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|---|---|
module sn-calculus-compatconf.split where
open import sn-calculus-compatconf.base
open import sn-calculus
open import utility renaming (_U̬_ to _∪_)
open import context-properties
using (unwrap-rho ; wrap-rho ; ->E-view ; plugc ; unplugc)
open import Esterel.Lang
open import Esterel.Lang.Properties
open import Est... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.PtdMapSequence
open import homotopy.CofiberSequence
open import groups.Exactness
open import groups.ExactSequence
open import groups.HomSequence
open import cohomology.Theory
module cohomology.Sigma {i} (CT : CohomologyTheory i)
(n : ℤ) (... | {
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module _ where
open import Agda.Builtin.Unit
open import Agda.Builtin.Reflection
data D (B : Set) {{b : B}} : Set where
c : D B
postulate
B : Set
instance b : B
T : D B → Set
macro
this : Term → Term → TC ⊤
this thing hole = unify hole thing
test₁ : _
test₁ = c {_} {{b}}
test₂ : D B
test₂ = c {_} {{b... | {
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-- {-# OPTIONS -v tc:10 -v tc.inj:100 #-}
-- 2013-02-18 reported by rotsor
module Issue796o where
data U : Set where
a b : U
data A : Set where
data B : Set where
abstract
A' B' : Set
A' = A
B' = B -- fails if changed to A. Should always fail.
[_] : U → Set
[_] a = A'
[_] b = B'
f : ∀ u → [ u ] → U
f u... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Functor.Instance.01-Truncation where
-- (0,1)-trucation of categories as a functor from Cats to Posets.
--
-- This is the right-adjoint of the inclusion functor from Posets to
-- Cats (see Categories.Functor.Adjoint.Instance.01-Truncation)
open import Level using ... | {
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module Oscar.Level where
open import Agda.Primitive public
using ()
renaming (Level to Ł̂; lzero to Ø̂; lsuc to ↑̂_; _⊔_ to _+̂_)
open import Agda.Primitive public
using ()
renaming (Level to Ł̂; lzero to lzero; lsuc to lsuc; _⊔_ to _⊔_)
𝑶 : ∀ a → Set (lsuc a)
𝑶 a = Set a
open import Agda.Primitive publi... | {
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module pushdown where
open import Level renaming ( suc to succ ; zero to Zero )
open import Data.Nat
open import Data.List
open import Data.Maybe
-- open import Data.Bool using ( Bool ; true ; false )
open import Relation.Binary.PropositionalEquality hiding ( [_] )
open import Relation.Nullary using (¬_; Dec; yes; no... | {
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-- Compiled things must have a Haskell type given by a COMPILED_TYPE pragma
module CompiledMustHaveHaskellType where
postulate
N : Set
foo : N
-- It is necessary add something like
-- {-# COMPILED_TYPE N Int #-}
{-# COMPILED foo bar #-}
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module FFI.IO where
open import Agda.Builtin.IO using (IO)
open import Agda.Builtin.Unit using (⊤)
open import Agda.Builtin.String using (String)
open import FFI.Data.HaskellString using (HaskellString; pack ; unpack)
infixl 1 _>>=_
infixl 1 _>>_
postulate
return : ∀ {a} {A : Set a} → A → IO A
_>>=_ : ∀ {a b} ... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties satisfied by posets
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Relation.Binary
module Relation.Binary.Properties.Poset
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------------------------------------------------------------------------------
-- The division result is correct
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Setoids.Setoids
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import Groups.Definition
module Groups.Abelian.Definition where
record AbelianGroup {a} {b} {A : Set a} {S : Setoid {a} {b} A} {_·_ : A → A → A} (G : Group S _·_) : Set (lsuc... | {
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{-# OPTIONS --allow-unsolved-metas #-}
-- The option is supplied to force a real error to pass the regression test.
module StronglyRigidOccurrence where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
data _≡_ {A : Set}(a : A) : A -> Set where
refl : a ≡ a
test : let X : Nat; X = _ in X ≡ suc X
test = refl
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Universal lifting of predicates over Vectors
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Data.Vec.Functional.Relation.Unary.All where
open... | {
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{-# OPTIONS --prop --rewriting #-}
open import Calf.CostMonoid
open import Data.Nat using (ℕ)
open import Examples.Sorting.Comparable
module Examples.Sorting.Core
(costMonoid : CostMonoid) (fromℕ : ℕ → CostMonoid.ℂ costMonoid)
(M : Comparable costMonoid fromℕ)
where
open Comparable M
open import Calf costMono... | {
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{-# OPTIONS --safe #-}
module Definition.Typed.Consequences.Canonicity where
open import Definition.Untyped
open import Definition.Typed
open import Definition.Typed.Weakening
open import Definition.Typed.Properties
open import Definition.Typed.EqRelInstance
open import Definition.LogicalRelation
open import Definit... | {
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{-# OPTIONS --cubical --safe #-}
module Data.Binary.PerformanceTests.Addition where
open import Prelude
open import Data.Binary.Definition
open import Data.Binary.Addition using (_+_)
sum-r : 𝔹 → ℕ → 𝔹
sum-r′ : 𝔹 → ℕ → 𝔹
sum-r′ x zero = x
sum-r′ x (suc n) = x + sum-r (2ᵇ x) n
sum-r x zero = x
sum-r x (su... | {
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module Issue2469 where
open import Agda.Builtin.Nat
open import Agda.Builtin.Unit
open import Agda.Builtin.IO renaming (IO to BIO)
open import Agda.Builtin.String
open import Agda.Builtin.IO
open import Common.IO
open import Common.Prelude
open import Common.Sum
open import Common.Product
data F : Nat → Set where
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{-# OPTIONS --type-in-type #-} -- enables cheating
-- 2:10 : why
-- https://www.youtube.com/watch?v=2LxtHeZlaVw
module HC-Lec3 where
open import HC-Lec1
open import HC-Lec2
postulate
-- equal inputs go to equal outputs
-- (whereas structural equality would require equal implement... | {
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9.
Copyright (c) 2020, 2021, Oracle and/or its affiliates.
Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl
-}
open import LibraBFT.Prelude
open import LibraBFT.Lemmas
open import Lib... | {
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data ⊤ : Set where
tt : ⊤
f : ⊤ → ⊤
f tt = tt
foo : ⊤ → ⊤
foo t with f t
... | x with f t
... | y with f t
... | z = {!z!}
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module InequalityReasoningExercise where
open import EqualityAux
infix 4 _≤_
data _≤_ : ℕ → ℕ → Set where
z≤n : ∀ {n : ℕ}
--------
→ zero ≤ n
s≤s : ∀ {m n : ℕ}
→ m ≤ n
-------------
→ suc m ≤ suc n
≤-refl : ∀ {n : ℕ}
-----
→ n ≤ n
≤-refl {zero} = z≤n
≤-refl {suc n} = s≤s ≤-refl
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------------------------------------------------------------------------------
-- Terminating mirror function
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{... | {
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{-# OPTIONS --without-K --safe #-}
open import Definition.Typed.EqualityRelation
module Definition.LogicalRelation.Application {{eqrel : EqRelSet}} where
open EqRelSet {{...}}
open import Definition.Untyped
open import Definition.Untyped.Properties
open import Definition.Typed
open import Definition.Typed.Weakening ... | {
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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
open import LibraBFT.Concrete.System.Paramete... | {
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open import Data.Product using ( _×_ ; _,_ ; proj₁ ; proj₂ )
open import FRP.LTL.RSet.Core using ( RSet ; ⟦_⟧ )
open import FRP.LTL.RSet.Globally using ( [_] )
open import FRP.LTL.RSet.Causal using ( _⊵_ ; arr )
open import FRP.LTL.RSet.Stateless using ( _⇒_ )
module FRP.LTL.RSet.Product where
infixr 2 _∧_
-- Conjun... | {
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{-# OPTIONS --without-K #-}
open import HoTT.Base
open import HoTT.Identity.Sigma
module HoTT.Pi.Transport where
transport-→ : ∀ {i j k} {X : 𝒰 i} (A : X → 𝒰 j) (B : X → 𝒰 k)
{x₁ x₂ : X} (p : x₁ == x₂) (f : A x₁ → B x₁) →
transport (λ x → A x → B x) p f == transport B p ∘ f ∘ transport ... | {
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{-# OPTIONS --no-unicode #-} -- turn off automatic unicode insertion
module 02-agda-start where
-------------------------------------------------------------------------------------------------------
-- ADDITIONAL RESOURCES |
-------------------------
-- допълнителни ресурси:
-- https://github.com/pigworker/CS410-17 ... | {
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{-# OPTIONS --without-K --rewriting #-}
open import Prelude
module Syntax where
data Con : (n : ℕ) → Set
Ctx : Set
Ctx = Σ ℕ Con
data Ty : Ctx → Set
data Tm : {Γ : Ctx} (A : Ty Γ) → Set
data Sub : Ctx → Ctx → Set
𝔻 : (n : ℕ) → Con n
dangling : {n : ℕ} (Γ : Con n) → Sub ... | {
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{-# OPTIONS --cubical --safe #-}
module Algebra.Construct.Dyck where
open import Prelude
open import Algebra
open import Data.Nat using (_+_)
import Data.Nat.Properties as ℕ
open import Agda.Builtin.Nat using (_-_)
record Bal : Type₀ where
constructor _⟩⟨_
field
left : ℕ
right : ℕ
open Bal public
infix... | {
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module Structure.Operator.Monoid.Invertible where
open import Functional
import Lvl
open import Logic.Propositional
open import Logic.Predicate
open import Structure.Setoid
open import Type
private variable ℓ ℓₗ ℓₑ : Lvl.Level
private variable T : Type{ℓ}
private variable _⨞_ : T → T → Type{ℓₗ}
module _ ⦃ equiv... | {
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module map-compose where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl; cong)
open Eq.≡-Reasoning
open import Function using (_∘_)
open import lists using (List; []; _∷_; map)
postulate
-- 外延性の公理
extensionality : ∀ {A B : Set} {f g : A → B}
→ (∀ (x : A) → f x ≡ g x)
-------... | {
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{-# OPTIONS --guardedness #-}
module induction-ex where
open import Relation.Binary.PropositionalEquality
open import Size
open import Data.Bool
data List (A : Set ) : Set where
[] : List A
_∷_ : A → List A → List A
data Nat : Set where
zero : Nat
suc : Nat → Nat
add : Nat → Nat → Nat
add zero x ... | {
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-- An ATP hint must be used with functions.
-- This error is detected by Syntax.Translation.ConcreteToAbstract.
module ATPBadHint1 where
data Bool : Set where
false true : Bool
{-# ATP hint false #-}
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{-
Given a type A with a UARel and a family B over A,
a SubstRel on B is a family of functions a ≅ a' → B a ≃ B a' path-equal to transport in that family.
Any SubstRel gives rise to a DUARel in which b and b' are related over p when the transport of b along p is
equial to b'.
-}
{-# OPTIONS --safe #-}
module ... | {
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-- Andreas, 2018-10-15, issue #3262 reported by Guillaume Brunerie
--
-- Missing with clauses should be reported close to problem location
-- not just at the type signature of the function which has this problem.
data T : Set where
a b c : T
f : T → Set
f a = ?
f b = ?
f c with c | c
... | _ = ?
-- Should trigger ... | {
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{-# OPTIONS --allow-unsolved-metas #-}
postulate
Nat : Set
Fin : Nat → Set
Foo : (n : Nat) → Fin n → Set
Bar : ∀ {n m} → Foo n m → Set
variable
n : Nat
m : Fin _
k : Foo _ m
l : Foo n m
open import Agda.Builtin.Equality
postulate
goal-type-error : Bar k
foo : Bar _
foo = goal-type-error _ _
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-- Andreas, 2017-07-11, issue #2639 reported by nad
--
-- Unsolvable size constraints were added to the constraint set
-- each time the size solver ran. This lead to exponentially
-- many size constraints.
-- {-# OPTIONS -v tc.size.solve:40 #-}
module Issue2639 (A : Set) where
open import Agda.Builtin.Nat
open impo... | {
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-- Andreas, 2012-04-18
module Issue611 where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
data Bool : Set where
true false : Bool
T : Bool -> Set
T true = {x : Bool} -> Nat
T false = {x : Bool} -> Bool
data D (b : Bool) : Set where
c : T b -> D b
d : D false
d = c {_} true
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module Data.Finitary.Permutation where
open import Data.Nat
open import Data.Fin
open import Relation.Binary.PropositionalEquality as P using (_≡_; _≢_)
open import Function.Inverse as Inv using (Inverse)
import Function.Equality as F
open import Function.LeftInverse using (_LeftInverseOf_)
open import Data.Finitary
o... | {
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{-
This second-order signature was created from the following second-order syntax description:
syntax STLC | Λ
type
N : 0-ary
_↣_ : 2-ary | r30
term
app : α ↣ β α -> β | _$_ l20
lam : α.β -> α ↣ β | ƛ_ r10
theory
(ƛβ) b : α.β a : α |> app (lam(x.b[x]), a) = b[a]
(ƛη) f : α ↣ β |> lam (x. ap... | {
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f : {A B : Set} → (@0 A → B) → A → B
f g x = g x
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-- Andreas, 2017-04-13, issue #2494, reported by identicalsnowflake
-- Consecutive hidden record fields confused the implicit argument insertion
-- due to lack of names in NamedArg.
-- {-# OPTIONS -v tc.lhs:30 #-}
-- {-# OPTIONS -v tc.term.args:100 #-}
postulate
Red Blue : Set
record Colors : Set where
field
... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Metavariables used in the reflection machinery
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
module Reflection.Meta where
import Data.Nat.Propertie... | {
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module Thesis.SIRelBigStep.SemEquiv where
open import Data.Nat
open import Data.Product
open import Relation.Binary.PropositionalEquality
open import Thesis.SIRelBigStep.Syntax public
open import Thesis.SIRelBigStep.OpSem
open import Thesis.SIRelBigStep.DenSem
⟦_⟧Val : ∀ {τ} → Val τ → ⟦ τ ⟧Type
⟦_⟧Env : ∀ {Γ} → ⟦ Γ ... | {
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------------------------------------------------------------------------
-- Applicative functors
------------------------------------------------------------------------
-- Note that currently the applicative functor laws are not included
-- here.
module Category.Applicative where
open import Data.Unit
open import C... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.CommAlgebra.FreeCommAlgebra where
open import Cubical.Algebra.CommAlgebra.FreeCommAlgebra.Base public
open import Cubical.Algebra.CommAlgebra.FreeCommAlgebra.Properties public
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{-# OPTIONS --cubical --safe #-}
module Cubical.Data.Prod.Properties where
open import Cubical.Core.Everything
open import Cubical.Data.Prod.Base
open import Cubical.Data.Sigma
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.HLevels
open import Cubical.Fo... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Example use case for a trie: a wee generic lexer
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe --sized-types #-}
module README.Data.Trie.NonDependent wh... | {
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{-# OPTIONS --without-K --exact-split --safe #-}
open import Fragment.Equational.Theory
module Fragment.Equational.FreeExtension.Properties (Θ : Theory) where
open import Fragment.Algebra.Algebra (Σ Θ) using (Algebra)
open import Fragment.Algebra.Homomorphism (Σ Θ)
open import Fragment.Algebra.Free (Σ Θ)
open import... | {
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{-# OPTIONS --rewriting #-}
postulate
_↦_ : {A : Set} → A → A → Set
idr : {A : Set} {a : A} → a ↦ a
{-# BUILTIN REWRITE _↦_ #-}
record _×_ (A B : Set) : Set where
constructor _,_
field
fst : A
snd : B
postulate
A B C : Set
g : A → B → C
f : A × B → C
f (x , y) = g x y
postulate
D : Set
P ... | {
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{-# OPTIONS --universe-polymorphism #-}
open import Categories.Category
module Categories.Object.Coproduct {o ℓ e} (C : Category o ℓ e) where
open Category C
open import Level
open import Categories.Opposite
import Categories.Object.Product as ProductObject
module Op× = ProductObject op
-- Borrowed from Dan Doel'... | {
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open import Agda.Builtin.Equality
open import Agda.Builtin.Nat
record NoEta : Set where
no-eta-equality
constructor _,_
field fst : Nat
snd : Nat
open NoEta
data ⊥ : Set where
soft-fail : (a : NoEta) (x : Nat) → (fst a , x) ≡ a → ⊥
soft-fail a x () -- Should be yellow (not sure if empty)
loop : ⊥
l... | {
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module NotStrictlyPositive where
data False : Set where
data Not (A : Set) : Set where
not : (A -> False) -> Not A
data Neg (A : Set) : Set where
neg : Not A -> Neg A
data Bad : Set where
bad : Neg Bad -> Bad
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------------------------------------------------------------------------
-- Some properties that hold for Erased do not hold for every
-- topological modality
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Equality
module Erased.Counterexamples... | {
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module Base.Prelude.Bool where
open import Data.Bool using (Bool; true; false; if_then_else_) renaming (_∧_ to _∧ᵖ_; _∨_ to _∨ᵖ_; not to notᵖ)
open import Base.Free using (Free; pure; _>>=_)
𝔹 : (Shape : Set) → (Shape → Set) → Set
𝔹 _ _ = Bool
True : ∀ {S P} → Free S P (𝔹 S P)
True = pure true
False : ∀ {S P} → ... | {
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data D (A : Set) : Set where
c₁ : D A
_ : (@0 A : Set) → D A
_ = λ A → c₁ {A = A}
_ : (@0 A : Set) → D A
_ = λ A → D.c₁ {A = A}
record R (A : Set) : Set where
constructor c₂
field
f : A → A
g : A → A
g x = f (f x)
open R public
_ : (@0 A : Set) → (A → A) → R A
_ = λ A → c₂ {A = A}
_ : (@0 A : Set) ... | {
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{-# OPTIONS --without-K #-}
module function.isomorphism.lift where
open import level
open import equality
open import function.isomorphism.core
-- lifting is an isomorphism
lift-iso : ∀ {i} j (X : Set i) → X ≅ ↑ j X
lift-iso j X = iso lift lower (λ _ → refl) (λ _ → refl)
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{-
Inductive eliminators to establish properties of all finite sets directly
-}
{-# OPTIONS --safe #-}
module Cubical.Data.FinSet.Induction where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Equiv renaming (_∙ₑ_ to _⋆_)
open import Cubical.Foundatio... | {
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module Data.List.Combinatorics where
import Lvl
open import Data
open import Data.List
open import Data.List.Functions
open Data.List.Functions.LongOper
open import Data.Tuple as Tuple using (_⨯_ ; _,_)
open import Data.Tuple.Raiseᵣ as Tuple₊ using (_^_)
import Data.Tuple.Raiseᵣ.Functions as Tuple₊
op... | {
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{-# OPTIONS --rewriting #-}
module _ where
open import Agda.Builtin.Bool
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Rewrite
data D (A : Set) : Set₁ where
c₁ : D A
c₂ : Set → D A
f : {A : Set} → D A → Set
f c₁ = Bool
f (c₂ X) = X
postulate
rew : (A : Set) → c₁ {A} ≡ c₂ A
-- This rewri... | {
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module Tactic.Reflection.Quote where
open import Prelude
open import Builtin.Reflection
open import Builtin.Float
open import Tactic.Reflection.Quote.Class public
open import Tactic.Deriving.Quotable
open import Container.Traversable
--- Instances ---
private
QuoteLit : {A : Set} → (A → Literal) → Quotable A
` ... | {
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-- This combination should not be allowed:
{-# OPTIONS --safe --guardedness --sized-types #-}
-- note that `--safe` turns off `--guardedness` and `--sized-types`,
-- hence `--guardedness --sized-types --safe` works, but does not
-- mean the above combination
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open import Data.Product using ( ∃ ; _×_ )
open import FRP.LTL.RSet.Core using ( RSet ; _[_,_⟩ )
open import FRP.LTL.Time using ( _≤_ )
module FRP.LTL.RSet.Until where
infixr 2 _U_
_U_ : RSet → RSet → RSet
(A U B) t = ∃ λ u → (t ≤ u) × (A [ t , u ⟩) × B u
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open import Data.Product using ( proj₁ ; proj₂ )
open import Data.Sum using ( _⊎_ ; inj₁ ; inj₂ )
open import Relation.Binary.PropositionalEquality using ( refl )
open import Web.Semantic.DL.ABox.Interp using ( ⌊_⌋ ; ind ; _*_ )
open import Web.Semantic.DL.ABox.Interp.Morphism using ( _,_ )
open import Web.Semantic.DL.... | {
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{-# OPTIONS --allow-unsolved-metas #-}
module ExtractDependent where
open import Agda.Builtin.Nat
open import Agda.Builtin.Bool
open import Agda.Builtin.String
apply : (A : Set) -> (B : A -> Set) ->
((x : A) -> B x) -> (a : A) -> B a
apply A B f a = f a
applySameName : (A : Set) -> (A : Set) -> (B : A ->... | {
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module FizzBuzz where
{-# IMPORT Data.Word #-}
{-# IMPORT FizzBuzz #-}
open import Data.Nat
open import IO.Primitive
open import Foreign.Haskell
postulate
ℕ′ : Set
zero′ : ℕ′
suc′ : ℕ′ → ℕ′
{-# COMPILED_TYPE ℕ′ Data.Word.Word32 #-}
{-# COMPILED zero′ 0 #-}
{-# COMPILED suc′ succ #-}
fromℕ : ℕ → ℕ′
fromℕ zer... | {
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--
-- Inspired by a blog post written by Arnaud Bailly
-- https://abailly.github.io/posts/dependently-typed-date.html
--
{-# OPTIONS --without-K #-}
module Date where
open import Data.Nat using (ℕ; zero; suc; _≡ᵇ_; _<_; _≤_; z≤n; s≤s; _≤?_; _<?_)
open import Data.Nat.DivMod using (_%_)
open import Data.Bool using (B... | {
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{-# OPTIONS --cubical --no-import-sorts --no-exact-split --safe #-}
module Cubical.Data.InfNat.Base where
open import Cubical.Data.Nat as ℕ using (ℕ)
open import Cubical.Core.Primitives
data ℕ+∞ : Type₀ where
∞ : ℕ+∞
fin : ℕ → ℕ+∞
suc : ℕ+∞ → ℕ+∞
suc ∞ = ∞
suc (fin n) = fin (ℕ.suc n)
zero : ℕ+∞
zero = fin ℕ.ze... | {
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module MissingTypeSignatureInMutual where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
mutual
pred zero = zero
pred (suc n) = n
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------------------------------------------------------------------------
-- "Basic" infinite grammars
------------------------------------------------------------------------
-- For a larger and possibly more convenient, but equivalent, grammar
-- interface, see Grammar.Infinite.
{-# OPTIONS --guardedness #-}
module... | {
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open import Mockingbird.Forest using (Forest)
-- The Forest Without a Name
module Mockingbird.Problems.Chapter16 {b ℓ} (forest : Forest {b} {ℓ}) where
open import Data.Product using (_×_; _,_; ∃-syntax)
open import Data.Sum using (_⊎_; inj₁; inj₂)
open import Function using (_$_; _⇔_; Equivalence)
open import Relatio... | {
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module Effect where
open import Data.List
open import Data.List.All
open import Data.List.Any
open import Level
open import Relation.Binary.PropositionalEquality hiding ([_])
open import Function
open import Category.Monad
open import Data.Product
open import EffectUtil
open import Membership-equality hiding (_⊆_; set... | {
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-- Andreas, 2021-05-07, issue #5358 reported by ecavallo
-- Do not expand clauses with tactics attached to the target type!
open import Agda.Builtin.Unit
open import Agda.Builtin.Bool
open import Agda.Builtin.Reflection renaming (bindTC to _>>=_)
defaultTo : {A : Set} (x : A) → Term → TC ⊤
defaultTo x goal = do
`x ... | {
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-- Errors should precede warnings in info buffer
-- Reported by nad 2018-11-27
module Issue3416 where
A : Set
A = A
B : Set
B = Set
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module ModuleMacro where
record ⊤
: Set
where
module M where
module N where
postulate
A
: Set
B
: Set
module O
= M
module P
= M
module Q
= P
module R
(x : ⊤)
= N
using (A)
module S
= N
renaming
( A
to A'
; B
to B'
)
y
: ⊤
y
= record {O}
C
: ⊤
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties of operations on the Colist type
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe --sized-types #-}
module Codata.Colist.Properties where
open ... | {
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module Cats.Category.Constructions.Epi where
open import Level
open import Cats.Category.Base
module Build {lo la l≈} (Cat : Category lo la l≈) where
private open module Cat = Category Cat
open Cat.≈-Reasoning
IsEpi : ∀ {A B} → A ⇒ B → Set (lo ⊔ la ⊔ l≈)
IsEpi {A} {B} f = ∀ {C} {g h : B ⇒ C} → g ∘ f ≈ h ∘... | {
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------------------------------------------------------------------------
-- A library for working with dependently typed syntax
-- Nils Anders Danielsson
------------------------------------------------------------------------
-- This library is leaning heavily on two of Conor McBride's papers:
--
-- * Type-Preserving... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Properties that are related to pointwise lifting of binary
-- relations to sigma types and make use of heterogeneous equality
------------------------------------------------------------------------
{-# OPTIONS ... | {
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{-# OPTIONS --rewriting --confluence-check #-}
open import Agda.Builtin.Bool
open import Agda.Builtin.Equality
open import Agda.Builtin.Equality.Rewrite
variable A : Set
postulate
f : (A → A) → Bool
f-id : f {A} (λ x → x) ≡ true
f-const : (c : A) → f (λ x → c) ≡ false
{-# REWRITE f-id #-}
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module ShouldBePi where
data One : Set where
one : One
err1 : One
err1 = \x -> x
err2 : One
err2 = one one
err3 : One
err3 x = x
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module Numeral.Natural.Oper.Modulo.Proofs.Algorithm where
import Lvl
open import Logic
open import Numeral.Natural
open import Numeral.Natural.Oper
open import Numeral.Natural.Oper.Modulo
open import Numeral.Natural.Oper.Proofs
open import Numeral.Natural.Oper.Proofs.Order
open import Numeral.Natural.Relation
open imp... | {
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{-# OPTIONS --without-K --safe #-}
module Categories.Adjoint.Relative where
-- Relative Adjoints, in their biased, level-restricted version
-- In other words, this uses the Hom-Setoid equivalent variant
-- of the adjoint formulation because relative adjoints don't
-- have a natural unit/counit formulation.
-- W... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Setoids.Setoids
open import Functions.Definition
open import Sets.EquivalenceRelations
open import Rings.Definition
module Rings.Divisible.Definition {a b : _} {A : Set a} {S : Setoid {a} {b} A} {_+_ _*_ : A → A → A} (R : Ring ... | {
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module Scratch.Subset where
open import Level renaming (zero to lzero; suc to lsuc)
open import Relation.Unary using (Pred; Satisfiable) renaming (Decidable to Dec₁)
open import Relation.Binary renaming (Decidable to Dec₂)
open import Relation.Binary.PropositionalEquality as Eq using (_≡_ ; _≢_; refl; cong; sym; trans... | {
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{-# OPTIONS --without-K --safe #-}
module Definition.Typed.Consequences.Inversion where
open import Definition.Untyped
open import Definition.Typed
open import Definition.Typed.Properties
open import Definition.Typed.Consequences.Syntactic
open import Definition.Typed.Consequences.Substitution
open import Tools.Pro... | {
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------------------------------------------------------------------------------
-- Totality properties for Tree
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
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------------------------------------------------------------------------
-- A universe for stream programs
------------------------------------------------------------------------
module Stream.Programs where
open import Codata.Musical.Notation renaming (∞ to ∞_)
import Stream as S
open S using (Stream; _≈_; _≺_; hea... | {
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{- Examples by Twan van Laarhoven -}
{-# OPTIONS --rewriting #-}
module _ where
open import Agda.Builtin.Equality
{-# BUILTIN REWRITE _≡_ #-}
const : ∀ {a b} {A : Set a} {B : Set b} → A → B → A
const x _ = x
_∘_ : ∀ {a b c} {A : Set a} {B : A → Set b} {C : {x : A} → B x → Set c}
→ (f : ∀ {x} (y : B x) → C y) (g... | {
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{-# OPTIONS --without-K --rewriting #-}
open import HoTT
open import homotopy.PtdAdjoint
module homotopy.SuspAdjointLoopLadder where
import homotopy.SuspAdjointLoop as A
step : ∀ {i} {X Y Z : Ptd i} (f : Y ⊙→ Z)
→ CommSquareEquiv
((f ⊙∘_) :> ((⊙Susp X ⊙→ Y) → (⊙Susp X ⊙→ Z)))
(⊙Ω-fmap f ⊙∘_)... | {
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{-# OPTIONS --rewriting --without-K #-}
open import Agda.Primitive
open import Prelude
open import GSeTT.Syntax
open import GSeTT.Rules
open import GSeTT.CwF-structure
open import GSeTT.Uniqueness-Derivations
{- Typed syntax for type theory for globular sets -}
module GSeTT.Typed-Syntax where
Ctx : Set₁
Ctx = Σ P... | {
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module Issue15 where
infix 7 _≡_
infixr 5 _∧_
infix 5 ∃
infixr 4 _∨_
data _∨_ (A B : Set) : Set where
inj₁ : A → A ∨ B
inj₂ : B → A ∨ B
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module Category.Comma where
open import Level
open import Data.Product
open import Category.Core
open import Relation.Binary as B using ()
open import Relation.Binary.Indexed
open import Relation.Binary.Indexed.Extra
open import Relation.Binary.PropositionalEquality as PropEq using (_≡_; refl)
_/_ : ∀ {𝒸 ℓ} → (C : ... | {
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{-# OPTIONS --cubical --no-import-sorts #-}
module Utils where -- thing that currently do not belong anywhere and do not have many dependencies
open import Agda.Primitive renaming (_⊔_ to ℓ-max; lsuc to ℓ-suc; lzero to ℓ-zero)
private
variable
ℓ ℓ' ℓ'' : Level
open import Cubical.Foundations.Everything renam... | {
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{-# OPTIONS --allow-unsolved-metas #-}
module _ where
open import Agda.Builtin.Nat
open import Agda.Builtin.List
open import Agda.Builtin.Unit
open import Agda.Builtin.Sigma
_×_ : Set → Set → Set
A × B = Σ A λ _ → B
data Vec (A : Set) : Nat → Set where
[] : Vec A 0
_∷_ : ∀ {n} → A → Vec A n → Vec A (suc n)
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postulate
A : Set
record R : Set where
field
a : A
b : A
b = a
open R
test : A
test = b
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module IsFormula where
open import Formula
data IsFormula : Formula → Set
where
⟨_⟩ : (φ : Formula) → IsFormula φ
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module LC.Parallel where
open import LC.Base
open import LC.Subst
open import LC.Reduction
open import Data.Nat
open import Relation.Binary.Construct.Closure.ReflexiveTransitive
-- parallel β-reduction
infix 3 _β⇒_
data _β⇒_ : Term → Term → Set where
β-var : {n : ℕ} → var n β⇒ var n
β-ƛ : ∀ {M M'} → (M⇒M' :... | {
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------------------------------------------------------------------------------
-- Conversion functions i, j and k.
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
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