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{-# OPTIONS --erased-cubical #-}
module Midi where
open import Agda.Builtin.String using (String)
open import Data.Fin using (toℕ)
open import Data.Nat using (ℕ)
open import Data.List using (List; []; _∷_; concatMap)
open import Data.Product using (_,_)
open import Data.Unit using (⊤)
open import MidiEvent using (Ti... | {
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module ParseTree where
open import Data.String
open import Data.Nat
open import Data.Bool
open import Data.List
{-# FOREIGN GHC import ParseTree #-}
data ParseTree : Set
data TypeSignature : Set
data Expr : Set
data Range : Set
data Identifier : Set
data RangePosition : Set
data Pragma : Set
data Comment : Set
data ... | {
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module Web.Semantic.DL.Category.Properties.Tensor where
open import Web.Semantic.DL.Category.Properties.Tensor.RespectsEquiv public using
( tensor-resp-≣ )
open import Web.Semantic.DL.Category.Properties.Tensor.Functor public using
( tensor-resp-id ; tensor-resp-compose )
open import Web.Semantic.DL.Category.Pro... | {
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module sn-calculus-confluence.recrec where
open import Data.Nat using (_+_)
open import Function using (_∋_ ; _∘_ ; id ; _$_)
open import Data.Nat.Properties.Simple using ( +-comm ; +-assoc )
open import utility
open import Esterel.Lang
open import Esterel.Lang.Properties
open import Esterel.Environment as Env
open im... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.Band.Properties where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Data.Nat
open import Cubical.Data.NatPlusOne
open import Cubical.Algebra
open import C... | {
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module _ where
data Unit : Set where
unit : Unit
module M (_ : Unit) where
record R₁ (A : Set) : Set₁ where
no-eta-equality
postulate
x : A
open R₁ ⦃ … ⦄ public
record R₂ (A : Set) : Set₁ where
field
instance
r₁ : R₁ A
open R₂ ⦃ … ⦄
open M unit
postulate
A : Set
in... | {
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-- 2014-04-06 Andreas, issue reported by Andres Sicard-Ramirez
-- {-# OPTIONS --termination-depth=100 -v term.matrices:40 #-}
data ℕ : Set where
zero : ℕ
succ : ℕ → ℕ
-- The following function is accepted by the termination checker in
-- Agda-2.3.2.2, but it is rejected by the termination checker in
-- the curre... | {
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module Oscar.Class.Monoid where
open import Oscar.Data.Equality
open import Oscar.Level
record Monoid {a} {A : Set a} {b} (_↠_ : A → A → Set b) : Set (a ⊔ b) where
field
ε : ∀ {m} → m ↠ m
_◇_ : ∀ {l m n} → m ↠ n → l ↠ m → l ↠ n
◇-left-identity : ∀ {m n} → (f : m ↠ n) → ε ◇ f ≡ f
◇-right-identity : ... | {
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-- {-# OPTIONS --sized-types #-} Option obsolete since 2014-04-12.
module SizedTypesLeqInfty where
open import Common.Size
data Nat : {size : Size} -> Set where
zero : {size : Size} -> Nat {↑ size}
suc : {size : Size} -> Nat {size} -> Nat {↑ size}
weak : {i : Size} -> Nat {i} -> Nat {∞}
weak x = x
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.types.Group
open import lib.types.Pi
open import lib.NType2
open import lib.types.Paths
open import lib.types.EilenbergMacLane1.Core
module lib.types.EilenbergMacLane1.FunElim where
module _ {i} {G : Group i} where
private
module G... | {
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{- SAMPLE PROGRAMS IN SOURCE LANGUAGE -}
{-# OPTIONS --no-termination-check #-}
open import Preliminaries
open import Source
module Samples where
{- dbl (n : nat) : nat = 2 * n -}
dbl : ∀ {Γ} → Γ |- (nat ->s nat)
dbl = lam (rec (var i0) z (suc (suc (force (var (iS i0))))))
{- add (m n : nat) : nat = m + n... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
open import Cubical.Core.Everything
module Cubical.Relation.Binary.Raw.Bundles {c : Level} (Carrier : Type c) where
open import Cubical.Foundations.Prelude using (isSet)
open import Cubical.Relation.Nullary using (¬_)
open import Cubical.Relation.Binary.Base
open i... | {
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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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{-# OPTIONS --without-K --safe --erased-cubical --no-import-sorts #-}
module Motif where
open import Prelude
open import SUtil using (lookup)
open import Yamanote using (counterp)
import Definition.Conversion
import Definition.Conversion.Whnf
import Definition.Typed
import Definition.Untyped
import Definition.Type... | {
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module FileIOEffect where
open import Effect
import IO.Primitive as IO
open import Data.String using (String)
open import Data.Bool using (Bool ; if_then_else_ ; false ; true)
open import Data.Unit using (⊤ ; tt)
open import Category.Monad using (RawMonad)
open import Level using (zero)
open import Data.List using (Li... | {
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{-
This file contains cospans, cones, pullbacks and maps of cones in precategories.
-}
{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Categories.Pullback where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Sigma
open import Cubical.Categories.Category
open Precategory
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module Algebra.Theorems where
open import Algebra
open import Reasoning
+pre-idempotence : ∀ {A} {x : Graph A} -> x + x + ε ≡ x
+pre-idempotence {_} {x} =
begin
(x + x) + ε ≡⟨ L (L (symmetry *right-identity)) ⟩
(x * ε + x) + ε ≡⟨ L (R (symmetry *right-identity)) ⟩
(x * ε + x * ε) + ε... | {
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{-# OPTIONS --cubical #-}
module Multidimensional.Data.Dir.Base where
open import Cubical.Core.Primitives
-- "Direction" type for determining direction in spatial structures.
-- We interpret ↓ as 0 and ↑ as 1 when used in numerals in
-- numerical types.
data Dir : Type₀ where
↓ : Dir
↑ : Dir
caseDir : ∀ {ℓ} → {A... | {
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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.Prelude
open import LibraBFT.Abstract.Types.EpochConfig
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module Nats.Multiply.Distrib where
open import Nats
open import Equality
open import Function
open import Nats.Multiply.Comm
open import Nats.Add.Assoc
open import Nats.Add.Comm
------------------------------------------------------------------------
-- internal stuffs
private
a*1+b=a+a*b : ∀ a b → a * suc b ≡ a... | {
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module Categories.CoProducts where
open import Data.Sum hiding ([_,_])
open import Library hiding (_+_ ; _,_)
open import Categories
record CoProd {l m}(C : Cat {l}{m}) : Set (m ⊔ l) where
open Cat C
field _+_ : Obj -> Obj -> Obj
inl : ∀{A B} -> Hom A (A + B)
inr : ∀{A B} -> Hom B (A + B)
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module Prelude.Number where
open import Agda.Builtin.FromNat public
open import Agda.Builtin.FromNeg public
NoNumConstraint : ∀ {a} {A : Set a} → Number A → Set a
NoNumConstraint Num = ∀ {n} → Number.Constraint Num n
NoNegConstraint : ∀ {a} {A : Set a} → Negative A → Set a
NoNegConstraint Neg = ∀ {n} → Negative.Con... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Structures.Group.Morphism where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Structures.Group.Base
private
variable
ℓ ℓ' : Level
-- The following definition of GroupHom and GroupEquiv are lev... | {
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module Prelude.Equality where
open import Prelude.Decidable
open import Agda.Builtin.Equality public
record Eq {a} (A : Set a) : Set a where
infix 4 _==_
field
_==_ : (x y : A) → Dec (x ≡ y)
open Eq {{...}} public
sym : ∀ {a} {A : Set a} {x y : A} → x ≡ y → y ≡ x
sym refl = refl
infixr 0 _⟨≡⟩_ _⟨≡⟩ʳ_ _ʳ⟨... | {
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data HasUniqueValues (A : Set) : List A → Set
where
[] : HasUniqueValues A []
_∷_ : {x : A} → {xs : List A} → x ∉ xs → (uxs : HasUniqueValues A xs) → HasUniqueValues A (x ∷ xs)
record AList (A : Set) (B : Set) : Set
where
field
domain : List A
uniquedomain : HasUniqueValues A domain
range : ∀ {x :... | {
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{-# OPTIONS --experimental-irrelevance #-}
record NonStrict (A : Set) : Set where
constructor [_]
field
..! : A
open NonStrict
map-ns : {A B : Set} (f : A → B) → NonStrict A → NonStrict B
map-ns f [ x ] = [ f x ]
open import Agda.Builtin.Nat
data Vec (A : Set) : NonStrict Nat → Set where
[] : Vec A [ 0 ... | {
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data Nat : Set where
zero : Nat
suc : (n : Nat) → Nat
test₁ : (n : Nat) → Nat
test₁ n with zero
... | x = {!x!}
data Tree : Set where
leaf : Tree
node : Tree → Tree → Tree
test₂ : (n : Tree) → Tree
test₂ n₁ with leaf
... | n = {!n!}
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{-
This second-order signature was created from the following second-order syntax description:
syntax Sub | S
type
L : 0-ary
T : 0-ary
term
vr : L -> T
sb : L.T T -> T
theory
(C) x y : T |> sb (a. x[], y[]) = x[]
(L) x : T |> sb (a. vr(a), x[]) = x[]
(R) a : L x : L.T |> sb (b. x[b], vr(a[])) = ... | {
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-- Andreas, 2017-05-24, issue #2590
-- Making variables visible by case splitting in with-clauses
-- {-# OPTIONS -v interaction.case:20 #-}
-- {-# OPTIONS -v reify:100 #-}
-- {-# OPTIONS -v tc.display:100 #-}
open import Agda.Builtin.Nat
test1 : {x : Nat} → Nat
test1 with Set
... | q = {!.x!} -- C-c C-c
-- Expecte... | {
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------------------------------------------------------------------------
-- Fixpoint combinators
------------------------------------------------------------------------
{-# OPTIONS --erased-cubical --safe #-}
open import Partiality-algebra as PA hiding (id; _∘_)
module Partiality-algebra.Fixpoints where
open impor... | {
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{-# OPTIONS --without-K #-}
module sets.nat.algebra where
open import equality.core
open import algebra.monoid.core
open import sets.nat.core
open import sets.nat.properties
+-monoid : Monoid _
+-monoid = record
{ carrier = ℕ
; is-mon = record
{ id = λ _ → 0
; _∘_ = _+_
; left-unit = +-left-unit
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module List.Permutation.Base.Bag (A : Set) where
open import Data.List
open import Data.List.Any as Any
open import Data.List.Any.BagAndSetEquality
open import Data.List.Any.Properties
open import Data.Sum renaming (_⊎_ to _∨_)
open import Function
open import Function.Inverse hiding (sym ; _∘_ ; id)
open import Funct... | {
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module DataRecordInductive where
module NotMutual where
record Nil (A : Set) : Set where
constructor []
record Cons (A X : Set) : Set where
constructor _∷_
field head : A
tail : X
open Cons
data List (A : Set) : Set where
nil : Nil A → List A
cons : Cons A (List A) → List A
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module Tactic.Monoid.Reflect where
open import Prelude
open import Tactic.Reflection
open import Tactic.Reflection.Match
open import Control.Monad.Zero
open import Control.Monad.State
open import Container.Traversable
open import Tactic.Monoid.Exp
open import Tactic.Reflection.Parse renaming (parseEqn to parseEq)
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{-# OPTIONS --type-in-type #-}
Ty : Set; Ty
= (Ty : Set)
(ι : Ty)
(arr : Ty → Ty → Ty)
→ Ty
ι : Ty; ι = λ _ ι _ → ι
arr : Ty → Ty → Ty; arr = λ A B Ty ι arr → arr (A Ty ι arr) (B Ty ι arr)
Con : Set;Con
= (Con : Set)
(nil : Con)
(snoc : Con → Ty → Con)
→ Con
nil : Con;nil
= λ Con nil snoc → n... | {
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-- Andreas, 2015-09-12, Issue 1637, reported by Nisse.
-- {-# OPTIONS -v tc.display:100 -v reify.display:100 #-}
record R (X : Set₁) : Set₁ where
field
f : X
postulate
A : Set₁
P : A → Set
module M (_ : Set₁) where
Unrelated-function : R Set → Set
Unrelated-function Y = R.f Y -- eta expansion is nece... | {
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module Structure.Category.Categories where
open import Data
open import Data.Proofs
open import Functional
open import Logic
import Lvl
import Relator.Equals as Eq
open import Structure.Setoid
open import Structure.Category
open import Structure.Categorical.Proofs
open import Structure.Categorical.Properties... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Relation.Binary.Raw.Definitions where
open import Cubical.Core.Everything
open import Cubical.Foundations.Function
open import Cubical.Data.Maybe.Base using (Maybe)
open import Cubical.Data.Prod.Base using (_×_)
open import Cubical.Data.Sigma.Base usi... | {
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module logic where
open import Level
open import Relation.Nullary
open import Relation.Binary hiding (_⇔_ )
open import Data.Empty
data Bool : Set where
true : Bool
false : Bool
record _∧_ {n m : Level} (A : Set n) ( B : Set m ) : Set (n ⊔ m) where
constructor ⟪_,_⟫
field
proj1 : A
proj... | {
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module Oscar.Class.Reflexivity where
open import Oscar.Level
record Reflexivity {a} {A : Set a} {ℓ} (_≋_ : A → A → Set ℓ) : Set (a ⊔ ℓ) where
field
reflexivity : ∀ {x} → x ≋ x
open Reflexivity ⦃ … ⦄ public
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module Text.Greek.SBLGNT.1Cor where
open import Data.List
open import Text.Greek.Bible
open import Text.Greek.Script
open import Text.Greek.Script.Unicode
ΠΡΟΣ-ΚΟΡΙΝΘΙΟΥΣ-Α : List (Word)
ΠΡΟΣ-ΚΟΡΙΝΘΙΟΥΣ-Α =
word (Π ∷ α ∷ ῦ ∷ ∙λ ∷ ο ∷ ς ∷ []) "1Cor.1.1"
∷ word (κ ∷ ∙λ ∷ η ∷ τ ∷ ὸ ∷ ς ∷ []) "1Cor.1.1"
∷ word (ἀ... | {
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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 Selective.Examples.TestAO where
open import Selective.ActorMonad
open import Prelude
open import Selective.Libraries.Call2
open import Selective.Libraries.ActiveObjects
open import Debug
open import Data.Nat.Show using (show)
ℕ-ReplyMessage : MessageType
ℕ-ReplyMessage = ValueType UniqueTag ∷ [ ValueType ℕ ]ˡ... | {
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module Everything where
open import Pi.Everything -- Formalization for Π
open import RevMachine -- Formalization of reversible machine and partial reversible machine
open import RevNoRepeat -- Non-repeating theorem for reversible machine
open import PartialRevNoRepeat -- Non-repeating theorem fo... | {
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module RecordUpdateSyntax where
open import Common.Prelude
open import Common.Equality
data Param : Nat → Set where
param : ∀ n → Param (suc n)
record R : Set where
field
{i} : Nat
p : Param i
s : Nat
old : R
old = record { p = param 0; s = 1 }
-- Simple update, it should be able to infer the type ... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Empty type
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Empty where
------------------------------------------------------------------... | {
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module StateSized.GUI.SpaceShipSimpleVar where
open import SizedIO.Base
open import StateSizedIO.GUI.BaseStateDependent
open import Data.Bool.Base
open import Data.List.Base
open import Data.Integer
open import Data.Product hiding (map)
open import SizedIO.Object
open import SizedIO.IOObject
open import NativeIO
o... | {
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{-# OPTIONS --without-K --exact-split --allow-unsolved-metas #-}
module 24-sequences where
import 23-id-pushout
open 23-id-pushout public
{- We introduce two types of sequences: one with the arrows going up and one
with the arrows going down. -}
Sequence :
( l : Level) → UU (lsuc l)
Sequence l = Σ (ℕ → UU l) (... | {
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module Container.Traversable where
open import Prelude
record Traversable {a} (T : Set a → Set a) : Set (lsuc a) where
field
traverse : ∀ {F : Set a → Set a} {A B} {{AppF : Applicative F}} → (A → F B) → T A → F (T B)
overlap {{super}} : Functor T
open Traversable {{...}} public
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-- This file tests that implicit record fields are not printed out (by
-- default).
module ImplicitRecordFields where
record R : Set₁ where
field
{A} : Set
f : A → A
{B C} D {E} : Set
g : B → C → E
postulate
A : Set
r₁ : R
r₂ : R
r₂ = record
{ A = A
; f = λ x →... | {
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{-# OPTIONS --cubical --safe #-}
module Data.Maybe where
open import Data.Maybe.Base public
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Equivalence (coinhabitance)
------------------------------------------------------------------------
module Function.Equivalence where
open import Function using (flip)
open import Function.Equality as F
usin... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
open import lib.types.Paths
open import lib.types.Pointed
open import lib.types.Pushout
open import lib.types.Span
module lib.types.PushoutFlip where
module _ {i j k} {d : Span {i} {j} {k}} where
module PushoutFlip = PushoutRec
(right {d = Span-fl... | {
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module Numeral.Natural.Prime where
import Lvl
open import Data.Boolean.Stmt
open import Logic
open import Logic.Propositional
open import Numeral.Natural
open import Numeral.Natural.Relation.Divisibility
open import Numeral.Natural.Oper
open import Numeral.Natural.Oper.Comparisons
open import Relator.Equals
PrimeProo... | {
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------------------------------------------------------------------------
-- Some simple binary relations
------------------------------------------------------------------------
module Relation.Binary.Simple where
open import Relation.Binary
open import Data.Unit
open import Data.Empty
-- Constant relations.
Const ... | {
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------------------------------------------------------------------------
-- Propositional equality
------------------------------------------------------------------------
-- This file contains some core definitions which are reexported by
-- Relation.Binary.PropositionalEquality.
module Relation.Binary.Propositional... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.HITs.S3 where
open import Cubical.HITs.S3.Base public
-- open import Cubical.HITs.S3.Properties public
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{-# OPTIONS --without-K #-}
module container.m.from-nat.core where
open import level
open import sum
open import equality
open import function
open import container.core
open import sets.nat.core
open import sets.nat.struct
open import sets.unit
open import hott.level
-- Definition 9 in Ahrens, Capriotti and Spadotti... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- A categorical view of the identity function
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Function.Identity.Categorical {ℓ} where
open impor... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Environments (heterogeneous collections)
------------------------------------------------------------------------
module Data.Star.Environment (Ty : Set) where
open import Data.Star
open import Data.Star.List
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------------------------------------------------------------------------
-- INCREMENTAL λ-CALCULUS
--
-- Congruence of application.
--
-- If f ≡ g and x ≡ y, then (f x) ≡ (g y).
------------------------------------------------------------------------
module Theorem.CongApp where
open import Relation.Binary.Propositio... | {
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-- Andreas, 2017-09-09
-- Builtin constructors may be ambiguous / overloaded.
data Semmel : Set where
false : Semmel
data Bool : Set where
true : Bool
false : Bool
{-# BUILTIN BOOL Bool #-}
{-# BUILTIN TRUE true #-}
{-# BUILTIN FALSE false #-} -- This is accepted.
data Brezel A : Set where
_∷_ : (x : A... | {
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module Test where
data _∨_ (A B : Set) : Set where
inj₁ : A → A ∨ B
inj₂ : B → A ∨ B
postulate
A B : Set
∨-comm : A ∨ B → B ∨ A
{-# ATP prove ∨-comm #-}
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{-
This second-order term syntax was created from the following second-order syntax description:
syntax Prod | P
type
_⊗_ : 2-ary | l40
term
pair : α β -> α ⊗ β | ⟨_,_⟩
fst : α ⊗ β -> α
snd : α ⊗ β -> β
theory
(fβ) a : α b : β |> fst (pair(a, b)) = a
(sβ) a : α b : β |> snd (pair(a, b)) ... | {
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module Issue363 where
infixl 0 _>>=_
postulate
A : Set
x : A
_>>=_ : A → (A → A) → A
P : A → Set
lemma : P ((x >>= λ x → x) >>= λ x → x)
lemma = {!!}
-- The type of the goal above was printed as follows:
--
-- P (x >>= λ x' → x' >>= λ x' → x')
--
-- This is not correct.
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-- Andreas, 2014-04-11, issue reported by James Chapman
-- {-# OPTIONS -v tc.decl.ax:100 #-}
-- {-# OPTIONS -v tc.polarity:100 #-}
{-# OPTIONS --copatterns --sized-types #-}
module _ where
open import Common.Size
module Works where
mutual
data Delay i (A : Set) : Set where
now : A → Delay i A
late... | {
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{-# OPTIONS --safe #-}
module Issue2728-3 where
foo = Set -- something to cache
postulate B : Set
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{-# OPTIONS --cubical --safe #-}
module Cubical.ZCohomology.Everything where
open import Cubical.ZCohomology.Base
open import Cubical.ZCohomology.Properties
open import Cubical.ZCohomology.S1.S1
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open import Level hiding ( suc ; zero )
open import Algebra
module Gutil {n m : Level} (G : Group n m ) where
open import Data.Unit
open import Function.Inverse as Inverse using (_↔_; Inverse; _InverseOf_)
open import Function
open import Data.Nat hiding (_⊔_) -- using (ℕ; suc; zero)
open import Relation.Nullary
open ... | {
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{-
Generate univalent reflexive graph characterizations for record types from
characterizations of the field types using reflection.
See end of file for an example.
-}
{-# OPTIONS --no-exact-split --safe #-}
module Cubical.Displayed.Record where
open import Cubical.Foundations.Prelude
open import Cubical.Foundation... | {
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module Pi.Eval where
open import Data.Empty
open import Data.Unit
open import Data.Sum
open import Data.Product
open import Data.List as L hiding (_∷_)
open import Relation.Binary.PropositionalEquality
open import Pi.Syntax
open import Pi.Opsem
open import Pi.NoRepeat
-- Stuck states must be of the form ［ c ∣ v ∣ ☐ ］
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{-# OPTIONS --no-termination-check #-}
module Pi where
open import Data.Empty
open import Data.Unit
open import Data.Sum hiding (map)
open import Data.Product hiding (map)
open import Relation.Binary.PropositionalEquality hiding (sym; [_])
infixr 30 _⟷_
infixr 30 _⟺_
infixr 20 _◎_
---------------------------------... | {
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-- {-# OPTIONS -v scope:20 #-}
module _ (X : Set) where
postulate
X₁ X₂ : Set
data D : Set where
d : D
module Q (x : D) where
module M1 (z : X₁) where
g = x
module M2 (y : D) (z : X₂) where
h = y
open M1 public
-- module Qd = Q d
-- This fails to apply g to d!
module QM2d = Q.M2 d d
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{-# OPTIONS --no-exact-split --safe #-}
module Cubical.Data.Nat.Base where
open import Cubical.Core.Primitives
open import Agda.Builtin.Nat public
using (zero; suc; _+_)
renaming (Nat to ℕ; _-_ to _∸_; _*_ to _·_)
open import Cubical.Data.Nat.Literals public
open import Cubical.Data.Bool.Base
open import Cubical... | {
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{-# OPTIONS --no-auto-inline #-}
module DefaultMethods where
open import Agda.Builtin.Equality
open import Agda.Builtin.Bool
open import Agda.Builtin.Nat using (Nat)
import Agda.Builtin.Nat as Nat
open import Agda.Builtin.List
open import Agda.Builtin.String renaming (primStringAppend to _++_)
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{-# OPTIONS --safe #-}
module Cubical.Algebra.OrderedCommMonoid.Base where
{-
Definition of an ordered monoid.
-}
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.SIP using (TypeWithStr)
open import Cubical.Foundations.Structure using (⟨_⟩)
open import Cubical.Algebra.CommMonoid.Base
open im... | {
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open import Auto.Prelude
mutual
data Even : ℕ → Set where
even-0 : Even zero
even-s : {n : ℕ} → Odd n → Even (succ n)
data Odd : ℕ → Set where
odd-1 : Odd (succ zero)
odd-s : {n : ℕ} → Even n → Odd (succ n)
double : ℕ → ℕ
double zero = zero
double (succ n) = succ (succ (double n))
h0 : ∀ {n} → Even (doub... | {
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module Selective.Examples.TestSelectiveReceive-calc where
open import Selective.ActorMonad
open import Prelude
open import Debug
open import Data.Nat.Show using (show)
UniqueTag = ℕ
TagField = ValueType UniqueTag
ℕ-ReplyMessage : MessageType
ℕ-ReplyMessage = ValueType UniqueTag ∷ [ ValueType ℕ ]ˡ
ℕ-Reply : InboxSh... | {
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module Issue535 where
data Nat : Set where
zero : Nat
suc : Nat → Nat
data Vec A : Nat → Set where
[] : Vec A zero
_∷_ : ∀ {n} → A → Vec A n → Vec A (suc n)
replicate : ∀ {A n} → A → Vec A n
replicate {n = n} x = {!n!}
replicate′ : ∀ {n A} → A → Vec A n
replicate′ {n} x = {!n!}
extlam : Nat → {n m : Nat}... | {
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open import Agda.Builtin.Nat
open import Agda.Builtin.Equality
data Vec (A : Set) : Nat → Set where
variable
A : Set
x : A
n : Nat
xs : Vec A n
postulate
IsHead : A → Vec A (suc n) → Set
-- Should also work if there is pruning
solve_==_by_ : (m n : Nat) → m ≡ n → Set
solve_==_by_ _ _ _ = Nat
mutual-b... | {
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-- This is not valid with magic mutual blocks that guess how far down the
-- file the mutual block extends
constructor
zero : Nat
suc : Nat → Nat
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{-# OPTIONS --cubical --safe --no-import-sorts #-}
module Cubical.Data.FinSet.Binary.Small where
open import Cubical.Data.FinSet.Binary.Small.Base public
open import Cubical.Data.FinSet.Binary.Small.Properties public
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module YonedaLemma where
open import Library
open import Categories
open import Categories.Sets
open import Functors
open import Naturals
open import FunctorCat
HomF[-,_] : ∀{l m}{C : Cat {l}{m}}(X : Cat.Obj C) -> Fun (C Op) (Sets {m})
HomF[-,_] {C = C} B = functor
(\ X -> Hom X B)
(\ f g -> comp g f)
(ext \ _ ... | {
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{-# OPTIONS --without-K #-}
{- This module serves to develop some basic theory about pointed types.
After defining the usual notions of pointed types, pointed equivalences,
and loop spaces, we derive a version of univalence for pointed equivalences
and observe that univalence between identical types is a poin... | {
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module StateSized.GUI.SpaceShipExtendedExample where
open import SizedIO.Base
open import StateSizedIO.GUI.BaseStateDependent
open import Data.Bool.Base
open import Data.List.Base
open import Data.Integer
open import Data.Product hiding (map)
open import SizedIO.Object
open import SizedIO.IOObject
open import Nat... | {
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record R (A : Set) : Set where
field
f : A → A
open R {{...}}
test : {A : Set} → R A
f {{test}} = {!!}
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------------------------------------------------------------------------------
-- Twice funcion
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --w... | {
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------------------------------------------------------------------------
-- From the Agda standard library
--
-- Sizes for Agda's sized types
------------------------------------------------------------------------
module Common.Size where
{-# BUILTIN SIZEUNIV SizeU #-}
{-# BUILTIN SIZE Size #-}
{-# BUILTIN SIZ... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Groups.Definition
open import Groups.Abelian.Definition
open import Groups.FiniteGroups.Definition
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Numbers.Naturals.Order.Lemmas
open import Se... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Convenient syntax for equational reasoning
------------------------------------------------------------------------
-- Example use:
-- n*0≡0 : ∀ n → n * 0 ≡ 0
-- n*0≡0 zero = refl
-- n*0≡0 (suc n) =
-- beg... | {
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module FixityOutOfScopeInRecord where
record R : Set where
infixl 30 _+_
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------------------------------------------------------------------------------
-- Testing the use of ATP axioms with data constructors
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-un... | {
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module CombiningProofs.CommAddGlobalHints where
open import PA.Axiomatic.Standard.Base
+-leftIdentity : ∀ n → zero + n ≡ n
+-leftIdentity = PA₃
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open import OutsideIn.Prelude
module OutsideIn.X where
open import Data.Product public hiding (map)
open import Relation.Nullary
record Types : Set₁ where
field Type : Set → Set
type-is-monad : Monad Type
funType : ∀ {n} → Type n → Type n → Type n
appType : ∀ {n} → Type ... | {
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module PatternSynonymOverloaded where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
pattern ss x = suc (suc x)
pattern ss x = suc x
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{-# OPTIONS --safe #-} -- --without-K #-}
open import Relation.Binary.PropositionalEquality using (_≢_; _≡_; refl; sym; subst; cong; trans)
open import Function using (_∘_)
open import Relation.Nullary using (yes; no)
import Data.Empty as Empty
import Data.Product as Product
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{-
Part 4: Higher inductive types
- Quotients via HITs
- Propositional truncation for logic?
- CS example using quotients (maybe finite multisets or queues)
- Synthetic homotopy theory (probably Torus = S^1 * S^1, pi_1(S^1) =
Z, pi_1(Torus) = Z * Z)
-}
{-# OPTIONS --cubical #-}
module Part4 where
open import Cub... | {
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--------------------------------------------------------------------
-- This file contains the definition of and facts about functors. --
--------------------------------------------------------------------
module Category.Funct where
open import Level
open import Relation.Relation
open import Relation.Binary.Propos... | {
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------------------------------------------------------------------------------
-- The alternating bit protocol (ABP) is correct
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-... | {
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module Syntax where
open import Stack public
-- Abstract symbols, or atoms.
abstract
Atom : Set
Atom = Nat
-- Types, or propositions in constructive modal logic S4.
infixl 9 _⩕_
infixl 8 _⩖_
infixr 7 _⇒_
data Type : Set where
α_ : Atom → Type
_⇒_ : Type → Type → Type
□_ : Type → Type
_⩕_ : Type ... | {
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