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{-# OPTIONS --without-K #-}
open import HoTT
open import cohomology.CofiberSequence
open import cohomology.Exactness
open import cohomology.FunctionOver
open import cohomology.Theory
open import cohomology.ProductRepr
open import cohomology.WedgeCofiber
{- Finite additivity is provable (and in a stronger form) withou... | {
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-- Andreas, 2014-01-17 Issue 1402
-- where clauses after a pointless rewrite
open import Common.Equality
postulate eq : Set1 ≡ Set1
test : Set1
test rewrite eq = bla
where bla = Set
-- should succeed (or maybe alert the user of the pointless rewrite)
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open import SystemT
open import Data.List using ([])
module Examples where
-- λ x . x
ex1 : [] ⊢ base ⟶ base
ex1 = lam (var i0)
-- λ x . λ y . y
ex2 : [] ⊢ base ⟶ base ⟶ base
ex2 = lam (lam (var i0))
-- λ x . λ y . x
ex3 : [] ⊢ base ⟶ base ⟶ base
ex3 = lam (lam (var (iS i0)))
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{-
Counting how many structured finite sets with a given cardinal
https://github.com/EgbertRijke/OEIS-A000001
-}
{-# OPTIONS --safe #-}
module Cubical.Experiments.CountingFiniteStructure where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Data.Nat
open import Cu... | {
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module Types where
import Level
open import Data.Unit as Unit renaming (tt to ∗)
open import Data.List as List
open import Categories.Category using (Category)
open import Function
open import Relation.Binary.PropositionalEquality as PE hiding ([_]; subst)
open import Relation.Binary using (module IsEquivalence; Seto... | {
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-- Simple test to check if constraint solving for injective
-- functions is working.
module Injectivity where
data Nat : Set where
zero : Nat
suc : Nat -> Nat
_+_ : Nat -> Nat -> Nat
zero + m = m
suc n + m = suc (n + m)
{-# BUILTIN NATURAL Nat #-}
{-# BUILTIN ZERO zero #-}
{-# BUILTIN SUC suc #-}
{-# ... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.Data.SumFin.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Data.Empty using (⊥; ⊥-elim) public
open import Cubical.Data.Unit using (tt) renaming (Unit to ⊤) public
open import Cubical.Data.Sum using (_⊎_; inl; inr) public
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module Issue318 where
data Bool : Set where
module A where
data _≤_ : Bool → Bool → Set where
open A hiding (_≤_)
data _≤_ : Bool → Bool → Set where | {
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module NestedProjectRoots where
import Imports.A
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{-# OPTIONS --guardedness-preserving-type-constructors #-}
module TypeConstructorsWhichPreserveGuardedness4 where
open import Common.Coinduction
data Rec (A : ∞ Set) : Set where
fold : ♭ A → Rec A
D : Set
D = Rec (♯ (D → D))
-- _·_ : D → D → D
-- fold f · x = f x
-- ω : D
-- ω = fold (λ x → x · x)
-- Ω : D
-- ... | {
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{-# OPTIONS --cubical --safe #-}
module Class where
open import Cubical.Core.Everything
open import Function.Base using (id; _$_)
private
variable
A B C : Set
ℓ ℓ′ ℓ″ : Level
-- Custom non-dependent definition, since the one in the prelude is too general
_∘_ : {A : Set ℓ} {B : Set ℓ′} {C : Set ℓ″} → (B → ... | {
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{-
The equivalent "goodness" of can w.r.t. the rmerge reduction.
The lemma proved in this file is
can-irr : ∀ {BV} {FV} θ₁ θ₂ q →
CorrectBinding q BV FV →
(distinct' (proj₁ FV) (proj₁ (Dom θ₂))) →
Can q θ₁ ≡ Can q (θ₁ ← θ₂)
That is, the result of the Can function will not change
provided that t... | {
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------------------------------------------------------------------------
-- Properties related to Fin, and operations making use of these
-- properties (or other properties not available in Data.Fin)
------------------------------------------------------------------------
module Data.Fin.Props where
open import Data.... | {
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{-# OPTIONS --safe #-}
module Cubical.Categories.Limits where
open import Cubical.Categories.Limits.Limits public
open import Cubical.Categories.Limits.BinProduct public
open import Cubical.Categories.Limits.BinCoproduct public
open import Cubical.Categories.Limits.Initial public
open import Cubical.Categories.Limits.... | {
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module FOT.FOTC.Program.Mirror.StructurallySmaller.StructurallySmaller where
open import FOTC.Base
open import FOTC.Base.List
open import FOTC.Pro... | {
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open import Oscar.Prelude
open import Oscar.Data.¶
module Oscar.Data.Descender where
-- m ≤ n, counting down from n-1 to m
data Descender⟨_⟩ {a} (A : ¶ → Ø a) (m : ¶) : ¶ → Ø a where
∅ : Descender⟨ A ⟩ m m
_,_ : ∀ {n} → A n → Descender⟨ A ⟩ m n → Descender⟨ A ⟩ m (↑ n)
Vec'⟨_⟩ = λ {a} (A : Ø a) N → Descender⟨ (... | {
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module Ferros.Resource.Untyped where
open import Ferros.Resource.Untyped.Base public
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module Selective.Simulate where
open import Selective.ActorMonad public
open import Selective.SimulationEnvironment
open import Selective.EnvironmentOperations
open import Prelude
open import Data.List.All.Properties using (++⁺)
open import Data.Nat.Properties using (≤-reflexive ; ≤-step)
open import Data.Product usi... | {
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module Oscar.Data.Vec.Core where
open import Data.Vec public using (Vec; []; _∷_)
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module OlderBasicILP.Indirect.Gentzen where
open import OlderBasicILP.Indirect public
-- Derivations, as Gentzen-style natural deduction trees.
mutual
data Tm : Set where
VAR : ℕ → Tm
LAM : Tm → Tm
APP : Tm → Tm → Tm
MULTIBOX : Cx Tm → Tm → Tm
DOWN : Tm → Tm
PAIR : T... | {
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module Luau.Type.ToString where
open import FFI.Data.String using (String; _++_)
open import Luau.Type using (Type; nil; _⇒_; none; any; number; _∪_; _∩_; normalizeOptional)
{-# TERMINATING #-}
typeToString : Type → String
typeToStringᵁ : Type → String
typeToStringᴵ : Type → String
typeToString nil = "nil"
typeToStr... | {
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{-# OPTIONS --allow-unsolved-metas #-}
module fin where
open import Data.Fin hiding (_<_ ; _≤_ )
open import Data.Fin.Properties hiding ( <-trans )
open import Data.Nat
open import logic
open import nat
open import Relation.Binary.PropositionalEquality
-- toℕ<n
fin<n : {n : ℕ} {f : Fin n} → toℕ f < n
fin<n {_} {ze... | {
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module SingleSorted.Context where
-- An attempt to define more structured context
-- that directly support the cartesian structure
data Context : Set where
ctx-empty : Context
ctx-slot : Context
ctx-concat : Context → Context → Context
-- the variables in a context
data var : Context → Set where
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{-# OPTIONS --cubical --safe --guardedness #-}
module Data.PolyP.RecursionSchemes where
open import Function hiding (_⟨_⟩_)
open import Data.Sum
open import Data.Sigma
open import Level
open import Data.Unit
open import Data.Nat
open import Data.Vec.Iterated
open import Data.Empty
open import WellFounded
open import ... | {
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module SystemF.WellTyped where
open import Prelude hiding (id; erase)
open import SystemF.Syntax public
open import SystemF.Substitutions
open import Data.Vec hiding ([_])
open import Data.Vec.Properties
open import Data.Product
infix 4 _⊢_∈_
data _⊢_∈_ {ν n} (Γ : Ctx ν n) : Term ν n → Type ν → Set where
var : (x ... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Foundations.Pointed.Homotopy where
{-
This module defines two kinds of pointed homotopies,
∙∼ and ∙∼P, and proves their equivalence
-}
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.GroupoidLaws
open import Cubical.Foundati... | {
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open import Prelude
open import core
module lemmas-matching where
-- matching produces unique answers for arrows, sums, and products
▸arr-unicity : ∀{ t t2 t3 } →
t ▸arr t2 →
t ▸arr t3 →
t2 == t3
▸arr-unicity MAHole MAHole = refl
▸arr-unicity MAArr MAArr = ref... | {
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-- Reported by Christian Sattler on 2019-12-07
open import Agda.Primitive
postulate
i : Level
X : Set i
mutual
j : Level
j = _
Y : Set j
Y = X
-- WAS: unsolved constraint i = _2
-- SHOULD: succeed with everything solved
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module Warnings where
-- empty rewrite pragma
{-# REWRITE #-}
-- termination checking error
A : Set
A = A
data Nat : Set where
zero : Nat
suc : Nat -> Nat
{-# BUILTIN NATURAL Nat #-}
-- deprecated BUILTIN ZERO
{-# BUILTIN ZERO zero #-}
-- An open goal
g : Set
g = {!!}
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------------------------------------------------------------------------
-- The Agda standard library
--
-- A universe which includes several kinds of "relatedness" for sets,
-- such as equivalences, surjections and bijections
------------------------------------------------------------------------
module Function.Rel... | {
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{-# OPTIONS --cubical --no-sized-types --guardedness --safe #-}
module Issue3564 where
record Stream (A : Set) : Set where
coinductive
field head : A
field tail : Stream A
open Stream
data A : Set where a : A
someA : Stream A
head someA = a
tail someA = someA
-- WAS: termination check failed
-- NOW: OK
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------------------------------------------------------------------------------
-- The gcd is a common divisor
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{... | {
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module Numeral.Natural.Function.GreatestCommonDivisor.Extended where
import Lvl
open import Data
open import Data.Tuple as Tuple using (_⨯_ ; _,_)
open import Logic.Propositional
open import Numeral.Integer as ℤ
open import Numeral.Integer.Oper
open import Numeral.Integer.Proofs hiding (_≤_)
open import Numeral.Natura... | {
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module Issue2229Reexport2 where
open import Issue2229Base public
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module View where
open import Data.Unit
open import Data.Char
open import Data.Maybe
open import Data.Container.Indexed
open import Signature
open import Model
open import IO.Primitive
------------------------------------------------------------------------
postulate
view : Model → IO ⊤
data VtyEvent : Set where... | {
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{- Basic combinators, basic permutations, and their relation -}
module CombPerm where
import Data.Fin as F
--
open import Data.Unit
open import Data.Nat using (ℕ ; zero ; suc ; _+_ ; _>_ )
open import Data.Sum using (inj₁ ; inj₂ ; _⊎_)
open import Data.Vec
open import Function using ( id ) renaming (_∘_ to _○_)
open ... | {
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{-# OPTIONS --cubical --safe #-}
module Container.List.Isomorphism where
open import Prelude
open import Container
open import Container.List
open import Data.Fin
open import Data.List using (tabulate; length ; _!_) renaming (_∷_ to _L∷_; [] to L[]; List to 𝕃)
open import Data.List.Properties
ℒ→𝕃 : List A → 𝕃 A
ℒ... | {
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-- Andreas, 2018-07-21, issue #3161
-- Insert space before brace if preceeded by `-`.
-- (Symmetric case was already fixed in #269).
data Pol : Set where
+ - : Pol
f : {x : Pol} → Set
f {x} = {!x!} -- Split on x here
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{-# OPTIONS --safe #-}
module Cubical.Relation.Nullary.DecidablePropositions where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Equiv renaming (_∙ₑ_ to _⋆_)
open import Cubical.Data.Bool
open import Cubical.Data.Sigma
open import Cubical.Relation.Nul... | {
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-- Andreas, 2011-09-21, reported by Nisse
-- {-# OPTIONS -v tc.lhs.unify:25 #-}
module Issue292-23 where
data ⊤ : Set where
tt : ⊤
data D : (A : Set) → A → Set₁ where
d : (A : Set) (x : A) → D A x
data P : (x : ⊤) → D ⊤ x → Set₁ where
p : (x : ⊤) → P x (d ⊤ x)
Foo : P tt (d ⊤ tt) → Set₁
Foo (p .tt) = Set
-- s... | {
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module Everything where
import Basic
import Category
import Functor
import Nat
import Yoneda
import Adjoint
import Monad
import TAlgebra
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-- Andreas, 2016-07-29, issue #1720 reported by Mietek Bak
postulate
A B : Set
a0 : A
b0 : B
record R (a1 : A) (b1 : B) : Set where
field fa : A
a : A
a = {!!}
field fb : B
b : B
b = {!!}
field f : A
-- Problem:
-- Interaction points are doubled.
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module L.Base.Unit.Core where
-- Import the unit type and its only element tt : ⊤
open import Agda.Builtin.Unit renaming (tt to ⋆) public
⊤-elim : ∀{c} (C : ⊤ → Set c) → C ⋆ → (a : ⊤) → C a
⊤-elim = λ C c a → c
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-- {-# OPTIONS -v tc.cc:12 -v tc.cover.splittree:10 #-}
-- {-# OPTIONS -v tc.cover.strategy:100 -v tc.cover.precomputed:100 #-}
-- {-# OPTIONS -v tc.cover.split.con:20 #-}
module CoverStrategy where
import Common.Level
open import Common.Prelude renaming (Nat to ℕ)
data _∼_ : ℕ → ℕ → Set where
pr : ∀ {n} → suc n ∼ ... | {
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{-# OPTIONS --without-K --safe #-}
-- 'Traditionally', meaning in nLab and in
-- "Lectures on n-Categories and Cohomology" by Baez and Shulman
-- https://arxiv.org/abs/math/0608420
-- (-2)-Categories are defined to be just a single value, with trivial Hom
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{-# OPTIONS --cumulativity #-}
open import Agda.Primitive
postulate
X : Set
P : (A : Set) → A → Set
id : ∀ a (A : Set a) → A → A
works : P (X → X) (id (lsuc lzero) X)
fails : P _ (id (lsuc lzero) X)
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{-# OPTIONS --cubical --safe #-}
module Cubical.HITs.Interval.Base where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
data Interval : Type₀ where
zero : Interval
one : Interval
seg : zero ≡ one
isContrInterval : isContr Interval
isContrInterval = (zero , (λ x → rem x))
where... | {
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-- Andreas, 2012-05-14, issue reported by Nisse
-- {-# OPTIONS -v term:20 #-}
module Issue636 where
open import Common.Coinduction
data ⊥ : Set where
data D : Set where
c : ∞ D → D
d : D
d = c (♯ d)
not-d : D → ⊥
not-d (c x) = not-d (♭ x)
bad : ⊥
bad = not-d d
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module xxx where
open import Agda.Builtin.Unit using (⊤)
open import IO as IO hiding (_>>=_; _>>_)
import IO.Primitive as Primitive
open import hcio as HCIO
main : Primitive.IO ⊤
main = run do
IO.putStrLn "enter file name:"
f ← HCIO.getLine
IO.putStrLn "enter file contents... | {
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{-# OPTIONS --without-K #-}
module GPerm where
-- Definition of a general permutation, and some combinators.
-- This is the 'abstract' view, in terms of functions. Contrast with the
-- concrete view in term of vectors (and restricted to Enumerable sets)
-- In some sense, even better would be to consider 'w... | {
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------------------------------------------------------------------------
-- Definitions of "free in" and "closed", along with some properties
------------------------------------------------------------------------
open import Atom
module Free-variables (atoms : χ-atoms) where
open import Dec
open import Equality.Pr... | {
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{-# OPTIONS --cubical --safe #-}
module README where
--------------------------------------------------------------------------------
-- Section 1: Introduction
--------------------------------------------------------------------------------
-- 0, 1, and 2 types
import Data.Empty using (⊥)
import Data.Unit using (⊤... | {
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-- 2010-10-14
-- {-# OPTIONS -v term:20 #-}
module FakeProjectionsDoNotPreserveGuardedness where
import Common.Level
open import Common.Coinduction
-- Products
infixr 4 _,_
infixr 2 _×_
-- fake product with projections
postulate
_×_ : (A B : Set) → Set
_,_ : {A B : Set}(a : A)(b : B) → A × B
proj₁ : {A B... | {
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-- Export only the experiments that are expected to compile (without
-- any holes)
module Cubical.Experiments.Everything where
open import Cubical.Experiments.Brunerie public
open import Cubical.Experiments.EscardoSIP public
open import Cubical.Experiments.Generic public
open import Cubical.Experiments.NatMinusTwo
ope... | {
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module StreamEnc where
open import Data.Unit hiding (_≤_)
open import Data.Nat
open import Data.Product
open import Data.Sum
open import Relation.Binary.PropositionalEquality as P
open ≡-Reasoning
≤-step : ∀{k n} → k ≤ n → k ≤ suc n
≤-step z≤n = z≤n
≤-step (s≤s p) = s≤s (≤-step p)
pred-≤ : ∀{k n} → suc k ≤ n → k ≤ n... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Equality over container extensions parametrised by some setoid
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Relation.Binary using (Seto... | {
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--{-# OPTIONS --rewriting #-}
--{-# OPTIONS --exact-split #-}
--{-# OPTIONS --show-implicit #-}
--{-# OPTIONS --allow-unsolved-metas #-}
module NaturalDeduction where
open import OscarPrelude
open import Delay
open import Successor
open import Membership
open import DecidableMembership renaming (DecidableMembership t... | {
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open import Level using (Level; _⊔_)
open import Function using (id; case_of_)
open import Data.Nat using (ℕ; suc)
open import Data.Fin using (Fin; suc; zero)
open import Data.Vec as Vec using (Vec) renaming (_∷_ to _,_; [] to ∅)
open import Data.List using (_∷_; [])
open import Data.List as List using (List; _++_) ren... | {
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{-# OPTIONS --copatterns #-}
{-# OPTIONS -v tc.constr.findInScope:15 #-}
-- One-place functors (decorations) on Set
module Control.Bug-Loop where
open import Function using (id; _∘_)
open import Relation.Binary.PropositionalEquality
open ≡-Reasoning
open import Control.Functor
open IsFunctor {{...}}
record IsDeco... | {
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{-# OPTIONS --without-K --rewriting #-}
open import lib.Basics
module lib.types.Empty where
Empty-rec : ∀ {i} {A : Type i} → (Empty → A)
Empty-rec = Empty-elim
⊥-rec : ∀ {i} {A : Type i} → (⊥ → A)
⊥-rec = Empty-rec
Empty-is-prop : is-prop Empty
Empty-is-prop = has-level-in Empty-elim
instance
Empty-level : {n :... | {
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data _≡_ {a} {A : Set a} (x : A) : A → Set a where
refl : x ≡ x
postulate
A : Set
a : A
record Eq (a : A) : Set where
constructor mkEq
field
v : A
p : a ≡ v
open Eq
record S : Set1 where
constructor mkS
field
u : A
e : Eq u
open Eq e public
open S
test : ∀ (b : A) → S
u (test b) = b... | {
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-- Jesper, 2018-11-29: Instances with explicit arguments will never be
-- used, so declaring them should give a warning.
postulate
X : Set
instance _ : Set → X -- this should give a warning
it : {{_ : X}} → X
it {{x}} = x
-- OTOH, this is fine as the instance can be used inside the module
module _ (A : Set) wher... | {
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-- {-# OPTIONS -v tc.cover.split.con:20 #-}
open import Common.Prelude renaming (Nat to ℕ)
open import Common.Equality
infix 3 ¬_
¬_ : Set → Set
¬ P = P → ⊥
-- Decidable relations.
data Dec (P : Set) : Set where
yes : ( p : P) → Dec P
no : (¬p : ¬ P) → Dec P
_≟_ : (m n : ℕ) → Dec (m ≡ n)
zero ≟ zero = y... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.HITs.Susp.Properties where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Path
open import Cubical.Data.B... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Fancy display functions for List-based tables
------------------------------------------------------------------------
{-# OPTIONS --safe --without-K #-}
module Text.Tabular.List where
open import Data.String ... | {
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-- Andreas, Ulf, 2015-06-03
-- Issue 473 was not fixed for records without constructor
record _×_ A B : Set where
constructor _,_
field
fst : A
snd : B
open _×_
data Nat : Set where
zero : Nat
suc : Nat → Nat
data Zero : Nat → Set where
zero : Zero zero
data Zero₂ : Nat → Nat → Set where
zero :... | {
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{-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.Monoid.MorphismProperties where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Equiv.HalfAdjoint
open import Cubical.Foundations.HLevels
o... | {
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module json where
open import lib
open import general-util
data json : Set where
json-null : json
json-raw : rope → json
json-string : string → json
json-nat : nat → json
json-array : 𝕃 json → json
json-object : trie json → json
json-escape-string : string → string
json-escape-string str = 𝕃char-to-str... | {
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-- Andreas, 2017-07-05, issue #2626 raised by cartazio
-- shrunk by gallais
-- There was an assignTerm inspite of
-- dontAssignMetas (issued by checking inequations involving ⊔ˢ)
-- {-# OPTIONS -v tc:45 #-}
{-# OPTIONS --allow-unsolved-metas #-}
module Issue2626 where
open import Agda.Builtin.Equality
open import ... | {
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module Example where
import Level
open import Signature
open import Function
open import Data.Empty
open import Data.Unit
open import Data.Nat
open import Data.Fin
open import Data.Product as Prod renaming (Σ to ⨿)
open import Data.Sum as Sum
open import Relation.Nullary
open import Relation.Unary hiding (_⇒_)
open im... | {
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open import Prelude
open import Nat
open import core
module binders-disjoint-checks where
-- these are fairly mechanical lemmas that show that the
-- judgementally-defined binders-disjoint is really a type-directed
-- function
mutual
lem-bdσ-lam : ∀{σ x τ d} → binders-disjoint-σ σ (·λ_[_]_ x τ d) → binder... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Left inverses
------------------------------------------------------------------------
module Function.LeftInverse where
open import Data.Product
open import Level
import Relation.Binary.EqReasoning as EqReason... | {
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-- Basic intuitionistic modal logic S4, without ∨, ⊥, or ◇.
-- Canonical model equipment for Kripke-style semantics.
module BasicIS4.Equipment.KripkeDyadicCanonical where
open import BasicIS4.Syntax.Common public
module Syntax
(_⊢_ : Cx² Ty Ty → Ty → Set)
(mono²⊢ : ∀ {A Π Π′} → Π ⊆² Π′ → Π ⊢ A → Π′ ⊢ A... | {
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{-
Definition of the Klein bottle as a HIT
-}
{-# OPTIONS --cubical --safe #-}
module Cubical.HITs.KleinBottle.Properties where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundation... | {
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-- An ATP hint must be used with functions.
-- This error is detected by TypeChecking.Rules.Decl.
module ATPBadHint2 where
data Bool : Set where
false true : Bool
{-# ATP hint Bool #-}
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-- Instances of semantic kits
module Semantics.Substitution.Instances where
open import Syntax.Types
open import Syntax.Context renaming (_,_ to _,,_)
open import Syntax.Terms
open import Syntax.Substitution.Kits
open import Syntax.Substitution.Instances
open import Semantics.Types
open import Semantics.Context
open... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- A larger example for sublists (propositional case):
-- Simply-typed lambda terms with globally unique variables
-- (both bound and free ones).
---------------------------------------------------------------------... | {
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{-# OPTIONS --rewriting #-}
module Properties.TypeNormalization where
open import Luau.Type using (Type; Scalar; nil; number; string; boolean; never; unknown; _⇒_; _∪_; _∩_)
open import Luau.Subtyping using (Tree; Language; ¬Language; function; scalar; unknown; left; right; function-ok₁; function-ok₂; function-err; f... | {
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-- Soundness proofs of structural lemmas and substitution
module Semantics.Substitution.Soundness where
open import Syntax.Types
open import Syntax.Context renaming (_,_ to _,,_)
open import Syntax.Terms
open import Syntax.Substitution.Kits
open import Syntax.Substitution.Instances
open import Syntax.Substitution.Lem... | {
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module Category.Monad.Maybe.Typeclass where
open import Category.Monad
open import Data.Maybe
record MaybeMonad (M : Set → Set) : Set₁ where
field
no : ∀ {A} → M A
yes : ∀ {A} → A → M A
open MaybeMonad
maybe-monad-ops : MaybeMonad Maybe
no maybe-monad-ops = nothing
yes maybe-monad-ops = just
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module Lib.Nat where
open import Lib.Bool
open import Lib.Logic
open import Lib.Id
data Nat : Set where
zero : Nat
suc : Nat -> Nat
{-# BUILTIN NATURAL Nat #-}
{-# BUILTIN ZERO zero #-}
{-# BUILTIN SUC suc #-}
infixr 50 _*_
infixr 40 _+_
_+_ : Nat -> Nat -> Nat
zero + m = m
suc n + m = suc (n + m)
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{-# OPTIONS --without-K --safe #-}
module Util.Relation.Binary.LogicalEquivalence where
open import Relation.Binary using (IsEquivalence ; Setoid)
open import Util.Prelude
private
variable
α β γ : Level
A B C : Set α
infix 4 _↔_
record _↔_ (A : Set α) (B : Set β) : Set (α ⊔ℓ β) where
field
forth... | {
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module Categories.Families where
open import Library
open import Categories
open Cat
Fam : Set → Cat
Fam I = record {
Obj = I → Set;
Hom = λ A B → ∀ {i} → A i → B i;
iden = id;
comp = λ f g → f ∘ g;
idl = refl;
idr = refl;
ass = refl}
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-- Functors on Set
module Control.Functor where
open import Function using (id; flip) renaming (_∘′_ to _∘_)
open import Relation.Binary.PropositionalEquality
open ≡-Reasoning
-- Operations of a functor.
module T-FunctorOps (F : Set → Set) where
-- Type of the map function.
T-map = ∀ {A B} → (A → B) → F A → F... | {
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module Homotopy where
infixr 20 _◎_
open import Data.Product
------------------------------------------------------------------------------
-- Level 0
-- Start with this set and its elements
data B : Set where
ZERO : B
ONE : B
PLUS : B → B → B
TIMES : B → B → B
-----------------------------------------... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Groups.Definition
open import Functions.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import LogicalFormulae
open import Setoids.Subset
open import Setoids.Setoids
open import Setoids.Orders.Partial.Definition
open import Field... | {
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module UniDB.Morph.StarPrime where
open import UniDB.Spec
open import UniDB.Morph.Depth
mutual
data Star* (Ξ : MOR) : MOR where
refl : {γ : Dom} → Star* Ξ γ γ
incl : {γ₁ γ₂ : Dom} (ξs : Star+ Ξ γ₁ γ₂) → Star* Ξ γ₁ γ₂
data Star+ (Ξ : MOR) : MOR where
step : {γ₁ γ₂ γ₃ : Dom} (ξs : Star* Ξ γ₁ γ₂) (ξ : Ξ... | {
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-- Andreas, 2015-12-28, issue reported by effectfully
-- {-# OPTIONS -v tc.data.fits:15 -v tc.conv.sort:30 -v tc.conv.nat:30 #-}
open import Common.Level
postulate
fun : Level → Level
data Test : Set (fun lzero) where
c : Test → Test
-- The primitive lzero in argument of neutral is what matters here.
-- Agda re... | {
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-- 2014-04-06 Andreas, issue reported by flickyfrans
-- {-# OPTIONS --show-implicit -v tc.section.apply:60 #-}
open import Common.Level renaming (lsuc to suc)
record RawMonad {α β : Level} (M : {γ : Level} → Set γ → Set γ) : Set (suc (α ⊔ β)) where
infixl 1 _>>=_
field
return' : {A : Set α} → A → M A
_>>=... | {
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------------------------------------------------------------------------
-- The Agda standard library
--
-- Some properties of reflexive closures
------------------------------------------------------------------------
{-# OPTIONS --safe --without-K #-}
module Relation.Binary.Construct.Closure.Reflexive.Properties wh... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Functions.Definition
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import LogicalFormulae
open import Sets.EquivalenceRelations
module Setoids.Setoids where
record Setoid {a} {b} (A : Set a) : Set (a ⊔ lsuc b) where
infix 1 _∼_
fiel... | {
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-- Andreas, 2012-06-30, case reported by Noam Zeilbereger
module Issue670 where
infix 4 _≡_
data _≡_ {A : Set} (x : A) : A → Set where
refl : x ≡ x
data Nat : Set where
zero : Nat
suc : Nat → Nat
{-# BUILTIN NATURAL Nat #-}
{-# BUILTIN SUC suc #-}
{-# BUILTIN ZERO zero #-}
record T : Set where
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module ConsoleLib where
open import NativeIO public
open import SizedIO.Console public hiding (main) renaming (translateIOConsole to run)
open import Size
open import SizedIO.Base
open import Data.List
WriteString : (s : String) → IOConsole ∞ Unit
WriteString s = Exec (putStrLn s)
GetLine : IOConsole ∞ String
GetLi... | {
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-- Andreas, 2014-08-30, reported by asr
-- All of the following corecursive functions from Data.Stream
-- should pass the termination checker.
{-# OPTIONS --cubical-compatible --guardedness #-}
-- {-# OPTIONS -v term:20 #-}
open import Common.Coinduction
open import Common.Prelude renaming (Nat to ℕ) hiding (_∷_; map... | {
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{-# OPTIONS --safe #-}
module Definition.Conversion.Symmetry where
open import Definition.Untyped
open import Definition.Typed
open import Definition.Typed.Properties
open import Definition.Conversion
open import Definition.Conversion.Stability
open import Definition.Conversion.Soundness
open import Definition.Conver... | {
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{-# OPTIONS --safe --warning=error --without-K #-}
open import LogicalFormulae
open import Functions.Definition
open import Functions.Lemmas
open import Numbers.Naturals.Semiring
open import Numbers.Naturals.Order
open import Numbers.Naturals.Order.Lemmas
open import Sets.Cardinality.Finite.Definition
open import Semi... | {
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{-# OPTIONS --safe #-}
module Cubical.Algebra.Ring.DirectProd where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.HLevels
open import Cubical.Data.Sigma
open import Cubical.Algebra.Ring.Base
private
variable
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{-# OPTIONS --safe --warning=error --without-K #-}
open import Agda.Primitive using (Level; lzero; lsuc; _⊔_)
open import LogicalFormulae
open import Sets.EquivalenceRelations
open import Setoids.Setoids
module Setoids.Union.Definition {a b : _} {A : Set a} (S : Setoid {a} {b} A) where
open Setoid S
open Equivalence... | {
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{-# OPTIONS --cubical --safe #-}
module Cubical.HITs.Everything where
import Cubical.HITs.Cylinder
import Cubical.HITs.Hopf
import Cubical.HITs.Interval
import Cubical.HITs.Ints.BiInvInt
import Cubical.HITs.Ints.DeltaInt
import Cubical.HITs.Ints.HAEquivInt
import Cubical.HITs.Ints.IsoInt
import Cubical.HITs.Ints.QuoIn... | {
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{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# OPTIONS --without-K #-}
module FOT.Common.FOL.Existential.RequiredWitness where
-- We need to use the existential witness in some proofs based on the
-- non-empty domain ... | {
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