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algebraic-stack_agda0000_doc_8505
{-# OPTIONS --with-K #-} open import Axiom.Extensionality.Propositional using (Extensionality) open import Relation.Nullary.Negation using (contradiction) open import Relation.Binary using (Irrelevant) open import Relation.Binary.PropositionalEquality using (_≡_; _≢_) open import Relation.Binary.PropositionalEquality.W...
algebraic-stack_agda0000_doc_8506
module _ where module A where postulate !_ : Set₂ → Set₃ infix 1 !_ module B where postulate !_ : Set₀ → Set₁ infix 3 !_ open A open B postulate #_ : Set₁ → Set₂ infix 2 #_ ok₁ : Set₁ → Set₃ ok₁ X = ! # X ok₂ : Set₀ → Set₂ ...
algebraic-stack_agda0000_doc_8507
module foldl where import Relation.Binary.PropositionalEquality as Eq open Eq using (_≡_; refl; sym; trans; cong) open Eq.≡-Reasoning open import lists using (List; []; _∷_; [_,_,_]) foldl : ∀ {A B : Set} → (B → A → B) → B → List A → B foldl _⊗_ e [] = e foldl _⊗_ e (x ∷ xs) = foldl _⊗_ (e ⊗ x) xs test-foldl ...
algebraic-stack_agda0000_doc_8508
------------------------------------------------------------------------ -- The Agda standard library -- -- The extensional sublist relation over setoid equality. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Relation.Binary module Data.List.R...
algebraic-stack_agda0000_doc_8509
open import MJ.Types import MJ.Classtable.Core as Core import MJ.Classtable.Code as Code import MJ.Syntax as Syntax module MJ.Semantics.Objects.Flat {c}(Ct : Core.Classtable c)(ℂ : Code.Code Ct) where open import Prelude open import Level renaming (suc to lsuc; zero to lzero) open import Data.Vec hiding (_++_; looku...
algebraic-stack_agda0000_doc_8510
-- Andreas, 2020-05-01, issue #4631 -- -- We should not allow @-patterns to shadow constructors! open import Agda.Builtin.Bool test : Set → Set test true@_ = true -- WAS: succees -- EXPECTED: -- -- Bool !=< Set -- when checking that the expression true has type Set -- -- ———— Warning(s) ————————————————————————————...
algebraic-stack_agda0000_doc_8511
------------------------------------------------------------------------------ -- Propositional equality on inductive PA ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymor...
algebraic-stack_agda0000_doc_8503
{-# OPTIONS --without-K --safe --no-universe-polymorphism --no-sized-types --no-guardedness --no-subtyping #-} module Agda.Builtin.Unit where record ⊤ : Set where instance constructor tt {-# BUILTIN UNIT ⊤ #-} {-# COMPILE GHC ⊤ = data () (()) #-}
algebraic-stack_agda0000_doc_16448
{-# OPTIONS --sized-types #-} module Rose where postulate Size : Set _^ : Size -> Size ∞ : Size {-# BUILTIN SIZE Size #-} {-# BUILTIN SIZESUC _^ #-} {-# BUILTIN SIZEINF ∞ #-} data List (A : Set) : {_ : Size} -> Set where [] : {size : Size} -> List A {size ^} _::_ : {size : Size} -> A -> List A {s...
algebraic-stack_agda0000_doc_16449
module Terms where open import Library -- * Variables ------------------------------------------------------------------------ data Ty : Set where base : Ty _→̂_ : (a b : Ty) → Ty -- Typing contexts. Cxt = List Ty -- Variables. data Var : (Γ : Cxt) (a : Ty) → Set where zero : ∀{Γ a} → Var (...
algebraic-stack_agda0000_doc_16450
{-# BUILTIN CUBEINTERVALUNIV IUniv #-}
algebraic-stack_agda0000_doc_16451
{-# OPTIONS --cubical --safe #-} -- | Quotient integer module QuoInt where open import Cubical.Core.Everything open import Cubical.HITs.Ints.QuoInt renaming (_+ℤ_ to _+_; ℤ to Z) open import Cubical.Data.Nat hiding (_+_) open import Cubical.Foundations.Prelude +-i-zero : ∀ a i → posneg i + a ≡ a +-i-zero a i = co...
algebraic-stack_agda0000_doc_16452
module Categories.Monoidal.CartesianClosed where
algebraic-stack_agda0000_doc_16453
{-# OPTIONS --safe #-} module Cubical.Algebra.Monoid.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.Equiv.HalfAdjoint open import Cubical.Foundations.Function open import Cubical.Foundations.HLevels open import Cubical.Foundations.Isomorphism op...
algebraic-stack_agda0000_doc_16454
module Numeral.Matrix where import Lvl open import Syntax.Number open import Data open import Data.Boolean open import Data.Tuple as Tuple using (_⨯_ ; _,_) open import Functional using (const) open import Numeral.Finite open import Numeral.Finite.Bound open import Numeral.Finite.Oper open import Numeral.Finite.O...
algebraic-stack_agda0000_doc_16455
module Data.Fin.Properties.Extra where open import Data.Nat renaming (suc to S; zero to Z; _+_ to _ℕ+_; _*_ to _ℕ*_) open ≤-Reasoning renaming (begin_ to start_; _∎ to _□; _≡⟨_⟩_ to _≈⟨_⟩_) open import Data.Nat.Properties open import Data.Nat.Properties.Extra renaming (cancel-suc to S-injective) open import Data.N...
algebraic-stack_agda0000_doc_16456
-- Martin-Löf identity type without the K axiom -- (we do not assume uniqueness of identity proofs). {-# OPTIONS --without-K --safe #-} module Tools.PropositionalEquality where -- We reexport Agda's builtin equality type. open import Tools.Empty public import Relation.Binary.PropositionalEquality as Eq open Eq usin...
algebraic-stack_agda0000_doc_16457
{-# OPTIONS --without-K #-} module sets.fin where open import sets.fin.core public open import sets.fin.properties public open import sets.fin.ordering public open import sets.fin.universe public
algebraic-stack_agda0000_doc_16458
{-# OPTIONS --without-K #-} open import Base open import Homotopy.TruncatedHIT {- The idea is that if [n : ℕ] and [A : Set i], then [τ n A] is defined by the following n-truncated higher inductive type: module Homotopy.TruncationHIT {i} (n : ℕ) (A : Set i) where (n)data τ : Set i where proj : A → τ M...
algebraic-stack_agda0000_doc_16459
-- Andreas, 2016-07-17 record R : Set₁ where abstract field T : Set -- Expected error: -- -- Using abstract here has no effect. Abstract applies only -- definitions like data definitions, record type definitions and -- function clauses.
algebraic-stack_agda0000_doc_16460
module Prelude.Unit where open import Agda.Builtin.Unit public record ⊤′ {a} : Set a where instance constructor tt -- To keep changes from compat-2.4.0 to a minimum. Unit = ⊤ pattern unit = tt
algebraic-stack_agda0000_doc_16461
{-# OPTIONS --without-K --safe #-} module Categories.Kan where -- Left and Right Kan extensions (known as Lan and Ran) open import Level open import Categories.Category using (Category) open import Categories.Functor open import Categories.NaturalTransformation using (NaturalTransformation; _∘ʳ_; _∘ᵥ_) open import Ca...
algebraic-stack_agda0000_doc_16463
{-# OPTIONS --prop --type-in-type #-} record × (A B : Prop) : Prop where field fst : A snd : B
algebraic-stack_agda0000_doc_16462
{-# OPTIONS --without-K --safe #-} open import Categories.Category open import Categories.Category.Complete.Finitely module Categories.Category.Complete.Finitely.Properties {o ℓ e} {C : Category o ℓ e} (finite : FinitelyComplete C) where open import Level using (Level) open import Data.Nat using (ℕ) open import Data...
algebraic-stack_agda0000_doc_16768
------------------------------------------------------------------------ -- The Agda standard library -- -- A type for expressions over a raw ring. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Tactic.RingSolver.Core.Expression where open import Da...
algebraic-stack_agda0000_doc_16769
{-# OPTIONS --cubical #-} module Exercises where open import Part2 open import Part3 open import Part4 open import Part5
algebraic-stack_agda0000_doc_16770
-- Some basic structures and operations for dealing -- with non-deterministic values. -- -- @author Sergio Antoy, Michael Hanus, Steven Libby module nondet where open import bool open import nat open import list infixr 8 _??_ ---------------------------------------------------------------------- -- A tree datatype ...
algebraic-stack_agda0000_doc_16771
open import Agda.Builtin.Equality module _ (A : Set) where data Wrap (X : Set) : Set where wrap : X → Wrap X data D (x : A) : ∀ y → Wrap (x ≡ y) → Set where c : ∀ y (x≡y : x ≡ y) → D x y (wrap x≡y) test : ∀ x y (x≡y x≡y' : Wrap (x ≡ y)) → D x y x≡y → D x y x≡y' → Set test y .y (wrap refl) .(wrap refl) (c .y .re...
algebraic-stack_agda0000_doc_16772
------------------------------------------------------------------------ -- INCREMENTAL λ-CALCULUS -- -- Environments -- -- This module defines the meaning of contexts, that is, -- the type of environments that fit a context, together -- with operations and properties of these operations. -- -- This module is parametri...
algebraic-stack_agda0000_doc_16773
------------------------------------------------------------------------ -- The Agda standard library -- -- Comonads ------------------------------------------------------------------------ -- Note that currently the monad laws are not included here. {-# OPTIONS --without-K --safe #-} module Category.Comonad where ...
algebraic-stack_agda0000_doc_16774
------------------------------------------------------------------------ -- Alternative definitions of weak bisimilarity ------------------------------------------------------------------------ {-# OPTIONS --sized-types #-} open import Prelude module Delay-monad.Bisimilarity.Alternative {a} {A : Type a} where open ...
algebraic-stack_agda0000_doc_16775
open import prelude -- Copied pretty much verbatim data Term : Set where true : Term false : Term if_then_else_end : Term → Term → Term → Term data Value : Term → Set where true : Value true false : Value false data _⟶_ : Term → Term → Set where E─IfTrue : ∀ {t₂ t₃} → ----------------------------...
algebraic-stack_agda0000_doc_16776
{-# OPTIONS --safe #-} module Cubical.Algebra.Polynomials.Multivariate.Base where open import Cubical.Algebra.CommRing.Instances.Polynomials.MultivariatePoly public {- The Multivariate Polynomials of size n over a CommRing A is a CommRing. This version is define as an instance of the more general constructions of gr...
algebraic-stack_agda0000_doc_16777
{-# OPTIONS --without-K #-} open import HoTT open import cohomology.Exactness open import cohomology.Theory module cohomology.Sn {i} (OT : OrdinaryTheory i) where open OrdinaryTheory OT C-Sphere-≠ : (n : ℤ) (m : ℕ) → (n ≠ ℕ-to-ℤ m) → C n (⊙Lift (⊙Sphere m)) == Lift-Unit-group C-Sphere-≠ n O neq = C-dimension n ne...
algebraic-stack_agda0000_doc_16778
------------------------------------------------------------------------ -- The Agda standard library -- -- Vectors ------------------------------------------------------------------------ module Data.Vec where open import Category.Applicative open import Data.Nat open import Data.Fin using (Fin; zero; suc) open impo...
algebraic-stack_agda0000_doc_16779
module Data.Union.Relation.Binary.Subtype where open import Data.List using (List) open import Data.List.Relation.Unary.Any using (here; there) open import Data.List.Relation.Binary.Subset.Propositional using (_⊆_) open import Data.Union using (Union; here; there; inj) open import Function using (_∘_; id) open impo...
algebraic-stack_agda0000_doc_16780
{-# OPTIONS --without-K --rewriting #-} module lib.types.Suspension.Trunc where open import lib.Basics open import lib.NType2 open import lib.types.Paths open import lib.types.Pointed open import lib.types.Truncation open import lib.types.Suspension.Core module _ {i} (A : Type i) (m : ℕ₋₂) where module SuspTrunc...
algebraic-stack_agda0000_doc_16781
{-# OPTIONS --without-K --safe #-} open import Definition.Typed.EqualityRelation module Definition.LogicalRelation.Substitution.Weakening {{eqrel : EqRelSet}} where open EqRelSet {{...}} open import Definition.Untyped open import Definition.Untyped.Properties open import Definition.LogicalRelation open import Defini...
algebraic-stack_agda0000_doc_16782
{-# OPTIONS --without-K #-} open import HoTT {- Move (parts of) faces of a cube around -} module lib.cubical.elims.CubeMove where square-push-rb : ∀ {i} {A : Type i} {a₀₀ a₀₁ a₁₀ a₁₁ b : A} {p₀₋ : a₀₀ == a₀₁} {p₋₀ : a₀₀ == a₁₀} {p₋₁ : a₀₁ == a₁₁} (p₁₋ : a₁₀ == b) (q : b == a₁₁) → Square p₀₋ p₋₀ p₋₁ (p₁₋ ∙ q) ...
algebraic-stack_agda0000_doc_16783
-- test termination using structured orders module TerminationTupledAckermann where data Nat : Set where zero : Nat succ : Nat -> Nat data _×_ (A B : Set) : Set where _,_ : A -> B -> A × B -- addition in tupled form add : Nat × Nat -> Nat add (zero , m) = m add (succ n , m) = succ (add (n , m)) -- a...
algebraic-stack_agda0000_doc_5648
module sn-calculus-confluence.helper where open import Data.List.All open import Function using (_∘_) open import Data.List.Any using (Any ; here ; there) open import Data.Nat using (_+_) open import utility open import Esterel.Lang open import Esterel.Lang.Properties open import Esterel.Environment as Env open impo...
algebraic-stack_agda0000_doc_5649
module Fail.TupleType where open import Haskell.Prelude idT : ∀ {as} → Tuple as → Tuple as idT x = x {-# COMPILE AGDA2HS idT #-}
algebraic-stack_agda0000_doc_5650
{-# OPTIONS --without-K --safe #-} module Categories.Adjoint.Equivalents where -- Theorems about equivalent formulations to Adjoint -- (though some have caveats) open import Level open import Data.Product using (_,_; _×_) open import Function using (_$_) renaming (_∘_ to _∙_) open import Function.Equality using (Π; ...
algebraic-stack_agda0000_doc_5651
{-# OPTIONS --safe --warning=error --without-K #-} open import LogicalFormulae open import Groups.DirectSum.Definition open import Setoids.Setoids open import Rings.Definition module Rings.DirectSum {a b c d : _} {A : Set a} {S : Setoid {a} {b} A} {_+1_ : A → A → A} {_*1_ : A → A → A} {C : Set c} {T : Setoid {c} {d}...
algebraic-stack_agda0000_doc_5652
{-# OPTIONS --without-K #-} open import Prelude import GSeTT.Typed-Syntax import Globular-TT.Syntax import Globular-TT.Rules module Globular-TT.Globular-TT {l} (index : Set l) (rule : index → GSeTT.Typed-Syntax.Ctx × (Globular-TT.Syntax.Pre-Ty index)) (assumption : G...
algebraic-stack_agda0000_doc_5653
-- {-# OPTIONS -v interaction:50 #-} x : Set → Set x = {!λ x → x!} -- "refine" (C-c C-r) should behave the same as "give" here -- Old, bad result: -- x = λ x₁ → x₁ -- New, expected result: -- x = λ x → x -- Expected interaction test case behavior: -- -- (agda2-give-action 0 'no-paren)
algebraic-stack_agda0000_doc_5654
module Luau.Type where data Type : Set where nil : Type _⇒_ : Type → Type → Type none : Type any : Type _∪_ : Type → Type → Type _∩_ : Type → Type → Type
algebraic-stack_agda0000_doc_5655
------------------------------------------------------------------------------ -- FOCT list terms properties ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} {-...
algebraic-stack_agda0000_doc_5656
module 030-semigroup where -- We need equivalence. open import 020-equivalence -- Semigroups are basically a set with equality and some binary -- operator which is associative and respects equality. record SemiGroup {M : Set} (_==_ : M -> M -> Set) (_*_ : M -> M -> M) : Set1 where field equiv : Equiv...
algebraic-stack_agda0000_doc_5657
{-# OPTIONS --sized-types #-} open import Relation.Binary.Core module SOList.Total.Properties {A : Set} (_≤_ : A → A → Set) (trans≤ : Transitive _≤_) where open import Bound.Total A open import Bound.Total.Order _≤_ open import Bound.Total.Order.Properties _≤_ trans≤ open import List...
algebraic-stack_agda0000_doc_5658
module test.AddInteger where open import Type open import Declarative open import Builtin open import Builtin.Constant.Type open import Builtin.Constant.Term Ctx⋆ Kind * # _⊢⋆_ con size⋆ open import Agda.Builtin.Sigma -- zerepoch/zerepoch-core/test/data/addInteger.plc addI : ∀{Γ} → Γ ⊢ con integer (size⋆ 8) ⇒ con ...
algebraic-stack_agda0000_doc_5659
-- {-# OPTIONS -v tc.proj.like:10 #-} {-# OPTIONS -v tc.conv:10 #-} import Common.Level module ProjectionLikeAndModules1 (A : Set) (a : A) where record ⊤ : Set where constructor tt data Wrap (W : Set) : Set where wrap : W → Wrap W data Bool : Set where true false : Bool -- `or' should be projection like in t...
algebraic-stack_agda0000_doc_5660
open import Everything module Test.SurjidentityP where module _ {𝔬₁} {𝔒₁ : Ø 𝔬₁} {𝔯₁} (_∼₁_ : 𝔒₁ → 𝔒₁ → Ø 𝔯₁) {𝔬₂} {𝔒₂ : Ø 𝔬₂} {𝔯₂} (_∼₂_ : 𝔒₂ → 𝔒₂ → Ø 𝔯₂) (_∼₂2_ : 𝔒₂ → 𝔒₂ → Ø 𝔯₂) {𝔯₂'} (_∼₂'_ : 𝔒₂ → 𝔒₂ → Ø 𝔯₂') {ℓ₂} (_∼̇₂_ : ∀ {x y} → x ∼₂ y → x ∼₂ y → Ø ℓ₂) ...
algebraic-stack_agda0000_doc_5661
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Algebra.Definitions where open import Cubical.Core.Everything open import Cubical.Relation.Binary open import Cubical.Data.Sigma using (_×_) open import Cubical.Data.Sum using (_⊎_) open import Cubical.HITs.PropositionalTruncation using (∥_∥) open impo...
algebraic-stack_agda0000_doc_5662
{-# OPTIONS --rewriting #-} module Luau.Heap where open import Agda.Builtin.Equality using (_≡_; refl) open import FFI.Data.Maybe using (Maybe; just; nothing) open import FFI.Data.Vector using (Vector; length; snoc; empty; lookup-snoc-not) open import Luau.Addr using (Addr; _≡ᴬ_) open import Luau.Var using (Var) open...
algebraic-stack_agda0000_doc_5663
{-# OPTIONS --without-K #-} open import lib.Basics open import lib.types.Paths open import lib.types.Pi open import lib.types.Unit open import lib.types.Nat open import lib.types.TLevel open import lib.types.Pointed open import lib.types.Sigma open import lib.NType2 open import lib.types.PathSeq open import nicolai.p...
algebraic-stack_agda0000_doc_5760
{-# OPTIONS --without-K --rewriting #-} module Basics where open import Base public open import PropT public open import hSet public open import lib.Basics public
algebraic-stack_agda0000_doc_5762
------------------------------------------------------------------------ -- The Agda standard library -- -- Finite sets ------------------------------------------------------------------------ -- Note that elements of Fin n can be seen as natural numbers in the -- set {m | m < n}. The notation "m" in comments below re...
algebraic-stack_agda0000_doc_5763
{-# OPTIONS --allow-unsolved-metas #-} postulate A : Set data Unit : Set where unit : Unit F : Unit → Set F unit = A postulate P : {A : Set} → A → Set Q : ∀ {x} → F x → Set f : ∀ {x} {y : F x} (z : Q y) → P z variable x : Unit y : F x g : (z : Q y) → P z g z with f z ... | p = p
algebraic-stack_agda0000_doc_5764
{-# OPTIONS --safe --experimental-lossy-unification #-} module Cubical.Categories.Instances.EilenbergMoore where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Function open import Cubical.Foundations.HLevels open import Cubical.Foundations.Isomorphism renaming (Iso to _≅_) open import Cubical...
algebraic-stack_agda0000_doc_5765
module _ where open import Issue1839.A open import Issue1839.B X : DontPrintThis -- should display as PrintThis X = {!!}
algebraic-stack_agda0000_doc_5766
------------------------------------------------------------------------ -- Some code suggesting that types used in "programs" might not -- necessarily be sets ------------------------------------------------------------------------ -- If lenses are only used in programs, and types used in programs are -- always sets,...
algebraic-stack_agda0000_doc_5767
------------------------------------------------------------------------ -- The Agda standard library -- -- Examples showing how the generic n-ary operations the stdlib provides -- can be used ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module README.Nar...
algebraic-stack_agda0000_doc_5768
{-# OPTIONS --without-K --safe #-} open import Categories.Category using (Category) -- A "canonical" presentation of cartesian closed categories. -- -- This presentation is equivalent to the one in -- Categories.Category.CartesianClosed but it is easier to work with -- in some circumstances. -- -- Here, exponentials a...
algebraic-stack_agda0000_doc_5769
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Data.Empty.Base where open import Cubical.Core.Everything open import Cubical.Foundations.Prelude private variable ℓ : Level data ⊥ : Type₀ where ⊥* : Type ℓ ⊥* = Lift ⊥ rec : {A : Type ℓ} → ⊥ → A rec () elim : {A : ⊥ → Type ℓ} → (x : ⊥) → A ...
algebraic-stack_agda0000_doc_5770
------------------------------------------------------------------------ -- A memoising backend for RecursiveDescent.Hybrid ------------------------------------------------------------------------ -- Following Frost/Szydlowski and Frost/Hafiz/Callaghan (but without -- the left recursion fix). An improvement has been m...
algebraic-stack_agda0000_doc_5771
module Data.Rational where import Data.Bool as Bool import Data.Nat as Nat import Data.Integer as Int open Int renaming ( _*_ to _*'_ ; _+_ to _+'_ ; -_ to -'_ ; _-_ to _-'_ ; !_! to !_!' ; _==_ to _=='_ ; _≤_ to _≤'_ ...
algebraic-stack_agda0000_doc_5772
{- This second-order signature was created from the following second-order syntax description: syntax Empty | E type 𝟘 : 0-ary term abort : 𝟘 -> α theory (𝟘η) e : 𝟘 c : α |> abort(e) = c -} module Empty.Signature where open import SOAS.Context -- Type declaration data ET : Set where 𝟘 : ET ope...
algebraic-stack_agda0000_doc_5773
module Issue1245 where postulate A B : Set [_] : A -> B module M (_ : B) where module N (a : A) = M [ a ]
algebraic-stack_agda0000_doc_5774
-- This file is the source Agda file -- Edit this file not Type.hs -- The warning below will be written to Type.hs module PlutusCore.Generators.NEAT.Type where -- warning to be written to Haskell file: {-# FOREIGN AGDA2HS {- !!! THIS FILE IS GENERATED FROM Type.agda !!! DO NOT EDIT THIS FILE. EDIT Type.agda !!! AND T...
algebraic-stack_agda0000_doc_5775
module Fail.MultiArgumentPatternLambda where open import Agda.Builtin.Bool tooManyPats : Bool → Bool → Bool tooManyPats = λ where false false → false true true → false _ _ → true {-# COMPILE AGDA2HS tooManyPats #-}
algebraic-stack_agda0000_doc_5761
{-# OPTIONS --without-K --safe #-} open import Categories.Category.Monoidal.Structure using (SymmetricMonoidalCategory) module Categories.Functor.Monoidal.Symmetric {o o′ ℓ ℓ′ e e′} (C : SymmetricMonoidalCategory o ℓ e) (D : SymmetricMonoidalCategory o′ ℓ′ e′) where open import Level open import Data.Product u...
algebraic-stack_agda0000_doc_8608
module L.Base.Nat where -- Reexport definitions open import L.Base.Nat.Core public -- Functions on Nats pred : Nat → Nat pred = ind (λ _ → Nat) zero (λ x _ → x) infixl 6 _+_ infixl 7 _*_ _+_ : Nat → Nat → Nat zero + y = y succ x + y = succ (x + y) {-# BUILTIN NATPLUS _+_ #-} _*_ : Nat → Nat → Nat zero * y = z...
algebraic-stack_agda0000_doc_8609
{-# OPTIONS --without-K #-} module sets.nat.solver where open import decidable open import equality open import function.core hiding (const) open import sets.nat.core open import sets.nat.properties open import sets.nat.ordering open import sets.fin.core hiding (_≟_) open import sets.vec.core open import sets.vec...
algebraic-stack_agda0000_doc_8610
{- This module defines the basic opens of the Zariski lattice and proves that they're a basis of the lattice. It also contains the construction of the structure presheaf and a proof of the sheaf property on basic opens, using the theory developed in the module PreSheafFromUniversalProp and its toSheaf.lemma. ...
algebraic-stack_agda0000_doc_8611
{-# OPTIONS --erased-cubical #-} open import Agda.Builtin.Cubical.Path -- Higher constructors must be erased when --erased-cubical is used. data ∥_∥ (A : Set) : Set where ∣_∣ : A → ∥ A ∥ trivial : (x y : ∥ A ∥) → x ≡ y
algebraic-stack_agda0000_doc_8612
------------------------------------------------------------------------ -- Lemmas related to application of substitutions ------------------------------------------------------------------------ -- The record below allows the application operation to be -- "heterogeneous", applying substitutions containing one kind o...
algebraic-stack_agda0000_doc_8614
------------------------------------------------------------------------ -- Excluded middle ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Equality module Excluded-middle {e⁺} (eq : ∀ {a p} → Equality-with-J a p e⁺) where open Derived-defini...
algebraic-stack_agda0000_doc_8615
------------------------------------------------------------------------------ -- Lists examples ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #-} {-# OPTIONS --...
algebraic-stack_agda0000_doc_8616
{-# OPTIONS --cubical --no-import-sorts #-} open import Cubical.Foundations.Everything renaming (_⁻¹ to _⁻¹ᵖ; assoc to ∙-assoc) import Cubical.Algebra.Semigroup as Std open import MorePropAlgebra.Bundles module MorePropAlgebra.Properties.Semigroup {ℓ} (assumptions : Semigroup {ℓ}) where open Semigroup assumptions re...
algebraic-stack_agda0000_doc_8617
------------------------------------------------------------------------ -- The Agda standard library -- -- Lexicographic ordering of lists ------------------------------------------------------------------------ -- The definition of lexicographic ordering used here is suitable if -- the argument order is a (non-stric...
algebraic-stack_agda0000_doc_8618
------------------------------------------------------------------------ -- Some definitions related to and properties of the Maybe type ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Equality module Maybe {reflexive} (eq : ∀ {a p} → Equality...
algebraic-stack_agda0000_doc_8619
{-# OPTIONS --without-K --safe #-} open import Level module Categories.Category.Instance.SimplicialSet.Properties (o ℓ : Level) where open import Function using (_$_) open import Data.Empty.Polymorphic using (⊥; ⊥-elim) open import Data.Nat using (ℕ) open import Data.Fin using (Fin) open import Data.Product using (...
algebraic-stack_agda0000_doc_8620
module PLRTree.Equality.Correctness {A : Set} where open import BTree.Equality {A} open import PLRTree {A} open import PLRTree.Equality {A} renaming (_≃_ to _≃'_) lemma-≃'-≃ : {l r : PLRTree} → l ≃' r → forget l ≃ forget r lemma-≃'-≃ ≃lf = ≃lf lemma-≃'-≃ (≃nd x x' l≃'r l'≃'r' l≃'l') = ≃nd x x' (lemma-≃'-≃ l≃'r) (lem...
algebraic-stack_agda0000_doc_8621
-- Andreas, 2019-07-15, issue #3901, requested by msuperdock -- -- Allow function spaces {A} → B and {{A}} → B. postulate A B : Set foo : {{A}} → B bar : {A} → B -- Original feature request: open import Agda.Builtin.Unit using (⊤; tt) data ⊥ : Set where data Nat : Set where zero : Nat suc : Nat → Nat...
algebraic-stack_agda0000_doc_8622
-- Jesper, 2018-11-23: Unsolved metas are turned into postulates -- when --allow-unsolved-metas is enabled, but there was no internal -- representation of postulated sorts. module Issue3256 where open import Issue3256.B -- WAS: -- An internal error has occurred. Please report this as a bug. -- Location of the error:...
algebraic-stack_agda0000_doc_8623
{-# OPTIONS --universe-polymorphism #-} module Categories.Graphs where open import Categories.Category hiding (module Heterogeneous) open import Data.Product open import Level open import Relation.Binary renaming (_⇒_ to _⊆_) open import Relation.Binary.PropositionalEquality using () renaming (_≡_ to _≣_; refl...
algebraic-stack_agda0000_doc_8613
module Abstract where data Bool : Set where true false : Bool not : Bool → Bool not true = false not false = true abstract Answer : Set Answer = Bool yes : Answer yes = true no : Answer no = false contradict : Answer → Answer contradict x = not x counter-contradict : Answer → Answer counter-c...
algebraic-stack_agda0000_doc_16912
module Common.Context where open import Common public -- Contexts. data Cx (U : Set) : Set where ∅ : Cx U _,_ : Cx U → U → Cx U -- Vector contexts. data VCx (U : Set) : ℕ → Set where ∅ : VCx U zero _,_ : ∀ {n} → VCx U n → U → VCx U (suc n) -- Inversion principles for contexts. module _ {U : Set} w...
algebraic-stack_agda0000_doc_16913
{-# OPTIONS --safe --warning=error --without-K #-} open import LogicalFormulae open import Groups.Definition open import Rings.Definition open import Rings.IntegralDomains.Definition open import Setoids.Setoids open import Sets.EquivalenceRelations module Fields.FieldOfFractions.Ring {a b : _} {A : Set a} {S : Setoid...
algebraic-stack_agda0000_doc_16914
module Oscar.Category.Semigroup where open import Oscar.Category.Setoid open import Oscar.Level module _ {𝔬 𝔮} (setoid : Setoid 𝔬 𝔮) where open Setoid setoid record IsSemigroup (_∙_ : ⋆ → ⋆ → ⋆) : Set (𝔬 ⊔ 𝔮) where field extensionality : ∀ {f₁ f₂} → f₁ ≋ f₂ → ∀ {g₁ g₂} → g₁ ≋ g₂ → g₁ ∙ f₁ ≋ g₂ ∙...
algebraic-stack_agda0000_doc_16915
{-# OPTIONS --rewriting #-} open import Luau.Type using (Type; Scalar; nil; number; string; boolean; never; unknown; _⇒_; _∪_; _∩_) open import Properties.Equality using (_≢_) module Luau.Subtyping where -- An implementation of semantic subtyping -- We think of types as languages of trees data Tree : Set where ...
algebraic-stack_agda0000_doc_16916
{-# OPTIONS --cubical --guarded -W ignore #-} module combinations-of-lift-and-list where open import Clocked.Primitives open import Cubical.Foundations.Prelude open import Cubical.Data.List as List open import Cubical.Data.List.Properties open import Cubical.Data.Sum using (_⊎_; inl; inr) --**************************...
algebraic-stack_agda0000_doc_16917
{-# OPTIONS --warning=error --safe --without-K #-} open import LogicalFormulae open import Agda.Primitive using (Level; lzero; lsuc; _⊔_) open import Categories.Definition module Categories.Functor.Definition where record Functor {a b c d : _} (C : Category {a} {b}) (D : Category {c} {d}) : Set (a ⊔ b ⊔ c ⊔ d) where...
algebraic-stack_agda0000_doc_16918
module Stuck where postulate I : Set i j : I data D : I → I → Set where d : D i i e : D j j f : ∀ {x} → D i x → Set₁ f d = Set
algebraic-stack_agda0000_doc_16919
module SetOmega where postulate IsType : ∀ {a} → Set a → Set Bad : IsType (∀ a → Set a)
algebraic-stack_agda0000_doc_16920
open import Agda.Builtin.Bool data Test : Set where CTest : Bool -> {Bool} -> Test {-# COMPILE AGDA2HS Test #-} getTest : Test → Bool getTest (CTest b) = b {-# COMPILE AGDA2HS getTest #-} putTest : Bool → Test → Test putTest b (CTest _ {b'}) = CTest b {b'} {-# COMPILE AGDA2HS putTest #-}
algebraic-stack_agda0000_doc_16921
open import Relation.Binary.Core using (Rel) module GGT.Definitions {a b ℓ₁ ℓ₂} {G : Set a} -- The underlying group carrier {Ω : Set b} -- The underlying space (_≈_ : Rel G ℓ₁) -- The underlying group equality (_≋_ : Rel Ω ℓ₂) -- The underlying space equality where open import Level open import ...
algebraic-stack_agda0000_doc_16922
module MJ.Examples.Exceptions where open import Prelude open import Data.Star import Data.Vec.All as Vec∀ open import Data.List open import Data.List.Any open import Data.List.Membership.Propositional open import Data.List.All hiding (lookup) open import Data.Product hiding (Σ) open import Relation.Binary.Propositiona...
algebraic-stack_agda0000_doc_16923
module STLC.Type.Relation where open import Data.Nat using (ℕ) open import Data.Fin using (Fin) open import STLC.Term open import STLC.Type open import STLC.Type.Context using (Ctxt) open import Data.Vec using (_∷_; lookup) open import Relation.Nullary using (¬_) open import Relation.Binary.PropositionalEquality ...