id stringlengths 27 136 | text stringlengths 4 1.05M |
|---|---|
algebraic-stack_agda0000_doc_11416 | -- {-# OPTIONS --show-implicit --show-irrelevant #-}
module Data.QuadTree.FoldableProofs.FoldableProof where
open import Haskell.Prelude renaming (zero to Z; suc to S)
open import Data.Logic
open import Data.QuadTree.Implementation.Definition
open import Data.QuadTree.Implementation.ValidTypes
open import Data.QuadTre... |
algebraic-stack_agda0000_doc_11417 | open import Nat
open import Prelude
open import List
open import contexts
open import core
-- This file is a glorious testament to all of agda's greatest strengths -
-- a beautiful work that will shine brightly throughout the ages and instill
-- hope for the future in many generations to come. May I never use any oth... |
algebraic-stack_agda0000_doc_11418 | {-# OPTIONS --cubical --no-import-sorts --safe --experimental-lossy-unification #-}
module Cubical.ZCohomology.Groups.Wedge where
open import Cubical.ZCohomology.Base
open import Cubical.ZCohomology.GroupStructure
open import Cubical.ZCohomology.Properties
open import Cubical.Foundations.HLevels
open import Cubical.Fo... |
algebraic-stack_agda0000_doc_11419 | ------------------------------------------------------------------------
-- The Agda standard library
--
-- Consequences of a monomorphism between group-like structures
------------------------------------------------------------------------
-- See Data.Nat.Binary.Properties for examples of how this and similar
-- mod... |
algebraic-stack_agda0000_doc_11420 | {-# OPTIONS --without-K --safe #-}
module Loop.Bundles where
open import Algebra.Core
open import Relation.Binary
open import Level
open import Loop.Structures
open import Algebra.Bundles
open import Algebra.Structures
record LeftBolLoop c ℓ : Set (suc (c ⊔ ℓ)) where
field
Carrier : Set c
_≈_ : Rel Ca... |
algebraic-stack_agda0000_doc_11421 | ------------------------------------------------------------------------
-- Support for reflection
------------------------------------------------------------------------
{-# OPTIONS --without-K --safe #-}
open import Equality
module TC-monad
{reflexive} (eq : ∀ {a p} → Equality-with-J a p reflexive) where
impor... |
algebraic-stack_agda0000_doc_11422 | ------------------------------------------------------------------------
-- The Agda standard library
--
-- The irrelevance axiom
------------------------------------------------------------------------
module Irrelevance where
import Level
------------------------------------------------------------------------
-- ... |
algebraic-stack_agda0000_doc_11423 | open import Agda.Builtin.Nat
open import Agda.Builtin.Bool
test1 : Nat → Nat
test1 zero = 0
test1 (suc zero) = 1
test1 (suc n) = {!n!}
test2 : Nat → Nat → Nat
test2 zero zero = zero
test2 zero (suc y) = y
test2 x y = {!x!}
test3 : Bool → Bool → Bool → Bool
test3 true true true = true
test3 x ... |
algebraic-stack_agda0000_doc_9872 | -- WARNING: This file was generated automatically by Vehicle
-- and should not be modified manually!
-- Metadata
-- - Agda version: 2.6.2
-- - AISEC version: 0.1.0.1
-- - Time generated: ???
{-# OPTIONS --allow-exec #-}
open import Vehicle
open import Vehicle.Data.Tensor
open import Data.Rational as ℚ using (ℚ)
op... |
algebraic-stack_agda0000_doc_9873 | module AgdaCheatSheet where
open import Level using (Level)
open import Data.Nat
open import Data.Bool hiding (_<?_)
open import Data.List using (List; []; _∷_; length)
-- https://alhassy.github.io/AgdaCheatSheet/CheatSheet.pdf
{-
------------------------------------------------------------------------------
-- depe... |
algebraic-stack_agda0000_doc_9874 | module Issue1486 where
open import Common.Prelude
postulate
QName : Set
{-# BUILTIN QNAME QName #-}
primitive
primShowQName : QName -> String
main : IO Unit
main = putStrLn (primShowQName (quote main))
|
algebraic-stack_agda0000_doc_9875 | -- Andreas, 2014-10-05, issue reported by Stevan Andjelkovic
{-# OPTIONS --cubical-compatible #-}
postulate
IO : Set → Set
record ⊤ : Set where
constructor tt
record Container : Set₁ where
field
Shape : Set
Position : Shape → Set
open Container public
data W (A : Set) (B : A → Set) : Set where
... |
algebraic-stack_agda0000_doc_9876 | open import Coinduction using ( ∞ )
open import Data.ByteString using ( ByteString ; strict ; lazy )
open import Data.String using ( String )
module System.IO.Primitive where
infixl 1 _>>=_
-- The Unit type and its sole inhabitant
postulate
Unit : Set
unit : Unit
{-# COMPILED_TYPE Unit () #-}
{-# COMPILED unit... |
algebraic-stack_agda0000_doc_9877 | ------------------------------------------------------------------------
-- The Agda standard library
--
-- Base definitions for the left-biased universe-sensitive functor and
-- monad instances for These.
--
-- To minimize the universe level of the RawFunctor, we require that
-- elements of B are "lifted" to a copy of... |
algebraic-stack_agda0000_doc_9878 | open import Data.Sum
open import Data.Fin
open import Data.Maybe
open import Signature
module MixedTest (Σ : Sig) (D : Set) where
-- Δ : Sig
-- Δ = record { ∥_∥ = D ; ar = λ x → Fin 1 }
mutual
data Term : Set where
cons : ⟪ Σ ⟫ (Term ⊎ CoTerm) → Term
record CoTerm : Set where
coinductive
field destr... |
algebraic-stack_agda0000_doc_9879 | {-# OPTIONS --safe --cubical #-}
module Erased-cubical.Cubical-again where
open import Agda.Builtin.Cubical.Path
open import Erased-cubical.Erased public
-- Code defined using --erased-cubical can be imported and used by
-- regular Cubical Agda code.
_ : {A : Set} → A → ∥ A ∥
_ = ∣_∣
-- The constructor trivialᶜ i... |
algebraic-stack_agda0000_doc_9880 | -- 2015-05-05 Bad error message
_=R_ : Rel → Rel → Set
R =R S : (R ⊆ S) × (S ⊆ R) -- here is a typo, : instead of =
ldom : Rel → Pred
ldom R a = ∃ λ b → R a b
-- More than one matching type signature for left hand side ldom R a
-- it could belong to any of: ldom R
|
algebraic-stack_agda0000_doc_9881 | module Data.Finitude.FinType where
open import Relation.Binary.PropositionalEquality as P using (_≡_)
open import Data.Nat as ℕ
open import Data.Fin as Fin using (Fin; #_)
open import Data.Finitude
open import Function.Equality using (_⟨$⟩_)
open import Function.Injection as Inj using (Injective)
open import Function.I... |
algebraic-stack_agda0000_doc_9882 | {-# OPTIONS --without-K #-}
open import lib.Basics
open import lib.types.Group
open import lib.types.Bool
open import lib.types.Nat
open import lib.types.Pi
open import lib.types.Sigma
open import lib.groups.Homomorphisms
open import lib.groups.Lift
open import lib.groups.Unit
module lib.groups.GroupProduct where
{-... |
algebraic-stack_agda0000_doc_9883 |
postulate
f : {A B : Set₁} (C : Set) → C → C
module _ (A B C : Set) where
test : Set
test = {!!}
|
algebraic-stack_agda0000_doc_9884 | module _ where
module A where
infix 2 c
infix 1 d
syntax c x = x ↑
syntax d x y = x ↓ y
data D : Set where
● : D
c : D → D
d : D → D → D
module B where
syntax d x y = x ↓ y
data D : Set where
d : D → D → D
open A
open B
rejected : A.D
rejected = ● ↑ ↓ ●
|
algebraic-stack_agda0000_doc_9885 | {-# NON_TERMINATING #-}
mutual
data D : Set where
c : T₁ → D
T₁ : Set
T₁ = T₂
T₂ : Set
T₂ = T₁ → D
|
algebraic-stack_agda0000_doc_9886 | {-# OPTIONS --safe #-}
module Cubical.Algebra.Polynomials.Multivariate.Base where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Data.Nat renaming (_+_ to _+n_)
open import Cubical.Data.Vec
open import Cubical.Algebra.Ring
open import Cubical.Algebra.CommRing
pri... |
algebraic-stack_agda0000_doc_9887 | ------------------------------------------------------------------------
-- The syntax of, and a type system for, the untyped λ-calculus with
-- constants
------------------------------------------------------------------------
module Lambda.Syntax where
open import Codata.Musical.Notation
open import Data.Nat
open i... |
algebraic-stack_agda0000_doc_11808 | {-# OPTIONS --without-K #-}
open import Base
open import HLevel
module Homotopy.Extensions.ToPropToConstSet {i}
{A B : Set i} ⦃ B-is-set : is-set B ⦄
(f : A → B) (f-is-const : ∀ a₁ a₂ → f a₁ ≡ f a₂) where
open import Homotopy.Truncation
open import Homotopy.Skeleton
private
skel : Set i
skel = π₀ ... |
algebraic-stack_agda0000_doc_11809 | -- The ATP pragma with the role <axiom> can be used with postulates.
module ATPAxiomPostulates where
postulate
D : Set
zero : D
succ : D → D
N : D → Set
postulate
zN : N zero
sN : ∀ {n} → N n → N (succ n)
{-# ATP axiom zN #-}
|
algebraic-stack_agda0000_doc_11810 | {-# OPTIONS --without-K --safe #-}
module Tools.List where
open import Data.List public using (List; []; _∷_)
module L where
open import Data.List public
|
algebraic-stack_agda0000_doc_11811 | ------------------------------------------------------------------------------
-- Conversion rules for the greatest common divisor
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-univer... |
algebraic-stack_agda0000_doc_11812 | -- Andreas, 2019-06-25, issue #3855 reported by nad
-- Constraint solver needs to respect erasure.
open import Agda.Builtin.Bool
module _ where
record RB (b : Bool) : Set where
bPar : Bool
bPar = b
myBPar : (@0 b : Bool) → RB b → Bool
myBPar b r = RB.bPar {b = {!b!}} r -- should be rejected
|
algebraic-stack_agda0000_doc_11813 | {-# OPTIONS --cubical #-}
module Type.Cubical.Quotient where
open import Functional
import Lvl
open import Structure.Type.Identity
open import Type.Cubical
open import Type.Cubical.Path.Equality
open import Type
open import Syntax.Function
private variable ℓ ℓₗ : Lvl.Level
private variable T A B : Type{ℓ}
priva... |
algebraic-stack_agda0000_doc_11814 | -- Solver for Category
{-# OPTIONS --without-K --safe #-}
open import Categories.Category
module Experiment.Categories.AnotherSolver.Category
{o ℓ e} (𝒞 : Category o ℓ e) where
open import Level
open import Relation.Binary using (Rel)
import Function.Base as Fun
open import Categories.Functor renaming (id to id... |
algebraic-stack_agda0000_doc_11815 | module Luau.TypeNormalization where
open import Luau.Type using (Type; nil; number; string; boolean; never; unknown; _⇒_; _∪_; _∩_)
-- Operations on normalized types
_∪ᶠ_ : Type → Type → Type
_∪ⁿˢ_ : Type → Type → Type
_∩ⁿˢ_ : Type → Type → Type
_∪ⁿ_ : Type → Type → Type
_∩ⁿ_ : Type → Type → Type
-- Union of functio... |
algebraic-stack_agda0000_doc_11816 | -- Andreas, 2013-10-21
-- There was a bug in Rules/Builtin such that NATEQUALS' equations
-- would be checked at type Nat instead of Bool.
-- This bug surfaced only because of today's refactoring in Conversion,
-- because then I got a strange unsolved constraint true == true : Nat.
module NatEquals where
import Comm... |
algebraic-stack_agda0000_doc_11817 | {-# OPTIONS --cubical --safe #-}
module Data.List.Sugar where
open import Data.List.Base
open import Prelude
[_] : A → List A
[ x ] = x ∷ []
pure : A → List A
pure = [_]
_>>=_ : List A → (A → List B) → List B
_>>=_ = flip concatMap
_>>_ : List A → List B → List B
xs >> ys = xs >>= const ys
_<*>_ : List (A → B) →... |
algebraic-stack_agda0000_doc_11818 | {-# OPTIONS --cubical --safe --postfix-projections #-}
module Data.Dyck.Payload where
open import Prelude
open import Data.Nat using (_+_)
open import Data.Vec.Iterated using (Vec; _∷_; []; foldlN; head)
private
variable
n : ℕ
--------------------------------------------------------------------------------
--... |
algebraic-stack_agda0000_doc_11819 | -- Andreas, 2019-11-08, issue #4154 reported by Yashmine Sharoda.
-- Warn if a `renaming` clause clashes with an exported name
-- (that is not mentioned in a `using` clause).
module _ where
module M where
postulate
A B : Set
-- These produce warnings (#4154):
module N = M renaming (A to B)
open M renaming (A... |
algebraic-stack_agda0000_doc_11820 | {-# OPTIONS --safe #-}
module Issue2442-postulate where
postulate
A : Set
|
algebraic-stack_agda0000_doc_11821 | {-# OPTIONS --without-K #-}
module FT-Nat where
open import Data.Empty
open import Data.Unit
open import Data.Nat renaming (_⊔_ to _⊔ℕ_)
open import Data.Sum renaming (map to _⊎→_)
open import Data.Product
import Data.Fin as F
open import Data.Vec
import Data.List as L
open import Function renaming (_∘_ to _○_)
open ... |
algebraic-stack_agda0000_doc_11822 | -- Andreas, 2016-12-31, re issue #1976
-- Allow projection pattern disambiguation by parameters
{-# OPTIONS --allow-unsolved-metas #-}
postulate
A B : Set
module M (_ : Set) where
record R : Set₂ where
field
F : Set₁
open R public
module Succeeds where
open M _
open M B
test : M.R B
F tes... |
algebraic-stack_agda0000_doc_11823 | module 747Connectives where
-- Library
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; refl)
open Eq.≡-Reasoning
open import Data.Nat using (ℕ)
open import Function using (_∘_)
-- Copied from 747Isomorphism.
postulate
extensionality : ∀ {A B : Set} {f g : A → B}
→ (∀ (x : A) → f x ≡ g x... |
algebraic-stack_agda0000_doc_9504 | module functions where
open import level
open import eq
open import product
{- Note that the Agda standard library has an interesting generalization
of the following basic composition operator, with more dependent typing. -}
_∘_ : ∀{ℓ ℓ' ℓ''}{A : Set ℓ}{B : Set ℓ'}{C : Set ℓ''} →
(B → C) → (A → B) → (A → C)... |
algebraic-stack_agda0000_doc_9505 | {-# OPTIONS --without-K --exact-split --allow-unsolved-metas #-}
module 06-universes where
import 05-identity-types
open 05-identity-types public
-- Section 6.3 Pointed types
-- Definition 6.3.1
UU-pt : (i : Level) → UU (lsuc i)
UU-pt i = Σ (UU i) (λ X → X)
type-UU-pt : {i : Level} → UU-pt i → UU i
type-UU-pt = p... |
algebraic-stack_agda0000_doc_9506 | module PatternSynonymMutualBlock where
data D : Set where
c : D
mutual
pattern p = c
|
algebraic-stack_agda0000_doc_9507 | {-# OPTIONS --without-K --safe #-}
module Categories.Category.CartesianClosed.Properties where
open import Level
open import Data.Product using (Σ; _,_; Σ-syntax; proj₁; proj₂)
open import Categories.Category
open import Categories.Category.CartesianClosed
module _ {o ℓ e} {𝒞 : Category o ℓ e} (𝓥 : CartesianClose... |
algebraic-stack_agda0000_doc_9508 | ------------------------------------------------------------------------------
-- The gcd program is correct
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-... |
algebraic-stack_agda0000_doc_9509 | -- Andreas, 2013-05-02 This ain't a bug, it is a feature.
-- {-# OPTIONS -v scope.name:10 #-}
module Issue836 where
open import Common.Equality
module M where
record R : Set₁ where
field
X : Set
open M using (R)
X : R → Set
X = R.X
-- The open directive did not mention the /module/ R, so (I think
-- t... |
algebraic-stack_agda0000_doc_9510 | module AnyBoolean where
open import Data.Bool
open import Data.Nat
open import Data.List hiding (any)
open import Relation.Binary.PropositionalEquality
even : ℕ → Bool
even zero = true
even (suc zero) = false
even (suc (suc n)) = even n
test-6-even : even 6 ≡ true
test-6-even = refl
odd : ℕ → Bool
odd zero = false
o... |
algebraic-stack_agda0000_doc_9511 | ------------------------------------------------------------------------------
-- Definition of the gcd of two natural numbers using the Euclid's algorithm
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-... |
algebraic-stack_agda0000_doc_9512 | {-# OPTIONS --without-K #-}
module Interval where
open import Pitch
open import Data.Bool using (Bool; true; false; _∨_; _∧_; not; if_then_else_)
open import Data.Integer using (+_; _-_; sign; ∣_∣)
open import Data.Fin using (toℕ)
open import Data.Nat using (ℕ; _≡ᵇ_)
open import Data.Nat.DivMo... |
algebraic-stack_agda0000_doc_9513 | ------------------------------------------------------------------------------
-- All the LTC-PCF modules
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymorphism #-}
{-# O... |
algebraic-stack_agda0000_doc_9514 |
module Tactic.Nat where
open import Prelude
open import Tactic.Nat.Generic (quote _≤_) (quote id) (quote id) public
{-
All tactics know about addition, multiplication and subtraction
of natural numbers, and can prove equalities and inequalities (_<_).
The available tactics are:
* auto
Prove an equation or i... |
algebraic-stack_agda0000_doc_9515 | module cantor where
data Empty : Set where
data One : Set where
one : One
data coprod (A : Set1) (B : Set1) : Set1 where
inl : ∀ (a : A) -> coprod A B
inr : ∀ (b : B) -> coprod A B
postulate exmid : ∀ (A : Set1) -> coprod A (A -> Empty)
data Eq1 {A : Set1} (x : A) : A -> Set1 where
refle... |
algebraic-stack_agda0000_doc_9516 | ------------------------------------------------------------------------
-- Precedence-correct expressions
------------------------------------------------------------------------
module Mixfix.Expr where
open import Data.Vec using (Vec)
open import Data.List using (List; []; _∷_)
open import Data.List.Membership.Pr... |
algebraic-stack_agda0000_doc_9517 | {-# OPTIONS --cubical --no-import-sorts --safe #-}
module Cubical.Algebra.Semigroup.Subsemigroup where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.HLevels
open import Cubical.Data.Sigma
open import Cubical.Algebra
open import Cubical.Algebra.Semigroup.Mo... |
algebraic-stack_agda0000_doc_9518 | {-# OPTIONS --safe --experimental-lossy-unification #-}
module Cubical.ZCohomology.CohomologyRings.Unit where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Function
open import Cubical.Foundations.Isomorphism
open import Cubical.Data.Nat renaming (_+_ to _+n_ ; _·_ to _·n_)
open import Cubic... |
algebraic-stack_agda0000_doc_9519 | -- Andreas, 2016-12-30, issue #1886
-- Make sure we do not duplicate types of parameters.
-- {-# OPTIONS --allow-unsolved-metas #-}
-- {-# OPTIONS -v tc.data:40 -v scope.data.def:40 -v tc.decl:10 -v tc:20 #-}
data D {A : Set} (x y : {!!}) : Set where
-- Expected: only one type and one sort meta.
|
algebraic-stack_agda0000_doc_9904 | module New.FunctionLemmas where
open import New.Changes
module BinaryValid
{A : Set} {{CA : ChAlg A}}
{B : Set} {{CB : ChAlg B}}
{C : Set} {{CC : ChAlg C}}
(f : A → B → C) (df : A → Ch A → B → Ch B → Ch C)
where
binary-valid-preserve-hp =
∀ a da (ada : valid a da)
b db (bdb : valid b db)
→ ... |
algebraic-stack_agda0000_doc_9905 | {-# OPTIONS --cubical --safe --postfix-projections #-}
module Relation.Nullary.Omniscience where
open import Prelude
open import Relation.Nullary.Decidable
open import Relation.Nullary.Decidable.Properties
open import Relation.Nullary.Decidable.Logic
open import Relation.Nullary
open import Data.Bool using (bool)
pr... |
algebraic-stack_agda0000_doc_9906 | -- Andreas, 2017-06-20, issue #2613, reported by Jonathan Prieto.
-- Regression introduced by fix of #2458 (which is obsolete since #2403)
module _ where
open import Agda.Builtin.Nat
module Prop' (n : Nat) where
data Prop' : Set where
_∧_ _∨_ : Prop' → Prop' → Prop'
open Prop' zero
data DView : Prop' → Set ... |
algebraic-stack_agda0000_doc_9907 | module #11 where
{-
Show that for any type A, we have ¬¬¬A → ¬A.
-}
open import Data.Empty
open import Relation.Nullary
tripleNeg : ∀{x}{A : Set x} → ¬ (¬ (¬ A)) → ¬ A
tripleNeg = λ z z₁ → z (λ z₂ → z₂ z₁)
|
algebraic-stack_agda0000_doc_9908 | {-# OPTIONS --safe #-}
module Cubical.Data.Vec where
open import Cubical.Data.Vec.Base public
open import Cubical.Data.Vec.Properties public
open import Cubical.Data.Vec.NAry public
open import Cubical.Data.Vec.OperationsNat public
|
algebraic-stack_agda0000_doc_9909 | ------------------------------------------------------------------------------
-- Properties related with lists of natural numbers
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-univer... |
algebraic-stack_agda0000_doc_9910 | -- a hodge-podge of tests
module Test where
import Test.Class
import Test.EquivalenceExtensionṖroperty
import Test.EquivalenceṖroperty
import Test.EquivalentCandidates
import Test.EquivalentCandidates-2
import Test.Factsurj3
import Test.Functor -- FIXME doesn't work with open import Everything
import Test.ProblemWi... |
algebraic-stack_agda0000_doc_9911 |
{-# OPTIONS --cubical #-}
open import Agda.Builtin.Cubical.Path using (_≡_)
open import Agda.Builtin.Sigma using (Σ; fst; _,_)
postulate
Is-proposition : Set → Set
subst : ∀ {A : Set} (P : A → Set) {x y} → x ≡ y → P x → P y
Proposition : Set₁
Proposition = Σ _ Is-proposition
data _/_ (A : Set) (R : A ... |
algebraic-stack_agda0000_doc_9912 | module _ where
module A where
infix 0 c
syntax c x = + x
data D₁ : Set where
b : D₁
c : D₁ → D₁
module B where
infix 1 c
syntax c x = + x
data D₂ : Set where
c : A.D₁ → D₂
open A
open B
test₁ : D₂
test₁ = + + + b
test₂ : D₂ → D₁
test₂ (+ + x) = x
test₂ (+ b) = + + + b
|
algebraic-stack_agda0000_doc_9913 | {-# OPTIONS --prop --rewriting #-}
module Examples.TreeSum where
open import Calf.CostMonoid
open import Calf.CostMonoids using (ℕ²-ParCostMonoid)
parCostMonoid = ℕ²-ParCostMonoid
open ParCostMonoid parCostMonoid
open import Calf costMonoid
open import Calf.ParMetalanguage parCostMonoid
open import Calf.Types.Nat
o... |
algebraic-stack_agda0000_doc_9914 | {-# OPTIONS --without-K --safe #-}
module Categories.NaturalTransformation.Core where
open import Level
open import Categories.Category
open import Categories.Functor renaming (id to idF)
open import Categories.Functor.Properties
import Categories.Morphism as Morphism
import Categories.Morphism.Reasoning as MR
priv... |
algebraic-stack_agda0000_doc_9915 | ------------------------------------------------------------------------
-- An alternative characterisation of the information ordering, along
-- with related results
------------------------------------------------------------------------
{-# OPTIONS --cubical --safe #-}
open import Prelude hiding (⊥)
module Partia... |
algebraic-stack_agda0000_doc_9916 | ------------------------------------------------------------------------------
-- Testing the translation of the universal quantified propositional symbols
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-... |
algebraic-stack_agda0000_doc_9917 | -- 2014-06-02 Andrea & Andreas
module _ where
open import Common.Equality
open import Common.Product
postulate
A : Set
F : Set → Set
test : let M : Set
M = _
N : Set × Set → Set
N = _
in ∀ {X : Set}
→ M ≡ F (N (X , X))
× N (A , A) ≡ A
test = refl , ... |
algebraic-stack_agda0000_doc_9918 |
-- Semantics of syntactic kits and explicit substitutions
module Semantics.Substitution.Kits where
open import Syntax.Types
open import Syntax.Context renaming (_,_ to _,,_)
open import Syntax.Terms
open import Syntax.Substitution.Kits
open import Semantics.Types
open import Semantics.Context
open import Semantics.T... |
algebraic-stack_agda0000_doc_9919 | ------------------------------------------------------------------------
-- Some alternative definitions of the concept of being an equivalence
------------------------------------------------------------------------
-- Partly based on the blog post "Universal properties without
-- function extensionality" by Mike Shu... |
algebraic-stack_agda0000_doc_11152 | {- 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.ImplShared.Base.Types
op... |
algebraic-stack_agda0000_doc_11153 | module Dummy where
-- Run this in Acme: go build && ./acme-agda -v
data ℕ : Set where
zero : ℕ
succ : ℕ -> ℕ
_+_ : ℕ → ℕ → ℕ
m + n = {!!}
_*_ : ℕ → ℕ → ℕ
m * n = {!m !} |
algebraic-stack_agda0000_doc_11154 | {-# OPTIONS --cubical --safe #-}
module Label where
open import Cubical.Core.Everything
open import Cubical.Foundations.Prelude using (isProp; transport)
open import Cubical.Data.Nat using (ℕ; zero; suc; isSetℕ)
open import Cubical.Data.Nat.Order using (_<_; _≤_; ≤-refl; <-weaken; ≤<-trans; m≤n-isProp; <-asym)
open i... |
algebraic-stack_agda0000_doc_11155 | {-# OPTIONS --cubical --no-import-sorts --safe #-}
{-
This file defines
sucPred : ∀ (i : Int) → sucInt (predInt i) ≡ i
predSuc : ∀ (i : Int) → predInt (sucInt i) ≡ i
discreteInt : discrete Int
isSetInt : isSet Int
addition of Int is defined _+_ : Int → Int → Int
as well as its commutativity and associativity
+-co... |
algebraic-stack_agda0000_doc_11156 | module *-distrib-+ where
import Relation.Binary.PropositionalEquality as Eq
open Eq using (_≡_; cong; sym)
open Eq.≡-Reasoning using (begin_; _≡⟨⟩_; step-≡; _∎)
open import Data.Nat using (ℕ; zero; suc; _+_; _*_)
open import Induction′ using (+-assoc; +-comm; +-suc)
-- 積が和に対して分配的であることの証明
*-distrib-+ : ∀ (m n p : ℕ) ... |
algebraic-stack_agda0000_doc_11157 | {-# OPTIONS --cubical --safe #-}
module Data.List.Kleene.Relation.Unary where
open import Data.List.Kleene
open import Prelude
open import Data.Fin
open import Relation.Nullary
private
variable
p : Level
◇⁺ : ∀ {A : Type a} (P : A → Type p) → A ⁺ → Type _
◇⁺ P xs = ∃[ i ] P (xs !⁺ i)
◇⋆ : ∀ {A : Type a} (P :... |
algebraic-stack_agda0000_doc_11158 | ------------------------------------------------------------------------------
-- Totality properties respect to OrdList (flatten-OrdList-helper)
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTI... |
algebraic-stack_agda0000_doc_11159 | {-# OPTIONS --universe-polymorphism #-}
module Categories.Functor.Product where
open import Categories.Category
open import Categories.Functor using (Functor)
import Categories.Object.Product as Product
import Categories.Object.BinaryProducts as BinaryProducts
-- Ugh, we should start bundling things (categories with ... |
algebraic-stack_agda0000_doc_11160 | module Sodium where
open import Category.Functor
open import Category.Applicative
open import Category.Monad
open import Data.Unit
open import Data.Bool
open import Data.Maybe
open import Data.Product
open import IO.Primitive
postulate
-- Core.
Reactive : Set → Set
sync : ∀ {A} → Reactive A → IO A
Even... |
algebraic-stack_agda0000_doc_11161 |
postulate
F : (Set → Set) → Set
syntax F (λ x → y) = [ x ] y
X : Set
X = [ ? ] x |
algebraic-stack_agda0000_doc_11162 | {-# OPTIONS --safe #-}
module SafeFlagPostulate where
data Empty : Set where
postulate inhabitant : Empty
|
algebraic-stack_agda0000_doc_11163 | {-# OPTIONS --cubical --safe --guardedness #-}
module Cubical.Codata.Stream.Properties where
open import Cubical.Core.Everything
open import Cubical.Data.Nat
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Isomorphism
open import Cubical.Foundations.Univa... |
algebraic-stack_agda0000_doc_11164 | #-}
|
algebraic-stack_agda0000_doc_11165 | module Monoids where
open import Library
record Monoid {a} : Set (lsuc a) where
field S : Set a
ε : S
_•_ : S → S → S
lid : ∀{m} → ε • m ≅ m
rid : ∀{m} → m • ε ≅ m
ass : ∀{m n o} → (m • n) • o ≅ m • (n • o)
infix 10 _•_
Nat+Mon : Monoid
Nat+Mon = record {
S = ℕ;... |
algebraic-stack_agda0000_doc_11166 | {-# OPTIONS --without-K --safe #-}
module Categories.Category.Species where
-- The Category of Species, as the Functor category from Core (FinSetoids) to Setoids.
-- Setoids used here because that's what fits best in this setting.
-- The constructions of the theory of Species are in Species.Construction
open import L... |
algebraic-stack_agda0000_doc_11167 |
module Issue451 where
infix 10 _==_
data _==_ {A : Set} (x : A) : (y : A) -> Set where
refl : x == x
postulate
Nat : Set
data G : Nat -> Nat -> Set where
I : (place : Nat) -> G place place
s : (n m : Nat) -> G n m
mul : (l m n : Nat) -> G m n -> G l m -> G l n
mul a b .b (I .b) x = x
mul a .a b x ... |
algebraic-stack_agda0000_doc_2272 | import Lvl
open import Type
module Type.Functions.Inverse.Proofs {ℓₗ : Lvl.Level}{ℓₒ₁}{ℓₒ₂} {X : Type{ℓₒ₁}} {Y : Type{ℓₒ₂}} where
open import Function.Domains
open import Relator.Equals
open import Type.Functions {ℓₗ}
open import Type.Functions.Inverse {ℓₗ}
open import Type.Properties.Empty
open import Type.Prop... |
algebraic-stack_agda0000_doc_2273 | {-# OPTIONS --without-K #-}
open import Types
open import Functions
open import Paths
open import HLevel
module Equivalences where
hfiber : ∀ {i j} {A : Set i} {B : Set j} (f : A → B) (y : B) → Set (max i j)
hfiber {A = A} f y = Σ A (λ x → f x ≡ y)
is-equiv : ∀ {i j} {A : Set i} {B : Set j} (f : A → B) → Set (max i... |
algebraic-stack_agda0000_doc_2274 | {-# OPTIONS --without-K --safe #-}
open import Categories.Category
module Categories.Functor.Construction.SubCategory {o ℓ e} (C : Category o ℓ e) where
open import Categories.Category.SubCategory C
open Category C
open Equiv
open import Level
open import Function.Base using () renaming (id to id→)
open import Dat... |
algebraic-stack_agda0000_doc_2275 | -- Andreas, 2014-10-05
{-# OPTIONS --cubical-compatible --sized-types #-}
-- {-# OPTIONS -v tc.size:20 #-}
open import Agda.Builtin.Size
data Nat : {size : Size} -> Set where
zero : {size : Size} -> Nat {↑ size}
suc : {size : Size} -> Nat {size} -> Nat {↑ size}
-- subtraction is non size increasing
sub : {si... |
algebraic-stack_agda0000_doc_2276 | module FlatDomInequality-1 where
postulate
A : Set
g : A → A
g x = x
h : (@♭ x : A) → A
h = g
|
algebraic-stack_agda0000_doc_2277 | {-# OPTIONS --universe-polymorphism #-}
module Categories.Object.BinaryProducts.Abstract where
open import Categories.Support.PropositionalEquality
open import Categories.Category
open import Categories.Object.BinaryProducts
open import Categories.Morphisms
module AbstractBinaryProducts {o ℓ e} (C : Category o ℓ e) (... |
algebraic-stack_agda0000_doc_2278 | ------------------------------------------------------------------------------
-- Inequalities on partial natural numbers
------------------------------------------------------------------------------
{-# OPTIONS --exact-split #-}
{-# OPTIONS --no-sized-types #-}
{-# OPTIONS --no-universe-polymo... |
algebraic-stack_agda0000_doc_2279 | ------------------------------------------------------------------------
-- The Agda standard library
--
-- Definitions for types of functions.
------------------------------------------------------------------------
-- The contents of this file should usually be accessed from `Function`.
{-# OPTIONS --without-K --sa... |
algebraic-stack_agda0000_doc_2280 | -- Andreas, 2015-07-16, issue reported by Nisse
postulate
A : Set₁
P : A → Set₁
T : Set₁ → Set₁
Σ : (A : Set₁) → (A → Set₁) → Set₁
T-Σ : {A : Set₁} {B : A → Set₁} → (∀ x → T (B x)) → T (Σ A B)
t : T (Σ Set λ _ → Σ (A → A) λ f → Σ (∀ x₁ → P (f x₁)) λ _ → Set)
t = T-Σ λ _ → T-Σ λ _ → T-Σ {!!}
-- WAS:... |
algebraic-stack_agda0000_doc_2281 |
module Successor where
open import OscarPrelude
record Successor {ℓᴬ} (A : Set ℓᴬ) {ℓᴮ} (B : Set ℓᴮ) : Set (ℓᴬ ⊔ ℓᴮ)
where
field
⊹ : A → B
open Successor ⦃ … ⦄ public
instance SuccessorNat : Successor Nat Nat
Successor.⊹ SuccessorNat = suc
instance SuccessorLevel : Successor Level Level
Successor.⊹ Success... |
algebraic-stack_agda0000_doc_2282 | open import Nat
open import Prelude
open import core
open import judgemental-erase
open import aasubsume-min
module determinism where
-- the same action applied to the same type makes the same type
actdet-type : {t t' t'' : τ̂} {α : action} →
(t + α +> t') →
(t + α +> t'') →
(t'... |
algebraic-stack_agda0000_doc_2283 | {-# OPTIONS --safe #-}
module Cubical.Algebra.CommRing.RadicalIdeal where
open import Cubical.Foundations.Prelude
open import Cubical.Foundations.Equiv
open import Cubical.Foundations.Function
open import Cubical.Foundations.Powerset
open import Cubical.Foundations.HLevels
open import Cubical.Data.Sigma
open import C... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.