zero : Set where
zero : Zero
data One : Set where
suc : Zero → One
one : One
one = suc zero
data _≤_ : One → Zero → Set where
leq : ∀ m n → Nat → Nat → m ≤ n → ⊥
leq (suc m) zero = λ i j ()
test : Nat → one ≤ zero → ⊥
tes... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Categories.Functor where
open import Cubical.Categories.Functor.Base public
open import Cubical.Categories.Functor.Properties public
open import Cubical.Categories.Functor.Compose public
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module Oscar.Data.Maybe.properties where
open import Data.Maybe public using (maybe)
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module STLC2.Kovacs.Convertibility where
open import STLC2.Kovacs.Substitution public
--------------------------------------------------------------------------------
-- Convertibility (_~_ ; ~refl ; _~⁻¹ ; lam ; app ; β ; η)
infix 3 _∼_
data _∼_ : ∀ {Γ A} → Γ ⊢ A → Γ ⊢ A → Set
where
refl∼ : ∀ {Γ A} → {M ... | {
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module Algebra.Dioid where
record Dioid A (_≡_ : A -> A -> Set) : Set where
field
zero : A
one : A
_+_ : A -> A -> A
_*_ : A -> A -> A
reflexivity : ∀ {r : A} -> r ≡ r
symmetry : ∀ {r s : A} -> r ≡ s -> s ≡ r
transitivity : ∀ {r s t : A} -> r ≡ s ... | {
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------------------------------------------------------------------------
-- Pointers to results from the paper
------------------------------------------------------------------------
module README.Pointers-to-results-from-the-paper where
open import Prelude using (Type)
open import Prelude.Size using (∞)
import Col... | {
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module Data.Lens.Proofs.LensPostulates where
open import Haskell.Prelude renaming (zero to Z; suc to S)
open import Data.Lens.Lens
open import Data.Logic
open import Agda.Primitive
open import Data.Lens.Proofs.LensLaws
---- Lens postulates
-- These are provable using the isomorphism to the getter+setter style
-- Howe... | {
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module examplesPaperJFP.Collatz where
open import Data.Nat.Base
open import Data.Nat.DivMod
open import Data.Fin using (Fin; zero; suc)
open import examplesPaperJFP.Colists
collatzStep : ℕ → ListF ℕ ℕ
collatzStep 1 = nil
collatzStep n with n divMod 2
... | result q zero _ = cons n q
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import Lvl
open import Type
module Type.Univalence where
open import Functional
import Logic.Predicate
import Relator.Equals
import Relator.Equals.Proofs
import Type.Cardinality
import Type.Cardinality.Proofs
import Type.Functions
import Type.Functions.Inverse
module _ {ℓₗ ℓₒ ... | {
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module static where
open import Data.Nat using (ℕ; _+_; zero; suc)
open import Data.Fin using (Fin; toℕ; zero; suc)
open import Data.Vec using (lookup; _∷_; [])
open import Data.Bool using (Bool; true; false)
open import LSsyntax
open import Relation.Binary.PropositionalEquality -- using (_≡_; refl)
-- inference rul... | {
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module sets.nat.core where
open import level
open import decidable
open import equality.core
open import function.core
open import function.isomorphism.core
open import sets.empty
infixr 8 _^_
infixl 7 _*_
infixl 6 _+_
data ℕ : Set where
zero : ℕ
suc : ℕ → ℕ
{-# BUILTIN NATURAL ℕ #-}
pred : ℕ → ℕ
pred zero... | {
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module _ where
module First where
postulate
C : Set → Set
it : {A : Set} ⦃ _ : C A ⦄ → A
X : Set
module Second where
open First
postulate instance iCX : C X
module Nested where
open First
x : X
x = it -- Second.iCX is in scope
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-- Andreas, 2016-07-08
-- Better error message for private modules
module _ where
module M where
private module Private where
module ShouldFail = M.Private
-- Current:
-- No such module M.Private
-- Better:
-- M.Private is not in scope since it is declared as private
-- Or (simpler):
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{-# OPTIONS --without-K #-}
open import Base
open import Homotopy.TruncatedHIT
open import Integers
module Algebra.FreeGroup {i} (A : Set i) where
{-
The definition is the following
(0)data freegroup : Set i where
e : freegroup
_·_ : A → freegroup → freegroup
_⁻¹·_ : A → freegroup → freegrou... | {
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{-# OPTIONS --cubical --safe --postfix-projections #-}
module Data.List.Relation.Binary.Permutation where
open import Prelude
open import Data.List
open import Data.Fin
open import Data.Fin.Properties
open import Data.List.Membership
open import Cubical.Foundations.Equiv
import Function.Isomorphism as Isomorphism
ope... | {
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module ImportTests.ExtractFunction where
open import ExtractFunction
open import Data.Nat
open import Data.Bool
checkFunction1 : ℕ
checkFunction1 = function1 2 3
checkFunction2 : ℕ
checkFunction2 = function2 4 true
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@0 F : @0 Set → Set
F A = λ { → A }
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{-# OPTIONS --safe #-}
module Cubical.HITs.FreeComMonoids.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Function
private variable
ℓ : Level
A : Type ℓ
data FreeComMonoid (A : Type ℓ) : Type ℓ where
⟦_⟧ : A → FreeComMonoid A
ε... | {
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--{-# OPTIONS --allow-unsolved-metas #-}
module Theorem1 where
open import OscarPrelude
open import HasSatisfaction
open import HasSubstantiveDischarge
open import LiteralFormula
open import 𝑱udgement
open import HasSalvation
open import Membership
open import Interpretation
open import HasNegation
open import ... | {
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-- Andreas, 2011-04-15
module NotStronglyRigidOccurrence where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
data _≡_ {A : Set}(a : A) : A -> Set where
refl : a ≡ a
-- Jason C. Read, PhD thesis, p. 109
test : (k : Nat) ->
let X : (Nat -> Nat) -> Nat
X = _
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{-# OPTIONS --rewriting #-}
module Oscar.AgdaRewriting where
open import Agda.Builtin.Equality
{-# BUILTIN REWRITE _≡_ #-}
record ⊤ : Set where
constructor tt
data List (A : Set) : Set where
∅ : List A
_∷_ : A → List A → List A
Nat = List ⊤
pattern ‼ xs = tt ∷ xs
syntax ‼ xs = ! xs
open import Agda.Builtin.... | {
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{-# OPTIONS --without-K --safe #-}
open import Algebra
module Data.FingerTree.Reasoning
{r m}
(ℳ : Monoid r m)
where
open Monoid ℳ renaming (Carrier to 𝓡)
open import Data.FingerTree.MonoidSolver ℳ using (solve-macro)
open import Data.Unit using (⊤)
open import Reflection using (TC; Term)
macro
_↯ : Term... | {
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module BBHeap.Perfect {A : Set}(_≤_ : A → A → Set) where
open import BBHeap _≤_
open import Bound.Lower A
open import Bound.Lower.Order _≤_
data Perfect {b : Bound} : BBHeap b → Set where
plf : Perfect (leaf {b})
pnd : {x : A}{l r : BBHeap (val x)}(b≤x : LeB b (val x))(l⋘r : l ⋘ r) → l ≃ r → Perfect (left b≤x l⋘... | {
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module Issue478 where
record Ko (Q : Set) : Set₁ where
field
T : Set
module Bo (P : Set) (ko : Ko P) where
open Ko ko
err : T
err = Set
{- The error message was:
Set₁ !=< T P ko of type Set₂
when checking that the expression Set has type T P ko
We now get the desired error message:
Set₁ !=< T o... | {
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{-# OPTIONS --cubical --safe #-}
module Ag08 where
open import Cubical.Core.Everything
open import Cubical.Foundations.Everything
open import Cubical.Data.Everything
-- maybe helpful when case splitting
record Reveal_·_is_ {a b} {A : Set a} {B : A → Set b}
(f : (x : A) → B x) (x : A) (y : B x) :
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{-# OPTIONS --without-K #-}
open import Data.Nat
open import Data.Two
open import Data.Zero
open import Data.Fin.NP
open import Type
open import Function
open import Relation.Binary.PropositionalEquality.NP
import Explore.Universe.Base
open import Explore.Core
open import Explore.Zero
open import Explore.One
open impo... | {
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------------------------------------------------------------------------
-- Preimages
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
-- Partly based on Voevodsky's work on so-called univalent
-- foundations.
open import Equality
module Preimage
{reflexi... | {
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module Money where
import Agda.Builtin.IO as Builtin using (IO)
import Data.Rational as ℚ using (_+_; _*_)
open import Codata.Musical.Notation using (♯_)
open import Data.Nat using (ℕ; suc)
open import Data.Integer as ℤ using (+_)
open import Data.List using (List; []; _∷_)
open import Data.Rational as ℚ using (ℚ; 0ℚ;... | {
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import cedille-options
module elab-util (options : cedille-options.options) where
open import general-util
open import cedille-types
open import syntax-util
open import type-util
open import ctxt
open import conversion
open import constants
open import instances
open import subst
open import rename
open import rewriti... | {
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open import Nat
open import Prelude
open import List
open import core
open import judgemental-erase
open import checks
module constructability where
-- we construct expressions and types by induction on their
-- structure. for each sub term, we call the relevant theorem, then
-- assemble the results with careful... | {
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-- Andreas, 2015-05-02 Integrate copatterns with with.
{-# OPTIONS --copatterns #-}
open import Common.Prelude hiding (map)
open import Common.Product
open import Common.Equality
dup : {A : Set} → A → A × A
proj₁ (dup a) = a
proj₂ (dup a) with a
proj₂ (dup a) | x = x
record Stream (A : Set) : Set where
coinductiv... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Data.FinData.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
import Cubical.Data.Empty as ⊥
open import Cubical.Data.Nat using (ℕ; zero; suc)
open import Cubical.Data.Bool.Base
open import Cubical.Relation.Nu... | {
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------------------------------------------------------------------------
-- Semi-heterogeneous vector equality
------------------------------------------------------------------------
module Data.Vec.Equality where
open import Data.Vec
open import Data.Nat using (suc)
open import Data.Function
open import Relation.Bi... | {
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module test where
open import cry.gfp
open import cry.ec
{-
-- open import IO.Primitive
-- open import Foreign.Haskell
open import Agda.Builtin.List using (List; []; _∷_)
open import Agda.Builtin.Char using (Char) renaming (primCharToNat to toNat)
open import Agda.Builtin.String using (String) renaming (primStringAp... | {
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module GUIgeneric.GUIFeaturesPart2 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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open import Agda.Builtin.Equality
open import Agda.Builtin.Nat
record Eta : Set where
constructor _,_
field fst : Nat
snd : Nat
open Eta
data ⊥ : Set where
hard-fail : (a : Eta) (x : Nat) → (fst a , x) ≡ a → ⊥
hard-fail a x () -- Should be error (refl is valid)
loop : ⊥
loop = hard-fail (0 , 0) 0 ref... | {
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{-# OPTIONS --without-K --safe #-}
open import Agda.Builtin.Bool
open import Data.Maybe.Base using (just; nothing)
open import Relation.Binary.PropositionalEquality
open import Relation.Nullary
open import Data.Integer.Base
open import Data.Integer.Properties using (+-*-commutativeRing)
open import Tactic.RingSolver.... | {
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{-# OPTIONS --universe-polymorphism #-}
module Categories.Fibration where
open import Level hiding (lift)
open import Data.Product
open import Categories.Category
open import Categories.Functor hiding (_∘_; _≡_)
open import Categories.Morphism.Cartesian
import Categories.Morphisms as Morphisms
record CartesianLiftin... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Convenient syntax for "equational reasoning" using a preorder
------------------------------------------------------------------------
-- Example uses:
--
-- u∼y : u ∼ y
-- u∼y = begin
-- u ≈⟨ u≈v ⟩
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{-# OPTIONS --rewriting -v rewriting:80 #-}
open import Agda.Builtin.Equality
{-# BUILTIN REWRITE _≡_ #-}
postulate
A : Set
f : A → A
h : .A → A → A
rew : ∀ {x} → h x x ≡ x
{-# REWRITE rew #-}
test2 : (x y : A) → h x y ≡ y
test2 x y = refl
postulate
r : .A → A
s : .A → A
rewr : ∀ x → r x ≡ s x
{-# RE... | {
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module PrettyPrinter where
open import Agda.Builtin.IO using (IO)
open import Agda.Builtin.Int using (pos)
open import Agda.Builtin.Unit using (⊤)
open import FFI.IO using (getContents; putStrLn; _>>=_; _>>_)
open import FFI.Data.Aeson using (Value; eitherDecode)
open import FFI.Data.Either using (Left; Right)
open i... | {
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{-# OPTIONS --without-K #-}
module hott.core.equality where
open import hott.core.universe
-- | The equality type. In hott we think of the equality type as paths
-- between two points in the space A. To simplify the types we first
-- fix the common parameters.
module common {a : Level}{A : Type a} where
data _≡_... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.Data.Empty where
open import Cubical.Data.Empty.Base public
open import Cubical.Data.Empty.Properties public
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open import Agda.Builtin.Equality
open import Agda.Builtin.Nat
data D (A : Set) : Set → Set₁ where
c₁ : {B : Set} → D A B
c₂ : D A A
record P {A B : Set} (p : D A B) : Set₁ where
constructor c
field
d : D A B
Q : {A B₁ B₂ C : Set} {x : D A (B₁ → C)} {y : D A B₂} →
P x → P y → B₁ ≡ B₂ → Nat
Q (c c₁) ... | {
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module List.Order.Simple.Properties {A : Set}
(_≤_ : A → A → Set)
(trans≤ : {x y z : A} → x ≤ y → y ≤ z → x ≤ z) where
open import Data.List
open import List.Order.Simple _≤_
open import List.Sorted _≤_
lemma-≤-*≤ : {x y : A}{xs : List A} → xs *≤ y → y ≤ x → xs *≤ x
lemma-≤... | {
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-- Andreas, 2020-03-21, issue #4456
{-# OPTIONS --safe #-}
postulate A : Set
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{-# OPTIONS --without-K --safe #-}
open import Categories.Category
module Categories.Category.Instance.Simplex where
open import Level
open import Data.Product
open import Data.Fin
open import Data.Nat using (ℕ)
open import Function renaming (id to idF; _∘_ to _∙_)
open import Relation.Binary
open import Relation.B... | {
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postulate
admit : ∀ {i} {X : Set i} → X
X Y Z : Set
data Id (z : Z) : Z → Set where
refl : Id z z
record Square : Set₁ where
field
U : Set
u : U
open Square
record RX : Set where
field x : X
open RX
record R : Set where
-- This definition isn't used; without it,
-- the internal error disappea... | {
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open import Agda.Builtin.Nat
record Pointed (A : Set) : Set where
field point : A
it : ∀ {A : Set} {{x : A}} → A
it {{x}} = x
instance _ = record { point = 3 - 4 }
_ : Pointed Nat
_ = {!!}
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{-# OPTIONS --without-K --safe #-}
-- This is more a pair of constructions that a property...
-- but show that one can build a Cone for the Twisted Arrow functor from a Wedge
-- and vice-versa.
open import Categories.Category
open import Categories.Functor.Bifunctor
module Categories.Diagram.Wedge.Properties {o ℓ e ... | {
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{-# OPTIONS --safe --cubical #-}
module Erased-cubical.Cubical where
open import Agda.Builtin.Cubical.Path
data ∥_∥ (A : Set) : Set where
∣_∣ : A → ∥ A ∥
trivial : (x y : ∥ A ∥) → x ≡ y
data D′ : Set where
@0 c′ : D′
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-- Andreas, 2015-12-01, test case to trigger error ModuleArityMismatch EmptyTel
module _ where
module M where
module M′ = M Set
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties of vector's Any
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Vec.Relation.Unary.Any.Properties where
open import Function
o... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
open import Cubical.Core.Everything
open import Cubical.Foundations.HLevels
module Cubical.Algebra.Magma.Construct.Right {ℓ} (Aˢ : hSet ℓ) where
open import Cubical.Foundations.Prelude
open import Cubical.Algebra.Magma
private
A = ⟨ Aˢ ⟩
isSetA = Aˢ .snd
_▸_ :... | {
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module Foundation.Equivalence where
open import Foundation.Primitive
record IsEquivalence {a} {A : Set a} {ℓ} (_≈_ : A → A → Set ℓ) : ℞ a ⊔ ℓ where
field
reflexivity : ∀ x → x ≈ x
symmetry : ∀ x y → x ≈ y → y ≈ x
transitivity : ∀ x y z → x ≈ y → y ≈ z → x ≈ z
open IsEquivalence ⦃ … ⦄ public
record Eq... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Categories.Morphism where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Sigma
open import Cubical.Categories.Category
private
variable
ℓ ℓ' : Level
module _ {C : Precategory ℓ ℓ'} where
open Precategory C
private
vari... | {
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module Structure.Real where
import Lvl
open import Data.Boolean
open import Data.Boolean.Proofs
import Data.Either as Either
open import Functional
open import Logic
open import Logic.Classical
open import Logic.Propositional
open import Logic.Predicate
open import Numeral.Natural using (ℕ)
import Numer... | {
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Id₁ Id₂ Id₃ : {A B : Set} → (A → B) → A → B
Id₁ F = F
Id₂ = Id₁
Id₃ = Id₁
syntax Id₁ (λ X → B) = ƛ X ⟶ B
syntax Id₂ (λ X → B) = X ↦ B
syntax Id₃ (λ X → B) = X ↦ B •
postulate
A : Set
a : A
module One where
example₀ : (A → A) → A
example₀ = ƛ _ ⟶ a
example₁ : A → A
example₁ = ƛ !_! ⟶ (!_!)
example₂ :... | {
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{-# OPTIONS --universe-polymorphism #-}
-- Support stuff mostly stolen or adapted from the Agda standard library
module Support where
data Level : Set where
zero : Level
suc : (i : Level) → Level
{-# BUILTIN LEVEL Level #-}
{-# BUILTIN LEVELZERO zero #-}
{-# BUILTIN LEVELSUC suc #-}
-- Maximum.
infix... | {
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{-# OPTIONS --without-K --safe #-}
open import Algebra
module Data.FingerTree.Cons
{r m}
(ℳ : Monoid r m)
where
open import Data.Product
open import Data.FingerTree.Measures ℳ
open import Data.FingerTree.Structures ℳ
open import Data.FingerTree.Reasoning ℳ
open σ ⦃ ... ⦄
open Monoid ℳ renaming (Carrier to �... | {
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-- Check that we can solve level inequalities involving three variables.
module _ where
open import Agda.Primitive
open import Agda.Builtin.Equality
data Constraint : Set where
mkConstraint : (a b : Level) → a ≡ b → Constraint
infix 0 _:=_
pattern _:=_ x y = mkConstraint x y refl
postulate l : Level
mutual-blo... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Instance.Posets where
-- The category of partially ordered sets and order-preserving maps.
open import Level
open import Relation.Binary using (Poset; IsEquivalence; _Preserves_⟶_)
open import Relation.Binary.Morphism using (IsOrderHomomorphism)
open impor... | {
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{-# OPTIONS --without-K #-}
open import Type
open import Data.Zero
open import Data.Fin using (Fin; zero; suc; #_)
open import Relation.Binary.PropositionalEquality.NP using (_≡_; refl)
open import HoTT
open Equivalences
open import Explore.Core
open import Explore.Properties
open import Explore.Explorable
open import... | {
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------------------------------------------------------------------------------
-- First-order Peano arithmetic
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
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module Issue3879 where
open import Issue3879.Fin using (Fin ; zero ; suc)
open import Agda.Builtin.Nat using (Nat ; zero ; suc)
foo : Nat → Nat → Nat
foo zero m = {!!}
foo (suc n) m = {!!}
-- WAS: case-splitting on m produces Issue3879.Fin.0F patterns
-- WANT: unqualified 0F is not in scope: do not resugar!
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----------------------------------------------------------------------------
-- Well-founded induction on the natural numbers
----------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-poly... | {
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module L.Base.Coproduct.Core where
open import Agda.Primitive
-- Introducing Coproduct types
data _+_ {a b} (A : Set a) (B : Set b) : Set (a ⊔ b) where
inl : A → A + B
inr : B → A + B
case : ∀{a b c} {A : Set a} {B : Set b}
→ (C : A + B → Set c)
→ ((x : A) → C (inl x)) → ((y : B) → C (inr y))
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{-# OPTIONS --cubical-compatible --rewriting #-}
module Generalize where
open import Agda.Primitive
-- Generalization in definitions
module Definitions where
variable
ℓ : Level
A B C : Set ℓ
A₀ B₀ : Set
a b c : A
-- Function signature
id : A → A
id x = x
-- Module signature
module M... | {
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open import Relation.Binary.PropositionalEquality using
( _≡_ ; refl ; sym ; trans ; subst ; subst₂ ; cong ; cong₂ )
import AssocFree.STLambdaC.Typ
import AssocFree.STLambdaC.Exp
import AssocFree.STLambdaC.NF
module AssocFree.STLambdaC.Redn
(TConst : Set)
(Const : AssocFree.STLambdaC.Typ.Typ TConst → Set) whe... | {
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module ModuleDefinedInOtherFile where
import Imports.B
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module Issue530 where
data Unit : Set where
unit : Unit
postulate
A : Set
a : A
k : A → Unit
data P (a : A) : Unit → Set where
p : P a (k a)
F : (u : Unit) → P a u → Set₁
F unit _ = Set
f : F (k a) p
f with k a
f | _ = ? | {
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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.Product
open import Data.I... | {
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{-# OPTIONS --cubical-compatible #-}
module Issue765 where
infixr 1 _⊎_
infixr 4 _,_
infix 4 _≡_
data ⊥ : Set where
⊥-elim : {A : Set} → ⊥ → A
⊥-elim ()
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
data _⊎_ (A : Set) (B : Set) : Set where
inj₁ : (x : A) → A ⊎ B
inj₂ : (y : B) → A ⊎ B
[_,_]₁ : ∀ ... | {
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------------------------------------------------------------------------------
-- The unary numbers are FOTC total natural numbers
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-univer... | {
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open import Agda.Builtin.Bool
open import Agda.Builtin.Nat
open import Agda.Builtin.Equality
_^_ : Nat → Nat → Nat
x ^ zero = 1
x ^ suc y = x * (x ^ y)
data Enum : Set where
makeEnum : (size : Nat) → (variants : Nat) →
.{{ _ : (variants < size) ≡ true }} → Enum
five : Enum
five = makeEnum (2 ^ 32) 5
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Categories.Functor where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Sigma
open import Cubical.Categories.Category
private
variable
ℓC ℓC' ℓD ℓD' : Level
record Functor (C : Precategory ℓC ℓC') (D : Precategory ℓD ℓD') : Ty... | {
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open import Agda.Builtin.Nat
bar : Nat → Nat
bar n = let _!_ : Nat → Nat → Nat
x ! y = 2 * x ! y -- should give scope error in RHS
in n ! n
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{-# OPTIONS --safe #-}
{- Ad-hoc polymorphism -}
module AdHoc where
open import Data.Char as C
open import Data.String as S
open import Data.List as L
open import Data.Integer as I
open import Data.Nat as N
open import Data.Bool as B
open import Agda.Builtin.Nat renaming (_==_ to natEquals)
record Eq {l} (A : Set l... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.AbGroup.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Equiv.HalfAdjoint
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Univalence... | {
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module _ where
data ⊤ : Set where tt : ⊤
pattern id x = x
postulate
X : Set
loops : X
loops = tt
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Existential lifting of predicates over Vectors
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Vec.Functional.Relation.Unary.Any where
op... | {
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module cfg where
open import jarsec using (Parser ; run-parser ; partial-parse ; _>>=_ ; _>>_ ; _<*>_)
open import Data.Bool
open import Data.List hiding (lookup)
open import Data.Vec renaming ([_] to V[_] ; _++_ to _vv_) hiding (_>>=_)
open import Data.Fin hiding (_+_)
open import Data.Char
open import Agda.Builtin.... | {
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-- 2010-09-06 Andreas
module IrrelevantVar where
-- type checker should fail and complain that x is irrelevant and cannot be used
f : {A : Set} -> .A -> A -> A
f x y = x
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{-# OPTIONS --type-in-type #-}
open import Data.Unit
open import Data.Product hiding ( curry ; uncurry )
open import Data.List hiding ( concat )
open import Data.String
open import Relation.Binary.PropositionalEquality
module Spire.Examples.PropositionalLevDesc where
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