text string | meta dict |
|---|---|
module Sets.IterativeSet.Relator where
import Lvl
open import Logic.Propositional
open import Logic.Predicate
open import Numeral.Natural
open import Sets.IterativeSet
open import Syntax.Function
open import Type
module _ where
private variable {ℓ ℓ₁ ℓ₂} : Lvl.Level
private variable {A B} : Iset{ℓ}
open Is... | {
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module SizedIO.Object where
open import Data.Product
record Interface : Set₁ where
field
Method : Set
Result : (m : Method) → Set
open Interface public
-- A simple object just returns for a method the response
-- and the object itself
record Object (i : Interface) : Set where
coinductive
field
ob... | {
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A : Set
B : Set₁
B = Set
C : Set
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-- Andreas, AIM XXIII, 2016-04-26 flight EDI-GOT home
-- {-# OPTIONS -v impossible:10 #-}
-- Parameter arguments of overloaded projection applications
-- should not be skipped!
record R A : Set where
field f : A
open R
record S A : Set where
field f : A
open S
module _ (A B : Set) (a : A) where
r : R A
f ... | {
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-- Andreas, 2011-10-03
{-# OPTIONS --experimental-irrelevance #-}
module MatchOnIrrelevantData1 where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
-- the index does not determine the constructor
data Fin : Nat -> Set where
zero : (n : Nat) -> Fin (suc n)
suc : (n : Nat) -> Fin n -> Fin (suc n)
-- shou... | {
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module Ints.Add.Comm where
open import Ints
open import Nats.Add.Comm
open import Equality
------------------------------------------------------------------------
-- internal stuffs
private
a+b=b+a : ∀ a b → a + b ≡ b + a
a+b=b+a (+ a) (+ b) = + (a :+: b)
≡⟨ cong +_ (nat-add-comm a b) ⟩ + (b :+: a) QED
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-- 2010-09-07 Andreas
-- 2011-10-04 may not work even in the presence of experimental irr.
{-# OPTIONS --experimental-irrelevance #-}
module SplitOnIrrelevant where
data Bool : Set where
true false : Bool
not : .Bool -> Bool
not true = false -- needs to fail
not false = true
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{-# OPTIONS --cubical --safe #-}
module Cubical.Algebra.BasicProp where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.HLevels
open import Cubical.Data.Sigma
open import Cubical.Structures.Group
private
variable
ℓ ℓ' : Level
--------------------... | {
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{-# OPTIONS --without-K #-}
module overloading where
-- An overloading system based on instance arguments. See `overloading.core` for
-- more details and documentation.
open import overloading.bundle public
open import overloading.core public
open import overloading.level public
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-- Raw terms, weakening (renaming) and substitution.
{-# OPTIONS --without-K --safe #-}
module Definition.Untyped where
open import Tools.Fin
open import Tools.Nat
open import Tools.Product
open import Tools.List
import Tools.PropositionalEquality as PE
infixl 30 _∙_
infix 30 Π_▹_
infixr 22 _▹▹_
infix 30 Σ_▹_
infi... | {
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module A.Issue1635 (A : Set₁) where
data Foo : Set where
foo : Foo
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module _ where
import Agda.Builtin.Equality
open import Agda.Builtin.Sigma
open import Agda.Builtin.Unit
open import Agda.Primitive
open import Common.IO
data ⊥ : Set where
record R₁ a : Set (lsuc a) where
field
R : {A : Set a} → A → A → Set a
r : {A : Set a} (x : A) → R x x
P : Set a → Set a
P A = (x... | {
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module kripke-semantics where
open import level
open import bool
open import closures
open import empty
open import eq
open import level
open import list
open import list-thms
open import nat
open import product
open import relations
open import string
open import sum
open import unit
data formula : Set where
$ : s... | {
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{-# OPTIONS --without-K #-}
open import HoTT hiding (_::_)
module algebra.DecidableFreeGroupIsReducedWord {i} (A : Type i) (dec : has-dec-eq A) where
open import algebra.Word A
open import algebra.ReducedWord A dec
-- Some helper functions.
tail-is-reduced : (x : A) (w : Word) → is-reduced (x :: w) → is-re... | {
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module GotoDefinition where
data ℕ : Set where
Z : ℕ
S : ℕ → ℕ
_+_ : ℕ → ℕ → ℕ
x + y = {! !} | {
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{-# OPTIONS --no-unicode #-}
module Issue2937.NoUnicode where
foo : _ -> _ -> Set
foo bar x = \x -> foo (bar x {!!}) x
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-- Possible improvements:
-- * Parts of the code are not reachable from main.
-- * The following primitives are not used at all: primPOr, primComp,
-- primHComp, prim^glueU and prim^unglueU.
{-# OPTIONS --erased-cubical --save-metas #-}
-- The code from Agda.Builtin.Cubical.Glue should not be compiled.
open import... | {
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{-# OPTIONS --prop --rewriting #-}
module Examples.Gcd.Euclid where
open import Calf.CostMonoid
import Calf.CostMonoids as CM
{- This file defines the parameters of the analysis of Euclid's algorithm for gcd
and its cost recurrence relation. -}
open import Calf CM.ℕ-CostMonoid
open import Calf.Types.Nat
open impo... | {
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data Bin : Set where
⟨⟩ : Bin
_O : Bin → Bin
_I : Bin → Bin
inc : Bin → Bin
inc n = ?
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module Generic where
import Category.Functor
import Category.Monad
open import Data.List using (List ; length ; replicate) renaming ([] to []L ; _∷_ to _∷L_)
open import Data.Maybe using (Maybe ; just ; nothing) renaming (setoid to MaybeEq)
open import Data.Nat using (ℕ ; zero ; suc)
open import Data.Product using (_×... | {
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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 --no-import-sorts --safe #-}
module Cubical.Algebra.Group.Higher where
open import Cubical.Core.Everything
open import Cubical.Data.Nat
open import Cubical.Data.Sigma
open import Cubical.Data.Unit
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Prelude hiding (comp)
open... | {
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module Type.Properties.MereProposition {ℓ ℓₑ} where
import Lvl
open import Lang.Instance
open import Structure.Setoid
open import Type
-- A type is a mere proposition type when there is at most one inhabitant (there is at most one object with this type).
-- In other words: If there is an inhabitant of type T, it... | {
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{-# OPTIONS --sized-types #-}
open import Relation.Binary.Core
module SelectSort.Correctness.Permutation {A : Set}
(_≤_ : A → A → Set)
(tot≤ : Total _≤_ ) where
open import Data.List
open import Data.Product
open import Data.Sum
open import List.Permutation.Base A
open import List.... | {
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import Structure.Logic.Classical.NaturalDeduction
-- TODO: Seems like Constructive does not work, but why?
module Structure.Logic.Constructive.Syntax.Algebra {ℓₗ} {Formula} {ℓₘₗ} {Proof} {ℓₒ} {Domain} ⦃ classicalLogic : _ ⦄ where
open Structure.Logic.Classical.NaturalDeduction.ClassicalLogic {ℓₗ} {Formula} {ℓₘₗ} ... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Functor.Hom where
-- The Hom Functor from C.op × C to Setoids,
-- the two 1-argument version fixing one object
-- and some notation for the version where the category must be made explicit
open import Data.Product
open import Function using () renaming (_∘_ to _∙_)... | {
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{-# OPTIONS --without-K --safe #-}
module Quasigroup where
open import Quasigroup.Bundles public
open import Quasigroup.Definitions public
open import Quasigroup.Structures public
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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 LibraBFT.Base.Types
import LibraBFT.Impl.Consensus.Consensus... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
{-
This file defines
deltaIntSec : ∀ b → toInt (fromInt b) ≡ b
succPred : ∀ n → succ (pred n) ≡ n
predSucc : ∀ n → pred (succ n) ≡ n
and proved DeltaInt ≡ DeltaInt by the above functions
succPredEq : DeltaInt ≡ DeltaInt
along with some interval-relevant lemmas
c... | {
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-- Andreas, 2017-03-08
-- Impredicative data types are incompatible with structural recursion
-- (Coquand, Pattern Matching with Dependent Types, 1992)
{-# OPTIONS --type-in-type #-}
data ⊥ : Set where
-- An impredicative data type
data D : Set where
c : (f : (A : Set) → A → A) → D
-- Structural recursion with ... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020 Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
{-# OPTIONS --allow-unsolved-metas #-}
open import Optics.All
open import Libra... | {
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{-
The module CanThetaContinuation contains the continuation-passing
variant of Canθ, which is used as a tool to simplify Canθ-Can
expressions.
The lemmas are mainly about the function Canθ' defined by the equation
unfold : ∀ sigs S'' p θ →
Canθ sigs S'' p θ ≡ Canθ' sigs S'' (Can p) θ
The main property... | {
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module Structure.Relator.Apartness where
import Lvl
open import Logic
open import Logic.Propositional
open import Structure.Relator.Properties
hiding (irreflexivity ; symmetry ; cotransitivity)
open import Type
private variable ℓ₁ ℓ₂ : Lvl.Level
-- An apartness relation is a irreflexive, symmetric and cotrans... | {
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module Issue852 where
open import Common.Level
const : ∀ {a b} {A : Set a} {B : Set b} → A → B → A
const x = λ _ → x
ℓ : Level
ℓ = const lzero (Set ℓ)
ℓ′ : Level
ℓ′ = const lzero (Set ℓ′)
-- Error message using Agda 2.3.2 (the batch-mode command, not the
-- Emacs interface):
--
-- Termination checking failed for... | {
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open import IO using ( run ; putStrLn )
open import Data.String using ( _++_ )
open import Data.Natural using ( # ; _+_ ; toString )
module Data.Bindings.Examples.HelloFour where
main = run (putStrLn ("Hello, " ++ toString (#(2) + #(2)) ++ ".")) | {
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-- Import all the material (useful to check that everything typechecks)
{-# OPTIONS --cubical #-}
module Everything where
import Warmup
import Part1
import Part2
import Part3
import Part4
import ExerciseSession1
import ExerciseSession2
import ExerciseSession3
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import cw.CW
module cw.examples.Unit where
cw-unit-skel : Skeleton {lzero} 0
cw-unit-skel = Unit , Unit-is-set
CWUnit = ⟦ cw-unit-skel ⟧
CWUnit-equiv-Unit : CWUnit ≃ Unit
CWUnit-equiv-Unit = ide _
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.DStructures.Structures.ReflGraph where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Structure
open impo... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Floating point numbers
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Float where
------------------------------------------------------... | {
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{-# OPTIONS --without-K --exact-split #-}
module 1-type-theory where
import 00-preamble
open 00-preamble public
-- Exercise 1.1 (From ../02-pi.agda)
_∘-1-1_ :
{i j k : Level} {A : UU i} {B : UU j} {C : UU k} →
(B → C) → ((A → B) → (A → C))
(g ∘-1-1 f) a = g (f a)
import 04-inductive-types
open 04-inductive-type... | {
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{-# OPTIONS --universe-polymorphism #-}
module Categories.Lan where
open import Level
open import Categories.Category
open import Categories.Functor hiding (_≡_)
open import Categories.NaturalTransformation
record Lan {o₀ ℓ₀ e₀} {o₁ ℓ₁ e₁} {o₂ ℓ₂ e₂}
{A : Category o₀ ℓ₀ e₀} {B : Category o₁ ℓ₁ e₁} {C : Ca... | {
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open import FRP.JS.Bool using ( Bool ; not )
open import FRP.JS.Event using ( Evt ; accumBy )
open import FRP.JS.RSet using ( RSet ; _⇒_ ; ⟦_⟧ ; ⟨_⟩ )
module FRP.JS.Behaviour where
postulate
Beh : RSet → RSet
map : ∀ {A B} → ⟦ A ⇒ B ⟧ → ⟦ Beh A ⇒ Beh B ⟧
map2 : ∀ {A B C} → ⟦ A ⇒ B ⇒ C ⟧ → ⟦ Beh A ⇒ Beh B ⇒ Beh ... | {
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module Records where
open import Common.Nat
open import Common.IO
open import Common.Unit
record Test : Set where
constructor mkTest
field
a b c : Nat
f : Test -> Nat
f (mkTest a b c) = a + b + c
open Test
g : Nat
g = (f (mkTest 34 12 54)) + (f (record {a = 100; b = 120; c = 140})) + a m + b m + c m
wher... | {
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------------------------------------------------------------------------
-- A depth-first backend
------------------------------------------------------------------------
-- Based on the parser combinators in Wadler's "How to Replace Failure
-- by a List of Successes".
module StructurallyRecursiveDescentParsing.Depth... | {
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------------------------------------------------------------------------------
-- Arithmetic properties using instances of the induction principle
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPT... | {
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postulate
A : Set
data B (a : A) : Set where
conB : B a → B a → B a
data C (a : A) : B a → Set where
conC : {bl br : B a} → C a bl → C a br → C a (conB bl br)
-- Second bug, likely same as first bug.
{-
An internal error has occurred. Please report this as a bug.
Location of the error: src/full/Agda/TypeChecki... | {
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------------------------------------------------------------------------
-- CCS
------------------------------------------------------------------------
{-# OPTIONS --sized-types #-}
open import Prelude
module Labelled-transition-system.CCS {ℓ} (Name : Type ℓ) where
open import Equality.Propositional
open import Pr... | {
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True : Prop
True = {P : Prop} → P → P
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{-# OPTIONS --keep-pattern-variables #-}
open import Agda.Builtin.Nat
open import Agda.Builtin.Equality
test₁ : (m : Nat) → m ≡ 0 → Set
test₁ m eq = {!eq!}
test₂ : (A B : Set) → A ≡ B → Set
test₂ A B eq = {!eq!}
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module Logic where
data Bool : Set where
true : Bool
false : Bool
_∧_ : Bool → Bool → Bool
false ∧ _ = false
true ∧ b = b
_∨_ : Bool → Bool → Bool
true ∨ _ = true
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{-# OPTIONS --allow-unsolved-metas #-}
{-# OPTIONS --rewriting #-}
module CBVNTranslations where
open import Library
open import Polarized
-- Intuitionistic propositional logic
data IPL : Set where
Atom : (P : Atoms) → IPL
True False : IPL
_∨_ _∧_ _⇒_ : (A B : IPL) → IPL
module CallByName where
_⁻... | {
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module UniDB.Morph.SubsPrime where
open import UniDB.Spec
open import Function
open import Data.Product
--------------------------------------------------------------------------------
mutual
data Subs* (T : STX) : MOR where
refl : {γ : Dom} → Subs* T γ γ
incl : {γ₁ γ₂ : Dom} (ξ : Subs+ T γ₁ γ₂) → Subs* T... | {
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------------------------------------------------------------------------
-- Brzozowski-style derivatives of parsers
------------------------------------------------------------------------
module TotalParserCombinators.Derivative.Definition where
open import Category.Monad
open import Codata.Musical.Notation
open imp... | {
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{-# OPTIONS --universe-polymorphism #-}
module Categories.Cone where
open import Level
open import Relation.Binary using (IsEquivalence; Setoid; module Setoid)
open import Categories.Support.PropositionalEquality
open import Categories.Category
open import Categories.Functor hiding (_≡_; _∘_)
module ConeOver {o ℓ e... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.types.Empty
open import lib.types.Group
open import lib.types.Word
open import lib.groups.GeneratedGroup
open import lib.groups.Homomorphism
module lib.groups.FreeGroup where
module FreeGroup {i} (A : Type i) where
private
module G... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.NConnected
open import lib.NType2
open import lib.types.Span
open import lib.types.Pointed
open import lib.types.Pushout
open import lib.types.PushoutFlip
open import lib.types.PushoutFmap
open import lib.types.PushoutFlattening
open import... | {
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-- {-# OPTIONS -v tc.meta:25 #-}
module Issue418 where
data _≡_ (A : Set₁) : Set₁ → Set₂ where
refl : A ≡ A
abstract
A : Set₁
A = Set
unfold-A : A ≡ _
unfold-A = refl
-- I don't think we should solve the meta-variable corresponding to
-- the underscore above. We have two obvious choices, A and Set, and
-... | {
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module _ where
id : (A B : Set₁) → (A → B) → A → B
id _ _ f = f
postulate
P : (A : Set₁) → A → Set₁
cong : (A B : Set₁) (f : A → B) (x : A) → P A x → P B (f x)
A : Set
record R₀ (B : Set) : Set₁ where
constructor mkR₀
no-eta-equality
field
proj₁ : Set
proj₂ : B
record R₁ (_ : Set) : Set₁ ... | {
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-- Jesper, 2018-12-04, Issue #3431 reported by François Thiré on the
-- Agda mailing list
-- (https://lists.chalmers.se/pipermail/agda/2018/010686.html)
-- The instance of the Reduce typeclass for pairs did not have an
-- implementation for reduceB' (only reduce'), which made it default
-- to the standard implementati... | {
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open import Agda.Builtin.Equality
open import Agda.Builtin.List
open import Agda.Builtin.Reflection renaming (bindTC to _>>=_)
open import Agda.Builtin.Unit
macro
pickWhatever : Term → TC ⊤
pickWhatever hole@(meta m _) = do
(cand ∷ _) ← getInstances m
where [] -> typeError (strErr "No candidates!" ∷ [])... | {
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module Definitions where
data ℕ : Set where
zero : ℕ
suc : (n : ℕ) → ℕ
data _≡_ (x : ℕ) : ℕ → Set where
refl : x ≡ x
data _≢_ : ℕ → ℕ → Set where
z≢s : ∀ {n} → zero ≢ suc n
s≢z : ∀ {n} → suc n ≢ zero
s≢s : ∀ {m n} → m ≢ n → suc m ≢ suc n
data Equal? (m n : ℕ) : Set where
yes : m ≡ n → Equal? m n
no... | {
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module STLC where
open import Data.Nat
open import Data.Empty
open import Relation.Binary.PropositionalEquality
-- infix 4 _⊢_
-- infix 4 _∋_∶_
-- infixl 5 _,_
infixr 7 _⟶_
infix 5 ƛ_
infixl 7 _∙_
-- infix 9 `_
infixl 10 _∶_
-- infix 5 μ_
-- infix 8 `suc_
-- infix 9 S_
-- infix 9 #_
data Type : Set whe... | {
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{-# OPTIONS --safe --experimental-lossy-unification #-}
module Cubical.Categories.Instances.CommAlgebras where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.Powerset
open import Cubical.Foundations.HLevels
open import Cubical.Data.Unit
open import Cub... | {
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module HT where
open import Prelude
open import T
open import SubstTheory
open import DynTheory
module HT where
---- Halting and Hereditary Termination
-- An old comment about lhs-halt
-- Mostly for fun, I didn't want to include "and it halts" as part
-- of the definition of HT for arrows, and I didn't wan... | {
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{-# OPTIONS --copatterns --sized-types #-}
module Copatterns where
open import Size
record Stream {i : Size} (A : Set) : Set where
coinductive
constructor _::_
field
head : A
tail : {j : Size< i} -> Stream {j} A
open Stream
map : ∀ {i A B} (f : A -> B) -> (s : Stream {i} A) -> Stream {i} B
head (map ... | {
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-- Kit instances and generic term traversals
module Syntax.Substitution.Instances where
open import Syntax.Types
open import Syntax.Context
open import Syntax.Terms
open import Syntax.Substitution.Kits
open import Data.Sum
open import Relation.Binary.PropositionalEquality as ≡
using (_≡_ ; refl ; sym ; cong ; su... | {
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module Terminal where
open import Base
open import Category
open import Unique
open import Dual
import Iso
module Term (ℂ : Cat) where
private ℂ' = η-Cat ℂ
private open module C = Cat ℂ'
private open module U = Uniq ℂ'
private open module I = Iso ℂ'
Terminal : (A : Obj) -> Set1
Terminal A = (B : Obj) -... | {
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module Ual.Eq where
open import Agda.Primitive
open import Ual.Void
record Eq {a} (A : Set a) : Set (lsuc a) where
infix 30 _==_
infix 30 _≠_
field
_==_ : A → A → Set
self : {x : A} → x == x
sym : {x y : A} → x == y → y == x
trans : {x y z : A} → x == y → y == z → x == z
_≠_ : A → A → Set... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Sets.EquivalenceRelations
open import Functions
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Numbers.Naturals.Definition
open import Numbers.Integers.Integers
open import Num... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Structures.Ring 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... | {
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{-# OPTIONS --no-positivity-check #-}
{- This file gives a standard example showing that if arguments to
constructors can use the datatype in a negative position (to the
left of one or an odd number of arrows), then termination and
logical consistency is lost. -}
module neg-datatype-nonterm where
open impo... | {
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import PiCalculus.Utils
import PiCalculus.Syntax
import PiCalculus.Syntax.Properties
import PiCalculus.Semantics
import PiCalculus.Semantics.Properties
import PiCalculus.LinearTypeSystem
import PiCalculus.LinearTypeSystem.Algebras
import PiCalculus.LinearTypeSystem.Algebras.Graded
import PiCalculus.LinearTypeSystem.Alg... | {
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module UnifyMgu where
open import UnifyTerm
open import Data.Product using (∃; _,_)
open import Data.Maybe using (Maybe; just; nothing)
open import Category.Monad using (RawMonad)
import Level
open RawMonad (Data.Maybe.monad {Level.zero})
amgu : ∀ {m} (s t : Term m) (acc : ∃ (AList m)) -> Maybe (∃ (AList m))
amgu l... | {
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module examplesPaperJFP.StatefulObject where
open import Data.Product
open import Data.String.Base as Str
open import Data.Nat.Base as N
open import Data.Vec as Vec using (Vec; []; _∷_; head; tail)
open import SizedIO.Console hiding (main)
open import Size
open import NativeIO
open import SizedIO.Base
StackStateˢ... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.types.Coproduct
open import lib.types.Fin
open import lib.types.Pi
open import lib.types.Truncation
module lib.types.Choice where
unchoose : ∀ {i j} {n : ℕ₋₂} {A : Type i} {B : A → Type j}
→ Trunc n (Π A B) → Π A (Trunc n ∘ B)
unchoose ... | {
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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
-}
-- This module defines Outputs produced by handlers, as well as functio... | {
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----------------------------------------------------------------------
-- Copyright: 2013, Jan Stolarek, Lodz University of Technology --
-- --
-- License: See LICENSE file in root of the repo --
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module Example where
open import Data.List
-- reverse
rev : ∀ {a} {A : Set a} → List A → List A
rev [] = []
rev (x ∷ xs) = rev xs ++ [ x ]
-- https://code.google.com/p/agda/issues/detail?id=1252 暫定対策
rev' = rev
{-# COMPILED_EXPORT rev' rev' #-}
private
open import Relation.Binary.PropositionalEquality
-- rever... | {
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module Issue4373.A where
postulate
T : Set
instance t : T
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module Languages.ILL.TypeSyntax where
open import bool
open import Utils.HaskellTypes
{-# IMPORT Languages.ILL.TypeSyntax #-}
data Type : Set where
TVar : String → Type
Top : Type
Imp : Type → Type → Type
Tensor : Type → Type → Type
Bang : Type → Type
{-# COMPILED_DATA Type Languages.ILL.TypeSyntax.Type ... | {
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-- Andreas, 2017-01-21, issue #2422 overloading inherited projections
-- {-# OPTIONS -v tc.proj.amb:100 #-}
-- {-# OPTIONS -v tc.mod.apply:100 #-}
postulate
A : Set
record R : Set where
field f : A
record S : Set where
field r : R
open R r public
-- The inherited projection (in the eyes of the scope check... | {
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{- Type class for functors. -}
module CategoryTheory.Functor where
open import CategoryTheory.Categories
open import Relation.Binary
-- Functor between two categories
record Functor {n} (ℂ : Category n) (𝔻 : Category n) : Set (lsuc n) where
private module ℂ = Category ℂ
private module 𝔻 = Category 𝔻
f... | {
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module Issue3579 where
open import Agda.Builtin.String
open import Agda.Builtin.Reflection
data _==_ {A : Set} (a : A) : A → Set where
refl : a == a
{-# BUILTIN EQUALITY _==_ #-}
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{-# OPTIONS --safe --without-K #-}
module Literals.Number where
open import Agda.Builtin.FromNat public
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module BTree.Complete.Alternative.Properties {A : Set} where
open import BTree {A}
open import BTree.Equality {A}
open import BTree.Equality.Properties {A}
open import BTree.Complete.Alternative {A}
open import Data.Sum renaming (_⊎_ to _∨_)
lemma-⋗-≃ : {t t' t'' : BTree} → t ⋗ t' → t' ≃ t'' → t ⋗ t''
lemma-⋗-≃ (⋗l... | {
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open import Relation.Binary.PropositionalEquality using ( refl )
open import Web.Semantic.DL.ABox.Interp using ( Interp ; ⌊_⌋ ; ind ; _*_ )
open import Web.Semantic.DL.ABox.Model using
( _⊨a_ ; ⊨a-resp-≡³ ; ⊨a-impl-⊨b ; ⊨b-impl-⊨a
; _,_ ; inb ; on-bnode ; bnodes )
open import Web.Semantic.DL.Category.Object using (... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Some properties imply others
------------------------------------------------------------------------
-- This file contains some core definitions which are reexported by
-- Relation.Binary.Consequences.
module ... | {
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{-# OPTIONS --without-K --safe #-}
module Data.Binary.Addition where
open import Data.Binary.Definition
open import Data.Binary.Increment
add₁ : 𝔹 → 𝔹 → 𝔹
add₂ : 𝔹 → 𝔹 → 𝔹
add₁ 0ᵇ ys = inc ys
add₁ (1ᵇ xs) 0ᵇ = 2ᵇ xs
add₁ (2ᵇ xs) 0ᵇ = 1ᵇ inc xs
add₁ (1ᵇ xs) (1ᵇ ys) = 1ᵇ add₁ xs ys
add₁ (1ᵇ ... | {
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--
-- Created by Dependently-Typed Lambda Calculus on 2020-09-24
-- Equal
-- Author: dplaindoux
--
module Equal where
open import Data.Nat using (ℕ; zero; suc)
open import Data.Bool using (Bool; true; false)
infix 30 _=?_
data Type : Set where
nat : Type
▲_ : Type → Set
▲ nat = ℕ
_=?_ : { a : Type } → ▲ a →... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Convenient syntax for "equational reasoning" in multiple Setoids
------------------------------------------------------------------------
-- Example use:
--
-- open import Data.Maybe
-- open import Relation.... | {
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{-# OPTIONS --warning=error --safe --without-K #-}
open import LogicalFormulae
open import Lists.Lists
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Naturals
open import Numbers.Naturals.Order
open import Numbers.BinaryNaturals.Definition
open import Numbers.BinaryNaturals.Addition
open import Num... | {
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import Lvl
open import Structure.Category
module Structure.Category.Functor.Equiv
{ℓₗₒ ℓᵣₒ ℓₗₘ ℓᵣₘ ℓₗₑ ℓᵣₑ : Lvl.Level}
{catₗ : CategoryObject{ℓₗₒ}{ℓₗₘ}{ℓₗₑ}}
{catᵣ : CategoryObject{ℓᵣₒ}{ℓᵣₘ}{ℓᵣₑ}}
where
open import Functional.Dependent as Fn using (_$_)
import Function.Equals
open Function.E... | {
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open import Agda.Builtin.Nat
open import Agda.Builtin.Unit
data ⊥ : Set where
data _⊎_ (A B : Set) : Set where
inj₁ : A → A ⊎ B
inj₂ : B → A ⊎ B
Fin : Nat → Set
Fin zero = ⊥
Fin (suc n) = ⊤ ⊎ Fin n
n = 49
postulate
P : Nat → Set
Q : Set → Set
f : (n : Nat) → Q (Fin n) → P n
q : Q (Fin n)
p : P n
p... | {
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-- Andreas, 2018-10-17
--
-- Cannot branch on erased argument.
open import Agda.Builtin.Bool
T : @0 Bool → Set
T true = Bool
T false = Bool → Bool
-- Should fail with error like:
--
-- Cannot branch on erased argument of datatype Bool
-- when checking the definition of T
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module MLib where
import MLib.Prelude
import MLib.Fin.Parts
import MLib.Fin.Parts.Simple
import MLib.Finite
import MLib.Finite.Properties
import MLib.Algebra.PropertyCode
import MLib.Matrix
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{-# OPTIONS --without-K #-}
module sets.nat where
open import sets.nat.core public
open import sets.nat.properties public
open import sets.nat.ordering public
open import sets.nat.solver public
open import sets.nat.struct public
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module _<?_ where
open import Data.Nat using (ℕ; zero; suc)
open import Relation.Nullary using (¬_)
open import decidable using (Dec; yes; no)
-- 厳密な不等式 (strict inequality)
infix 4 _<_
data _<_ : ℕ → ℕ → Set where
z<s : ∀ {n : ℕ}
------------
→ zero < suc n
s<s : ∀ {m n : ℕ}
→ m < n
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-- Andrea & Andreas, 2014-11-12
-- Pruning projected vars during solving
open import Common.Product
open import Common.Equality
postulate
A : Set
works1 : {q1 : Set} {q2 : Set → Set} ->
let M : Set -> Set; M = _ in {z : Set} -> q1 ≡ M (q2 z)
works1 = refl
works2 : {q1 : Set} {q2 : Set → Set} ->
let ... | {
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module Syntax where
open import Data.Fin
open import Data.List hiding (reverse)
open import Data.List.All
open import Data.Nat
open import Data.Product
open import Typing hiding (send ; recv)
-- expressions
data Expr Φ : Type → Set where
var : ∀ {t}
→ (x : t ∈ Φ)
→ Expr Φ t
nat : (unr-Φ : All Unr Φ)... | {
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{-# OPTIONS --without-K --safe --no-universe-polymorphism --sized-types
--no-guardedness --no-subtyping #-}
module Agda.Builtin.Size where
{-# BUILTIN SIZEUNIV SizeUniv #-}
{-# BUILTIN SIZE Size #-}
{-# BUILTIN SIZELT Size<_ #-}
{-# BUILTIN SIZESUC ↑_ #-}
{-# BUILTIN SIZEINF ∞ #... | {
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