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text string | meta dict |
|---|---|
module MetaOccursInItself where
data List (A : Set) : Set where
nil : List A
_::_ : A -> List A -> List A
data One : Set where one : One
postulate
f : (A : Set) -> (A -> List A) -> One
err : One
err = f _ (\x -> x)
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{-# OPTIONS --omega-in-omega --no-termination-check --overlapping-instances #-}
module Light.Implementation.Data.Boolean where
open import Light.Library.Data.Boolean using (Library ; Dependencies)
open import Light.Variable.Sets
open import Light.Library.Data.Unit as Unit using (Unit ; unit)
open import Light.Level ... | {
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{-# OPTIONS --without-K --rewriting #-}
{-
favonia:
On 2017/05/08, I further partition the results into multiple
independent index[n].agda files because the garbage collection
is not really working.
-}
module index3 where
{- van kampen -}
import homotopy.VanKampen
{- blakers massey -}
import homotopy.Blaker... | {
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module System.Directory where
open import System.FilePath
open import Prelude
open import Container.Traversable
{-# FOREIGN GHC import System.Directory #-}
private
module Internal where
postulate
listContents : String → IO (List String)
doesFileExist : String → IO Bool
{-# COMPILE GHC listCont... | {
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open import Algebra.Bundles using (CommutativeRing)
module Algebra.Module.Diff
{r ℓr} {CR : CommutativeRing r ℓr}
where
open import Assume using (assume)
import Data.Nat as ℕ
open ℕ using (ℕ; zero; suc)
open import Relation.Binary using (Rel)
open import Algebra.Module using (Module)
open Module
open import F... | {
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-- 2014-01-15 Andreas, reported by fredrik.forsberg
data Unit : Set where
tt : Unit
foo : Unit
foo = {!!}
-- Refine here should give tt
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module Conversion where
open import Agda.Builtin.Nat
nonDependent : Nat -> Nat -> Nat
nonDependent a b = a
dependent : {A : Set} -> A -> A
dependent a = a
stuff : {A : Set} -> {B : Nat} -> Nat -> Nat
stuff zero = zero
stuff (suc c) = dependent c
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module Cats.Category.Setoids.Facts.Products where
open import Data.Product as P using (_,_ ; <_,_>)
open import Relation.Binary using (Setoid)
open import Relation.Binary.Product.Pointwise using (×-setoid)
open import Cats.Category
open import Cats.Category.Setoids as Setoids using (Setoids ; ≈-intro ; ≈-elim)
open i... | {
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data Id (A : Set) : Set where
wrap : A → Id A
data Maybe (A : Set) : Set where
nothing : Maybe A
just : A → Maybe A
maybe : {A : Set} {B : Maybe A → Set} →
((x : A) → B (just x)) → B nothing → (x : Maybe A) → B x
maybe j n (just x) = j x
maybe j n nothing = n
record MaybeT (M : Set → Set) (A : Set... | {
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module ZisRing where
open import Data.Product using (_×_; _,_)
open import Function using (_∘_)
open import Relation.Binary.PropositionalEquality
as PropEq using (_≡_; refl; cong; sym)
open import Integer10 -- 整数の定義
-- ---------- record ----------
record IsSemiGroup (A : Set) (_∙_ : A → A → A) : Set whe... | {
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{-
This file contains:
- Definition of the Bouquet of circles of a type aka wedge of A circles
-}
{-# OPTIONS --safe #-}
module Cubical.HITs.Bouquet.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Pointed
private
variable
ℓ : Level
data Bouquet (A : Type ℓ) : Type ℓ where... | {
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-- Only forced indices can be large.
data Img {a b} {A : Set a} {B : Set b} (f : A → B) : B → Set where
inv : ∀ x → Img f (f x)
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module Proof where
open import Agda.Primitive hiding (_⊔_)
open import Reflection
open import Data.Fin hiding (_+_)
open import Data.Fin.Properties using (eq? ; _≟_ )
open import Data.Nat hiding (eq? ; _⊔_)
open import Data.Nat.Properties
open import Data.List
open import Data.String hiding (setoid)
open import Data.B... | {
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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
-}
{-# OPTIONS --allow-unsolved-metas #-}
open import Optics.All
open impor... | {
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module InstanceArguments where
postulate A₁ A₂ B : Set
f₁ : {{a : A₁}} → B
f₂ : {{a : A₂}} → B
a₁ : A₁
-- resolve from signature
test₁ : B
test₁ = f₁
-- resolve from context
test₂ : {{a : A₂}} → B
test₂ = f₂
postulate F : Set → Set
fA₁ : F A₁
fA₂ : F A₂
f₃... | {
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-- Andreas, 2015-06-11
-- testing with in copattern matching with dependent record
-- {-# OPTIONS -v tc.with:20 #-}
open import Common.Prelude
open import Common.Equality
data Dec P : Set where
yes : (p : P) → Dec P
no : (¬p : P → ⊥) → Dec P
postulate
_≟_ : (n m : Nat) → Dec (n ≡ m)
boring : {A : Set} → A
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module Prelude.Monad.Indexed {i} {I : Set i} where
open import Agda.Primitive
open import Prelude.Function
open import Prelude.Functor
open import Prelude.Applicative.Indexed {I = I}
record IMonad {a b} (M : I → I → Set a → Set b) : Set (i ⊔ lsuc a ⊔ b) where
infixr 1 _=<<_
infixl 1 _>>=_ _>>_
field
_>>=_ ... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Rings.Definition
open import Rings.IntegralDomains.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
module Rings.Irreducibles.Definition {a b : _} {A : Set a} {S : Setoid {a} {b... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
module groups.ReducedWord {i} {A : Type i} (dec : has-dec-eq A) where
is-reduced : Word A → Type i
is-reduced nil = Lift ⊤
is-reduced (_ :: nil) = Lift ⊤
is-reduced (inl x :: inl y :: w) = is-reduced (inl y :: w)
is-reduc... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Base definitions for the left-biased universe-sensitive functor and
-- monad instances for the Product type.
--
-- To minimize the universe level of the RawFunctor, we require that
-- elements of B are "lifted" t... | {
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module Data.Maybe.Instance where
open import Category.FAM
open import Data.Maybe
open import Function using (_∘_; id)
open import Relation.Binary.PropositionalEquality
instance
MaybeFunctor : ∀ {ℓ} → Functor {ℓ} Maybe
MaybeFunctor {ℓ} = record
{ _<$>_ = map
; isFunctor = record
{ i... | {
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open import Coinduction using ( ♭ )
open import Data.Product using ( _,_ )
open import Relation.Binary using ( Poset )
open import Relation.Binary.PropositionalEquality using ( _≡_ ; refl ; sym ; trans ; cong ; subst₂ ) renaming ( setoid to ≡-setoid )
open import System.IO.Transducers using ( _⇒_ ; inp ; out ; done ; ⟦... | {
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{-# OPTIONS --without-K --safe #-}
module Source.Size where
open import Util.HoTT.HLevel.Core
open import Util.Prelude
infix 4 _<_
infixl 4 _∙_
mutual
data Ctx : Set where
[] : Ctx
_∙_ : (Δ : Ctx) (n : Size Δ) → Ctx
data Var : (Δ : Ctx) → Set where
zero : ∀ {Δ n} → Var (Δ ∙ n)
suc : ∀ {Δ n} ... | {
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module Prelude where
open import Agda.Primitive using (Level; lzero; lsuc) renaming (_⊔_ to lmax)
-- empty type
data ⊥ : Set where
-- from false, derive whatever
abort : ∀ {C : Set} → ⊥ → C
abort ()
-- unit
data ⊤ : Set where
<> : ⊤
-- sums
data _+_ (A B : Set) : Set where
Inl : A → A + ... | {
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{-# OPTIONS --universe-polymorphism #-}
module Categories.Monoidal.Cartesian.Pentagon where
open import Categories.Support.PropositionalEquality using (_≣_; ≣-refl)
open import Categories.Category using (Category; module Category)
open import Categories.Object.BinaryProducts
open import Categories.Square
module Law {... | {
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module Data.Vec.Membership.Propositional.Disjoint where
open import Data.Vec
open import Data.Vec.Membership.Propositional
open import Relation.Binary.PropositionalEquality as P using (_≡_; _≢_)
open import Data.Empty using (⊥; ⊥-elim)
open import Function using (flip)
Disjoint : ∀ {a} {A : Set a} {n m} → Vec A n → Ve... | {
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module Formalization.SimplyTypedLambdaCalculus where
import Lvl
open import Numeral.Natural
open import Type as _ using (TYPE)
data Type (B : TYPE) : TYPE₁ where
Base : B → Type(B)
Function : Type(B) → Type(B) → Type(B)
data Term (B : TYPE) : TYPE₁ where
Apply : Term(B) → Term(B) → Term(B)
Abstract : Ty... | {
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module _ where
open import Common.Prelude
open import Common.Equality
primitive primForce : ∀ {a b} {A : Set a} {B : A → Set b} (x : A) → (∀ x → B x) → B x
force = primForce
not-stuck : (b : Bool) → force b not ≡ not b
not-stuck true = refl
not-stuck false = refl
stuck : (b : Bool) → force b not ≡ not b
stuck b =... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
{- Useful lemmas for computing the effect of transporting a function
- across an equivalence in the domain or codomain.
- TODO move these lemmas into lib.types.Pi or lib.types.PointedPi -}
-- XXX Naming convensions?
module stash.homotopy.FunctionOver where
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-- Example by Simon Huber
{-# OPTIONS --cubical-compatible #-}
data _≡_ {A : Set} (a : A) : A → Set where
refl : a ≡ a
ap : {A B : Set} (f : A → B) {a b : A} (p : a ≡ b) → f a ≡ f b
ap f refl = refl
-- \bub
_•_ : {A : Set} {a b c : A} → a ≡ b → b ≡ c → a ≡ c
p • refl = p
infixr 30 _•_
! : {A : Set} {a b : A} → ... | {
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-- Andreas, 2016-01-22
-- special size checking j : Size< i |- j : Size< ↑ j
-- was missing from checkInternal
-- {-# OPTIONS -v tc.polarity:10 #-}
-- {-# OPTIONS -v tc.with.type:50 #-}
-- {-# OPTIONS -v tc.check.internal:30 -v tc.infer.internal:30 #-}
open import Common.Unit
open import Common.Size
postulate
axio... | {
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{-# OPTIONS --without-K --safe #-}
-- There are really all 'private' sub-pieces of
-- Categories.Category.Monoidal.Closed.IsClosed, but that is taking
-- forever to typecheck, so the idea is to split things into pieces and
-- hope that that will help.
open import Categories.Category using (Category)
open import Categ... | {
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{-# OPTIONS --without-K #-}
module H where
open import Data.Product using (_×_; _,_)
import Relation.Binary.Core as C
import Relation.Binary.PropositionalEquality as P
open P.≡-Reasoning
------------------------------------------------------------------------------
-- Some abbreviations and lemmas about paths
infix... | {
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module helloworld where
open import IO
main = run (putStrLn "Hello, World!")
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module FairStream where
open import Level as Level using (zero)
open import Size
open import Function
open import Relation.Binary
open import Relation.Binary.PropositionalEquality as P
open ≡-Reasoning
-- open import Data.List using (List; module List; []; _∷_; _++_; length)
open import Data.Nat using (ℕ; zero; suc)... | {
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{-# OPTIONS --without-K #-}
open import lib.Basics
open import lib.NType2
open import lib.PathGroupoid
open import lib.types.Bool
open import lib.types.IteratedSuspension
open import lib.types.Lift
open import lib.types.LoopSpace
open import lib.types.Nat
open import lib.types.Paths
open import lib.types.Pi
open impo... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.CommRing.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 C... | {
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postulate
S : Set
id : S
comp : S → S → S
module C where
_∘_ = comp
postulate
R : (S → S) → Set
T : R (C._∘ id) → R (id C.∘_) → Set
t : Set
t = T {!!} {!!}
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module Issue124 where
module A where
data A : Set where
c : A
module B where
data B : Set where
c : B
module C where
open A public
open B public
open C
f : B → B
f c = c | {
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module Linear where
open import Data.Product
open import Data.Sum
open import Data.Empty
-- 1. PROPOSITIONAL FRAGMENT
infixr 0 _⊸_
infixr 1 _⊕_ _⅋_
infixr 2 _&_ _⊗_
-- Linear propositions consist of a positive part (affirmation, φ₊) and a negative
-- part (refutation, φ₋). We prove a linear proposition by proving... | {
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module Data.Show where
import Prelude
import Data.Nat
import Data.Integer
import Data.String
import Data.List
open Prelude
open Data.Nat
open Data.Integer using (Int; pos; neg)
open Data.String
open Data.List hiding (_++_)
showNat : Nat -> String
showNat zero = "0"
showNat n = fromList $ reverse $ toList $ show ... | {
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{-# OPTIONS --cubical --no-import-sorts #-}
open import Agda.Primitive renaming (_⊔_ to ℓ-max; lsuc to ℓ-suc; lzero to ℓ-zero)
module Number.Postulates where
private
variable
ℓ ℓ' ℓ'' : Level
open import Cubical.Foundations.Everything renaming (_⁻¹ to _⁻¹ᵖ; assoc to ∙-assoc)
open import Cubical.Relation.Nulla... | {
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{-# OPTIONS --rewriting --confluence-check #-}
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Rewrite
postulate
A : Set
a b : A
f : A → A
rew₁ : f a ≡ b
rew₂ : f ≡ λ _ → a
{-# REWRITE rew₁ #-}
{-# REWRITE rew₂ #-}
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{-# OPTIONS --no-termination-check #-}
module qsort where
_o_ : {a : Set} -> {b : Set} -> {c : Set} -> (b -> c) -> (a -> b) -> a -> c
f o g = \x -> f (g x)
data Bool : Set where
true : Bool
false : Bool
not : Bool -> Bool
not true = false
not false = true
if_then_else_ : {a : Set} -> Bool -... | {
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{-# OPTIONS --safe --experimental-lossy-unification #-}
module Cubical.Algebra.Polynomials.Multivariate.EquivCarac.A[X]X-A where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Data.N... | {
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module builtinInModule where
module Str where
{-# BUILTIN STRING S #-}
primitive primStringAppend : S → S → S
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{-# OPTIONS --without-K #-}
{- In this module, we derive the truncations of
* a truncated type,
* the unit type,
* dependent sums (and product types),
* path spaces
given truncations of their components.
More commonly later on, we will be given a truncation operator Tr
that returns a truncation for any ... | {
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-- Categories with objects parameterised by a sort
module SOAS.Sorting {T : Set} where
open import SOAS.Common
import Categories.Category.CartesianClosed.Canonical as Canonical
import Categories.Category.CartesianClosed as CCC
open import Categories.Category.Cocartesian
open import Categories.Category.BicartesianClo... | {
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------------------------------------------------------------------------------
-- Conversion rules for the division
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism... | {
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-- Imports from the standard library
module Library where
-- open import Level using () renaming (suc to lsuc) public
open import Data.Fin using (Fin; zero; suc) public
open import Data.List using (List; []; _∷_; map) public
open import Data.Nat
using (ℕ; zero; suc; z≤n; s≤s; pred; _≤′_; ≤′-refl; ≤′-step )
re... | {
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{-# OPTIONS --without-K #-}
module F0 where
import Level as L
open import Data.Unit
open import Data.Sum
open import Data.Product
open import Function using (id ; _$_ )
infixr 90 _⊗_
infixr 80 _⊕_
infixr 60 _∘_
infix 30 _⟷_
---------------------------------------------------------------------------
-- Our own vers... | {
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open import Agda.Primitive
record Order {ℓ} ℓ' (A : Set ℓ) : Set (ℓ ⊔ lsuc ℓ') where
field
_≤_ : A → A → Set ℓ'
open Order {{...}} public
data ℕ : Set where
Zero : ℕ
Succ : ℕ → ℕ
data _≤ⁿ_ : ℕ → ℕ → Set where
Zero : ∀ {n} → Zero ≤ⁿ n
Succ : ∀ {n₁ n₂} → n₁ ≤ⁿ n₂ → Succ n₁ ≤ⁿ Succ n₂
instance
Order[ℕ... | {
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{-# OPTIONS --without-K --safe #-}
-- Monoidal natural isomorphisms between lax and strong symmetric
-- monoidal functors.
--
-- NOTE. Symmetric monoidal natural isomorphisms are really just
-- monoidal natural isomorphisms that happen to go between symmetric
-- monoidal functors. No additional conditions are necessa... | {
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{-# OPTIONS --without-K #-}
open import HoTT
module homotopy.S1SuspensionS0 where
{- To -}
module To = S¹Rec (north Bool) (merid _ true ∙ ! (merid _ false))
to : S¹ → Suspension Bool
to = To.f
{- From -}
from-merid : Bool → base == base
from-merid true = loop
from-merid false = idp
module From = SuspensionRec B... | {
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module Prelude.Bytes where
open import Prelude.Bool
open import Prelude.Decidable
open import Prelude.Equality
open import Prelude.Equality.Unsafe
{-# FOREIGN GHC import qualified Data.ByteString as B #-}
postulate
Bytes : Set
{-# COMPILE GHC Bytes = type B.ByteString #-}
private
module Internal where
post... | {
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open import Prelude
open import Relation.Binary.PropositionalEquality
open import RW.Language.RTerm using (Name)
open import RW.Strategy.PropEq
open import RW.RW (≡-strat ∷ [])
open import Data.Nat.Properties.Simple
using (+-comm; +-right-identity; +-assoc)
module PropEqTest where
++-assoc : ∀{a}{A : Set a}(... | {
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module split where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; sym; trans; cong)
open Eq.≡-Reasoning
open import Data.Nat using (ℕ; zero; suc; _+_; _*_; _∸_; _≤_; s≤s; z≤n; _≤?_)
open import Relation.Nullary using (¬_; Dec; yes; no)
open import Data.Product using (_×_; ∃; ∃-syntax) ren... | {
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------------------------------------------------------------------------
-- A proof of univalence for an arbitrary "equality with J"
------------------------------------------------------------------------
{-# OPTIONS --cubical --safe #-}
import Equality.Path as P
module Equality.Path.Isomorphisms.Univalence
{e⁺} ... | {
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{-
Types Summer School 2007
Bertinoro
Aug 19 - 31, 2007
Agda
Ulf Norell
-}
-- Let's have a closer look at the module system
module Modules where
{-
Importing and opening modules
-}
-- You can import a module defined in a different ... | {
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-- The point of this test is to check that we don't create needlessly
-- large anonymous modules when we open a module application.
{-# OPTIONS -vscope.mod.inst:10 -vtc.section.apply:20 #-}
module Optimised-open where
postulate A : Set
module M₁ (A : Set) where
postulate
P : A → Set
X : Set
-- There is n... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Category.Instance.Quivers where
-- The Category of Quivers
open import Level using (Level; suc; _⊔_)
open import Relation.Binary.PropositionalEquality.Core using (refl)
open import Data.Quiver using (Quiver)
open import Data.Quiver.Morphism using (Morphism; id; _∘... | {
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-- Andreas, 2018-10-16, runtime erasure
id : (@0 A : Set) (@0 x : A) → A
id A x = x
-- Expected error:
--
-- Variable x is declared erased, so it cannot be used here
-- when checking that the expression x has type A
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module Numeral.Natural.Induction{ℓ} where
open import Logic
open import Logic.Propositional
open import Functional
open import Numeral.Natural
-- The induction proof method on natural numbers
-- TODO: There seems to be a problem making i implicit with unsolved metas.
-- TODO: Maybe rename to elim because this is the ... | {
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module Common.PredicateBasedContext where
open import Common.Predicate public
-- Predicate-based context membership.
module _ {U : Set} where
infix 3 _∈_
_∈_ : U → Pred (Cx U)
A ∈ Γ = Any (_≡ A) Γ
infix 3 _∉_
_∉_ : U → Pred (Cx U)
A ∉ Γ = Not (A ∈ Γ)
lookup : ∀ {Γ P} → All P Γ → (∀ {A} → A ∈ Γ → P A... | {
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open import ExtractSac as ES using ()
open import Extract (ES.kompile-fun)
open import Data.Nat as N using (ℕ; zero; suc; _≤_; _≥_; _<_; s≤s; z≤n)
import Data.Nat.DivMod as N
open import Data.Nat.Properties as N
open import Data.List as L using (List; []; _∷_)
open import Data.Vec as V using (Vec; []; _∷_)
import... | {
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module Structure.Relator.Ordering.Proofs where
import Lvl
open import Functional
open import Lang.Instance
open import Logic
open import Structure.Relator.Ordering
open import Structure.Relator.Properties
open import Syntax.Transitivity
open import Type
private variable ℓ : Lvl.Level
private variable A B : Type{... | {
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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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------------------------------------------------------------------------
-- INCREMENTAL λ-CALCULUS
--
-- Dependently typed changes with the Nehemiah plugin.
------------------------------------------------------------------------
module Nehemiah.Change.Validity where
open import Nehemiah.Syntax.Type
open import Nehem... | {
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open import Oscar.Prelude
open import Oscar.Data.𝟘
module Oscar.Data.Proposequality where
module _ where
data Proposequality {𝔬} {𝔒 : Ø 𝔬} (𝓞 : 𝔒) : 𝔒 → Ø₀ where
instance ∅ : Proposequality 𝓞 𝓞
{-# BUILTIN EQUALITY Proposequality #-}
Proposequality⟦_⟧ : ∀ {𝔬} (𝔒 : Ø 𝔬) → 𝔒 → 𝔒 → Ø₀
Propo... | {
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-- Andreas, 2016-02-09, should not record sections have all hidden parameters?
module _ (A : Set) where
record R : Set where
postulate
P : (a : A) → Set
-- Records have some magic to make record parameters hidden
-- in record section.
-- This leads to an error in @checkInternal@.
-- Should the pa... | {
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-- Category of sets and functions
module Control.Category.SetsAndFunctions where
open import Level using (zero; suc; _⊔_)
open import Relation.Binary.PropositionalEquality
open import Relation.Binary
open import Data.Product
open import Axiom.FunctionExtensionality
open import Control.Category
open import Control.C... | {
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------------------------------------------------------------------------
-- A lemma
------------------------------------------------------------------------
open import Mixfix.Expr
open import Mixfix.Acyclic.PrecedenceGraph using (acyclic)
module Mixfix.Acyclic.Lemma
(g : PrecedenceGraphInterface.PrecedenceG... | {
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{-# OPTIONS --copatterns --sized-types #-}
open import Function
open import Data.Unit as Unit renaming (tt to ∗)
open import Data.List as List
TyCtx = List ⊤
data TyVar : (Γ : TyCtx) → Set where
zero : ∀{Γ} → TyVar (∗ ∷ Γ)
succ : ∀{Γ} → (x : TyVar Γ) → TyVar (∗ ∷ Γ)
data Type (Γ : TyCtx... | {
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module Fold where
open import Prelude
myfold : {ac b : Set} -> (ac -> b -> ac) -> ac -> List b -> ac
#ifdef strict
myfold = foldl!
#else
myfold = foldl
#endif
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------------------------------------------------------------------------
-- The double-negation monad
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Equality
module Double-negation
{reflexive} (eq : ∀ {a p} → Equality-with-J a p reflexive) wh... | {
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-- {-# OPTIONS -v tc.lhs.unify:100 #-}
module Issue811 where
module ParamIndex where
-- Report by stevan:
-- When case-splitting, I think dots end up at the wrong places,
-- consider:
data _≡_ {A : Set}(x : A) : A → Set where
refl : x ≡ x
-- If you case-split on p in:
dot : ∀ {A}(x : A)(y : A) → x ≡ ... | {
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module plfa-code.Lists where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; sym; trans; cong)
open Eq.≡-Reasoning
open import Data.Bool using (Bool; true; false; T; _∧_; _∨_; not)
open import Data.Nat using (ℕ; zero; suc; _+_; _*_; _∸_; _≤_; s≤s; z≤n)
open import Data.Nat.Properties using... | {
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------------------------------------------------------------------------
-- Code related to the paper "Higher Lenses"
--
-- Nils Anders Danielsson
--
-- The paper is coauthored with Paolo Capriotti and Andrea Vezzosi.
------------------------------------------------------------------------
-- Most of the code referenc... | {
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module Formalization.Polynomial where
import Lvl
open import Data.ListSized
open import Numeral.Natural as ℕ using (ℕ)
open import Type
private variable ℓ ℓₑ : Lvl.Level
private variable T : Type{ℓ}
private variable n n₁ n₂ : ℕ
-- TODO: Some of the operations should work with arbitrary Rg structures, not just ℕ... | {
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module Text.Greek.SBLGNT.Titus where
open import Data.List
open import Text.Greek.Bible
open import Text.Greek.Script
open import Text.Greek.Script.Unicode
ΠΡΟΣ-ΤΙΤΟΝ : List (Word)
ΠΡΟΣ-ΤΙΤΟΝ =
word (Π ∷ α ∷ ῦ ∷ ∙λ ∷ ο ∷ ς ∷ []) "Titus.1.1"
∷ word (δ ∷ ο ∷ ῦ ∷ ∙λ ∷ ο ∷ ς ∷ []) "Titus.1.1"
∷ word (θ ∷ ε ∷ ο ∷ ... | {
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------------------------------------------------------------------------------
-- From ListN as the least fixed-point to ListN using data
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no... | {
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{-# OPTIONS --allow-unsolved-metas #-}
module TermNode where
open import OscarPrelude
open import TermCode
record TermNode : Set
where
inductive
field
children : List (TermCode × TermNode)
number : Nat
open TermNode public
open import Membership
_child∈_ : TermCode → TermNode → Set
_child∈_ 𝔠 𝔫 = 𝔠... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Data.Unit where
open import Cubical.Data.Unit.Base public
open import Cubical.Data.Unit.Properties public
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-- Laws for weakenings and substitutions.
{-# OPTIONS --without-K --safe #-}
module Definition.Untyped.Properties where
open import Definition.Untyped
open import Tools.Fin
open import Tools.Nat
open import Tools.List
open import Tools.PropositionalEquality hiding (subst)
private
variable
ℓ m n : Nat
ρ ρ... | {
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{-# OPTIONS --without-K --safe #-}
open import Algebra
open import Relation.Unary
open import Relation.Binary hiding (Decidable)
module Data.FingerTree.Split.Point
{r m}
(ℳ : Monoid r m)
{s}
{ℙ : Pred (Monoid.Carrier ℳ) s}
(ℙ-resp : ℙ Respects (Monoid._≈_ ℳ))
(ℙ? : Decidable ℙ)
where
open import Relati... | {
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module Category.Profunctor where
open import Agda.Primitive using (Level; _⊔_; lsuc)
open import Data.Product using (_,_; _×_)
open import Function using (id)
open import Relation.Binary.PropositionalEquality using (_≡_)
Dimap : ∀ {a b} (p : Set a → Set a → Set b) → Set (lsuc a ⊔ b)
Lmap : ∀ {a b} (p : Set a → Set a →... | {
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module Cats.Category.Op where
open import Relation.Binary using (Rel ; _Preserves₂_⟶_⟶_)
open import Relation.Binary.PropositionalEquality as ≡
open import Level
open import Cats.Category
open import Cats.Category.Cat using (Cat)
module _ {lo la l≈} (C : Category lo la l≈) where
infixr 9 _∘_
infixr 4 _≈_
p... | {
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module AgdalightTelescopeSyntax where
postulate
A : Set
B : A -> Set
g : (x y : A; z : B x) -> A
-- this is Agdalight syntax, should not parse | {
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{-# OPTIONS --safe #-}
module Cubical.Data.Graph.Examples where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.Isomorphism
open import Cubical.Data.Empty
open import Cubical.Data.Unit renaming (Unit to ⊤)
open import Cubical.Data.Nat
open import Cubica... | {
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{-# OPTIONS --safe --warning=error --without-K --guardedness #-}
open import Setoids.Setoids
open import Rings.Definition
open import Rings.Lemmas
open import Rings.Orders.Partial.Definition
open import Rings.Orders.Total.Definition
open import Groups.Definition
open import Groups.Lemmas
open import Fields.Fields
open... | {
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open import Common.IO
open import Common.Unit
open import Common.String
-- Currently, it is not actually a test.
-- I need a wat to check that Erasure does not happen when it normally would.
{-# FOREIGN OCaml
type i =
| Bar of string;;
#-}
data I : Set where
bar : String → I
{-# COMPILE OCaml I No-Erasure ... | {
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------------------------------------------------------------------------------
-- The LTC-PCF Booleans type
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-#... | {
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-- An ATP conjecture cannot have duplicate local hints.
-- This error is detected by Syntax.Translation.ConcreteToAbstract.
module ATPBadLocalHint2 where
postulate
D : Set
foo : D
bar : D
{-# ATP prove foo bar bar #-}
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module tuple where
data ℕ : Set where
Z : ℕ
S : ℕ -> ℕ
_+_ : ℕ -> ℕ -> ℕ
n + Z = n
n + S m = S (n + m)
infixr 30 _+_
data Nil : Set where
[] : Nil
infix 20 _::_
data Cons (A B : Set) : Set where
_::_ : A -> B -> Cons A B
Tuple : Set -> ℕ -> Set
Tuple A Z = Nil
Tuple A (S n) = Cons A (Tuple... | {
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-- Andreas, 2012-09-15
module InstanceArgumentsDontDiscardCandidateUponUnsolvedConstraints where
import Common.Level
data ⊥ : Set where
record ⊤ : Set where
data Nat : Set where
zero : Nat
suc : Nat → Nat
_≤_ : Nat → Nat → Set
zero ≤ m = ⊤
(suc n) ≤ zero = ⊥
(suc n) ≤ (suc m) = n ≤ m
data Vec (A :... | {
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module SN.AntiRename where
open import Relation.Unary using (_∈_; _⊆_)
open import Library
open import Terms
open import Substitution
open import SN
mutual
-- To formulate this, we need heterogeneous SNholes, going from Γ to Δ
-- unRenameSNh : ∀{a b Γ Δ} (ρ : Δ ≤ Γ) {t : Tm Γ b} {E : ECxt Γ a b} {t' : Tm Γ a}... | {
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-- Andreas, 2016-12-29, issue #2363
data Nat : Set where
zero : Nat
suc : Nat → Nat
test : Nat → Nat
test (suc n) with zero
test zero | q = zero
test zero = zero
-- Error WAS:
-- With clause pattern zero is not an instance of its parent pattern (suc "n")
-- Expected error:
-- With clause pattern zero is not an ... | {
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module Oscar.Class.AlphaConversion where
open import Oscar.Data.Nat
open import Oscar.Data.Fin
open import Oscar.Data.Equality
open import Oscar.Function
open import Oscar.Relation
open import Oscar.Level
record AlphaConversion {a} {A : Set a} {b} (B : A → Set b) {c} (C : A → Set c) : Set (a ⊔ b ⊔ c) where
infixr ... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.Data.Sigma.Base where
open import Cubical.Core.Primitives public
-- Σ-types are defined in Core/Primitives as they are needed for Glue types.
_×_ : ∀ {ℓ ℓ'} (A : Type ℓ) (B : Type ℓ') → Type (ℓ-max ℓ ℓ')
A × B = Σ A (λ _ → B)
infixr 5 _×_
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module StrictApplication where
open import Data.Nat
{-# NON_TERMINATING #-}
loop : ℕ
loop = loop
foo : ℕ
foo = (λ _ → 0) loop
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