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algebraic-stack_agda0000_doc_4408
module BTree.Complete.Alternative.Correctness {A : Set} where open import BTree {A} open import BTree.Equality {A} open import BTree.Equality.Properties {A} open import BTree.Complete.Base {A} open import BTree.Complete.Base.Properties {A} open import BTree.Complete.Alternative {A} renaming (Complete to Complete' ; ...
algebraic-stack_agda0000_doc_4409
import Bundles import Construct.DirectProduct import Definitions import Definitions.Semiring import Morphism.Structures import Properties.RingWithoutOne import Structures
algebraic-stack_agda0000_doc_4410
{-# OPTIONS --show-irrelevant #-} -- {-# OPTIONS -v tc:20 #-} open import Agda.Primitive open import Issue2408.LevelDependentOnIrrelevant -- Provoke error message mentioning (ℓ a) provokeError : Set₁ provokeError = X where X = _ F' : (a : A) → X F' = F -- If #2408 is solved by replacing irrelevant vars in ...
algebraic-stack_agda0000_doc_4411
module HasSalvation where open import OscarPrelude record HasSalvation (A : Set) : Set₁ where field ▷_ : A → Set open HasSalvation ⊃ 
 ⩄ public {-# DISPLAY HasSalvation.▷_ _ = ▷_ #-} record HasDecidableSalvation (A : Set) : Set₁ where field ⊃ hasSalvation ⩄ : HasSalvation A ▷?_ : (x : A) → Dec $...
algebraic-stack_agda0000_doc_4412
-- Andreas, 2014-04-23 test case by Andrea Vezzosi {-# OPTIONS --sized-types --copatterns #-} -- {-# OPTIONS --show-implicit -v term:60 #-} module _ where open import Common.Size -- Invalid coinductive record, since not recursive. record ▾ (A : Size → Set) (i : Size) : Set where coinductive -- This should b...
algebraic-stack_agda0000_doc_4414
{-# OPTIONS --without-K --safe #-} open import Algebra using (Monoid) module Data.FingerTree.MonoidSolver {ℓ₁ ℓ₂} (mon : Monoid ℓ₁ ℓ₂) where open import Data.Nat as ℕ using (ℕ; suc; zero) open import Data.List as List using (List; _∷_; []; foldr; _++_) open import Data.Vec as Vec using (Vec; _∷_; []) open import Dat...
algebraic-stack_agda0000_doc_4415
{-# OPTIONS --cubical --safe #-} module Data.Pi where open import Data.Pi.Base public
algebraic-stack_agda0000_doc_4413
{-# OPTIONS --allow-unsolved-metas #-} module _ where open import Agda.Builtin.Equality module Case₀ where postulate I : Set P : I → Set variable p : P _ postulate D : P _ → Set d : D p module Case₁ where postulate I : Set P : I → Set Q : ∀ n → P n → Set variable q ...
algebraic-stack_agda0000_doc_4000
module Prelude.Variables where open import Agda.Primitive open import Agda.Builtin.Nat open import Agda.Builtin.List variable ℓ ℓ₁ ℓ₂ ℓ₃ : Level A B C : Set ℓ F M : Set ℓ₁ → Set ℓ₂ x y z : A xs ys zs : List A n m : Nat
algebraic-stack_agda0000_doc_4001
-- Solver for functors {-# OPTIONS --without-K --safe #-} open import Categories.Category open import Categories.Functor renaming (id to idF) module Experiment.Categories.Solver.MultiFunctor {o ℓ e} where import Categories.Morphism.Reasoning as MR open import Level open import Relation.Binary using (Rel) infixr 9...
algebraic-stack_agda0000_doc_4002
-- Andreas, 2017-05-17, issue #2574 reported by G. Allais open import Issue2574Import -- The imported module should be clickable. open import Issue2574ImportBlank -- The imported module should be clickable.
algebraic-stack_agda0000_doc_4003
-- Currently this test case is broken. Once Issue 3451 has been fixed -- it should be moved to test/Fail (and this comment should be -- removed). -- The option --guardedness turns off sized types. {-# OPTIONS --guardedness #-} open import Agda.Builtin.Size record Stream (A : Set) (i : Size) : Set where coinductiv...
algebraic-stack_agda0000_doc_4004
module Class.MonadTrans where open import Class.Monad open import Level record MonadTrans {a} (T : (Set a -> Set a) -> Set a -> Set a) : Set (suc a) where field embed : {A : Set a} {M : Set a -> Set a} {{_ : Monad M}} -> M A -> T M A open MonadTrans {{...}} public
algebraic-stack_agda0000_doc_4005
module Numeral.Natural.Relation.Order where import Lvl open import Functional open import Logic open import Logic.Propositional open import Logic.Predicate open import Numeral.Natural open import Numeral.Natural.Oper open import Relator.Equals open import Relator.Equals.Proofs open import Relator.Ordering -- Inequali...
algebraic-stack_agda0000_doc_4006
module Eq.ObsTheory where open import Prelude open import T open import DynTheory open import SubstTheory open import Contexts open import Eq.Defs open import Eq.KleeneTheory open ObservEq ---- Proofs about observational equivalence -- observational equivalence being an equiv reln follows trivially from kleene equiv...
algebraic-stack_agda0000_doc_4007
{-# OPTIONS --without-K #-} module function.fibration where open import level open import sum open import equality.core open import function.core open import function.isomorphism.core open import function.isomorphism.coherent open import function.isomorphism.lift open import function.isomorphism.univalence open impor...
algebraic-stack_agda0000_doc_4008
{-# OPTIONS --without-K --rewriting #-} open import HoTT module Reflective where record ReflectiveSubuniverse {ℓ} : Type (lsucc ℓ) where field P : Type ℓ → Type ℓ R : Type ℓ → Type ℓ η : (A : Type ℓ) → A → R A -- replete : (A B : Type ℓ) → P A → A ≃ B → P B
algebraic-stack_agda0000_doc_4010
------------------------------------------------------------------------ -- Pi with partiality algebra families as codomains ------------------------------------------------------------------------ {-# OPTIONS --erased-cubical --safe #-} module Partiality-algebra.Pi where open import Equality.Propositional.Cubical o...
algebraic-stack_agda0000_doc_4011
-- {-# OPTIONS -v tc.with.strip:40 #-} module Issue824 where record R : Set where data D : Set → Set₁ where d : ∀ {A} → D A → D A postulate d′ : D R data P : R → D R → Set₁ where p : {x : R} {y : D R} → P x y → P x (d y) Foo : P _ (d d′) → Set₁ Foo (p _) with Set Foo (p _) | _ = Set -- Bug.agda:18,1-19,20 -...
algebraic-stack_agda0000_doc_4012
------------------------------------------------------------------------ -- Call-by-value (CBV) reduction in pure type systems (PTS) ------------------------------------------------------------------------ module Pts.Reduction.Cbv where open import Data.Fin.Substitution open import Data.Fin.Substitution.ExtraLemmas o...
algebraic-stack_agda0000_doc_4013
module LocalVsImportedModuleClash where X = TODO--This-shouldn't-happen-if-the-scope-checker-does-it's-job
algebraic-stack_agda0000_doc_4014
{-# OPTIONS --without-K --safe #-} module Categories.NaturalTransformation.NaturalIsomorphism.Equivalence where -- a certain notion of equivalence between Natural Isomorphisms. open import Level open import Data.Product using (_×_; _,_; map; zip) open import Relation.Binary using (IsEquivalence) open import Categori...
algebraic-stack_agda0000_doc_4015
{-# OPTIONS --safe #-} module Cubical.Algebra.Group.Instances.DiffInt where open import Cubical.HITs.SetQuotients open import Cubical.Foundations.Prelude open import Cubical.Data.Int.MoreInts.DiffInt renaming (â„€ to â„€Type ; _+_ to _+â„€_ ; _-_ to _-â„€_) open import Cubical.Algebra.Group.Base open import Cubical.Algebra.Se...
algebraic-stack_agda0000_doc_4009
{-# OPTIONS --safe #-} module Cubical.Categories.Morphism where open import Cubical.Foundations.Prelude open import Cubical.Data.Sigma open import Cubical.Categories.Category private variable ℓ ℓ' : Level -- C needs to be explicit for these definitions as Agda can't infer it module _ (C : Category ℓ ℓ') where...
algebraic-stack_agda0000_doc_4464
{-# OPTIONS --without-K --rewriting #-} {- Adapted from Ulrik's work in Lean (released under Apache License 2.0) https://github.com/leanprover/lean/blob/master/hott/homotopy/cellcomplex.hlean -} open import HoTT renaming (pt to pt⊙) open import homotopy.DisjointlyPointedSet module cw.CW {i} where open import cw...
algebraic-stack_agda0000_doc_4465
module MLib.Finite where open import MLib.Prelude import MLib.Fin.Parts as P import MLib.Fin.Parts.Simple as PS open import MLib.Prelude.RelProps open import Data.List.All as All using (All; []; _∷_) hiding (module All) open import Data.List.Any as Any using (Any; here; there) hiding (module Any) import Data.List.Mem...
algebraic-stack_agda0000_doc_4466
open import Prelude open import MJ.Classtable.Core module MJ.LexicalScope c where open import Data.List open import Data.List.Membership.Propositional open import MJ.Types Ctx : Set Ctx = List (Ty c) Var : Ctx → Ty c → Set Var Γ a = a ∈ Γ _+local_ : Ctx → Ty c → Ctx _+local_ Γ a = a ∷ Γ
algebraic-stack_agda0000_doc_4467
{-# OPTIONS --no-qualified-instances #-} module JVM.Printer.Printer {t} (T : Set t) where open import Function using (_$_; _∘_) open import Data.Unit open import Data.Nat open import Data.Nat.Show as Nat open import Data.Product open import Data.List as List open import Data.List.Relation.Unary.All open import Relatio...
algebraic-stack_agda0000_doc_4468
{-# OPTIONS --without-K -v 2 #-} module Leftovers.Monad where open import Category.Functor open import Category.Applicative open import Category.Monad open import Level open import Data.Unit open import Data.List import Reflection as TC open import Reflection.TypeChecking.Monad.Instances open import Reflection.Abst...
algebraic-stack_agda0000_doc_4469
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.DStructures.Structures.Higher where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.HLevels open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Function open import Cu...
algebraic-stack_agda0000_doc_4470
open import Agda.Primitive using (lzero; lsuc; _⊔_ ;Level) open import Relation.Binary.PropositionalEquality using (_≡_; refl; sym; setoid; cong; trans) import Function.Equality open import Relation.Binary using (Setoid) import Categories.Category import Categories.Functor import Categories.Category.Instance.Setoids i...
algebraic-stack_agda0000_doc_4471
module Issue759a where import Common.Level abstract record Wrap (A : Set) : Set where field wrapped : A open Wrap public wrap : {A : Set} → A → Wrap A wrap a = record { wrapped = a } -- WAS: Broken error message: -- Not in scope: -- Issue759a.recCon-NOT-PRINTED at -- when checking the definition of wrap...
algebraic-stack_agda0000_doc_4472
open import SOAS.Common -- Free construction with respect to a forgetful functor between categories module SOAS.Construction.Free {ℂ 𝕊 : Category 1ℓ 0ℓ 0ℓ} (U : Functor 𝕊 ℂ) where open import Categories.Adjoint import Categories.Morphism.Reasoning as MR open import Categories.Categor...
algebraic-stack_agda0000_doc_4473
-- The following deeply left-nested expression illustrates both a -- problem in a previous implementation of the occurrence machinery, -- and a problem in the one that is current at the time of writing. F : Set → Set F X = ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((...
algebraic-stack_agda0000_doc_4474
------------------------------------------------------------------------ -- Function setoids and related constructions ------------------------------------------------------------------------ module Relation.Binary.FunctionSetoid where open import Data.Function open import Relation.Binary infixr 0 _↝_ _⟶_ _⇹_ _≡⇚_ ...
algebraic-stack_agda0000_doc_4475
------------------------------------------------------------------------ -- A binary representation of natural numbers ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} open import Equality import Erased.Without-box-cong module Nat.Binary {c⁺} (eq : ∀ {a ...
algebraic-stack_agda0000_doc_4477
open import Structures open import SacTy module ExtractSac where open import Data.String as S hiding (_++_) renaming (_≟_ to _≟s_) open import Data.List as L hiding (_++_) open import Data.List.Categorical open import Data.List.Properties as L open import Data.Nat as N open import Agda.Builtin.Nat using (div-helper; m...
algebraic-stack_agda0000_doc_4478
------------------------------------------------------------------------ -- The Agda standard library -- -- Properties satisfied by strict partial orders ------------------------------------------------------------------------ open import Relation.Binary module Relation.Binary.Properties.StrictPartialOrder {s₁...
algebraic-stack_agda0000_doc_4479
module Function.DomainRaise where open import Data open import Data.Boolean import Functional as Fn import Lvl open import Numeral.Natural open import Numeral.Natural.Oper.Comparisons open import Syntax.Number open import Type private variable ℓ ℓ₁ ℓ₂ : Lvl.Level private variable T X Y Z : Type{ℓ} private v...
algebraic-stack_agda0000_doc_4476
module Structure.Operator.Monoid.Submonoid where import Lvl open import Logic open import Logic.Predicate open import Logic.Predicate.Equiv open import Sets.PredicateSet renaming (_≡_ to _≡ₛ_) open import Structure.Setoid open import Structure.Operator.Monoid open import Structure.Operator.Properties open import ...
algebraic-stack_agda0000_doc_3745
{-# OPTIONS --cubical #-} module Multidimensional.Data.DirNum.Properties where open import Cubical.Foundations.Prelude open import Cubical.Data.Empty open import Cubical.Data.Prod open import Cubical.Data.Bool open import Cubical.Data.Nat open import Cubical.Relation.Nullary open import Multidimensional.Data.Dir op...
algebraic-stack_agda0000_doc_3746
{-# OPTIONS --verbose=10 #-} module leafs where open import Data.Nat open import Data.Vec open import Agda.Builtin.Sigma open import Data.Product open import Data.Fin using (fromℕ) open import trees open import optics open import lemmas leafsTree : {A : Set} -> Tree A -> ∃[ n ] (Vec A n × (Vec ...
algebraic-stack_agda0000_doc_3747
{-# OPTIONS --without-K --safe #-} module Categories.Yoneda where -- Yoneda Lemma. In total, provides: -- * the Yoneda Embedding (called embed here) from any Category C into Presheaves C -- Worth noticing that there is no 'locally small' condition here; however, if one looks at -- the levels involved, there is in...
algebraic-stack_agda0000_doc_3748
module Pi.Everything where open import Pi.Syntax -- Syntax of Pi open import Pi.Opsem -- Abstract machine semantics of Pi open import Pi.AuxLemmas -- Some auxiliary lemmas about opsem for forward/backward deterministic proof open import Pi.NoRepeat -- Forward/backward deterministic lemmas and Non-repeating ...
algebraic-stack_agda0000_doc_3749
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.HITs.Ints.DiffInt where open import Cubical.HITs.Ints.DiffInt.Base public open import Cubical.HITs.Ints.DiffInt.Properties public
algebraic-stack_agda0000_doc_3750
{- This second-order signature was created from the following second-order syntax description: syntax Sum | S type _⊕_ : 2-ary | l30 term inl : α -> α ⊕ β inr : β -> α ⊕ β case : α ⊕ β α.γ β.γ -> γ theory (lβ) a : α f : α.γ g : β.γ |> case (inl(a), x.f[x], y.g[y]) = f[a] (rβ) b : β f...
algebraic-stack_agda0000_doc_3751
-- New feature by Jesper Cockx in commit be89d4a8b264dd2719cb8c601a2c7f45a95ba220 : -- disabling the universe check for a data or record type. -- Andreas, 2018-10-27, re issue #3327: restructured test cases. module _ where -- Pragma is naturally attached to definition. module DataDef where data U : Set T : U →...
algebraic-stack_agda0000_doc_3752
open import Nat open import Prelude open import core open import contexts open import typed-elaboration open import lemmas-gcomplete open import lemmas-complete open import progress-checks open import finality module cast-inert where -- if a term is compelete and well typed, then the casts inside are all -- identi...
algebraic-stack_agda0000_doc_3753
-- Andreas, 2018-11-03, issue #3364 -- -- Better error when trying to import with new qualified module name. open import Agda.Builtin.Nat as Builtin.Nat -- WAS: Error: -- Not in scope: -- as at ... -- when scope checking as -- NOW: Warning -- `as' must be followed by an unqualified name -- when scope checking the ...
algebraic-stack_agda0000_doc_3754
{-# OPTIONS --cubical --no-import-sorts --safe #-} open import Cubical.Core.Everything open import Cubical.Relation.Binary.Raw module Cubical.Relation.Binary.Reasoning.PartialOrder {c ℓ} {A : Type c} (P : PartialOrder A ℓ) where open PartialOrder P import Cubical.Relation.Binary.Raw.Construct.NonStrictToStrict _≀_...
algebraic-stack_agda0000_doc_3755
-- exercises -- * basic logic properties (implication, and, or, bot, not, forall, exists) -- * data types -- * records -- * non-dep, non-rec, non-indexed case splits -- * including elimination constants as hints -- * hidden arguments open import Auto.Prelude h0 : (A : Set) → A → A h0 = {!!} --h0 = λ A z → z h1 : (A...
algebraic-stack_agda0000_doc_3756
module TLP02 where open import Data.Bool open import Data.Nat open import Data.String open import Relation.Binary.PropositionalEquality as PropEq using (_≡_; refl) -- ----- Star型の定矩 ----- data Star : Set where NIL : Star TRU : Star N : ℕ → Star S : String → Star C : Star → Star → Star ...
algebraic-stack_agda0000_doc_3757
------------------------------------------------------------------------ -- The Agda standard library -- -- Definitions of algebraic structures defined over some other -- structure, like modules and vector spaces -- -- Terminology of bundles: -- * There are both *semimodules* and *modules*. -- - For M an R-semimodule...
algebraic-stack_agda0000_doc_3758
------------------------------------------------------------------------ -- The Agda standard library -- -- The universal binary relation ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Relation.Binary.Construct.Always where open import Relation.Bina...
algebraic-stack_agda0000_doc_3759
module Oscar.Category.Action where open import Oscar.Category.Setoid open import Oscar.Function open import Oscar.Level record Action {𝔬} (⋆ : Set 𝔬) 𝔄𝔬 𝔄𝔮 : Set (𝔬 ⊔ lsuc (𝔄𝔬 ⊔ 𝔄𝔮)) where field 𝔄 : ⋆ → Setoid 𝔄𝔬 𝔄𝔮 ⊃ isSetoid ⩄ : ∀ {x} → IsSetoid (Setoid.⋆ (𝔄 x)) 𝔄𝔮 ↥ : ⋆ →...
algebraic-stack_agda0000_doc_3744
module Verifier where open import ModusPonens using (modusPonens) check : ∀ {P Q : Set} → (P → Q) → P → Q check = modusPonens
algebraic-stack_agda0000_doc_4320
import MJ.Classtable.Core as Core module MJ.Classtable.Membership {c}(Ct : Core.Classtable c) where open Core c open Classtable Ct open import Prelude open import Data.Star open import Data.Product hiding (Σ) open import Data.List open import Data.List.Relation.Unary.Any open import Data.List.Relation.Unary.Any.Pro...
algebraic-stack_agda0000_doc_4321
{-# OPTIONS --without-K --exact-split #-} module rings-with-properties where import rings open rings public -------------------------------------------------------------------------------- {- Commutative rings -} is-commutative-Ring : { l : Level} → Ring l → UU l is-commutative-Ring R = (x y : type-Ring R) → I...
algebraic-stack_agda0000_doc_4323
------------------------------------------------------------------------ -- Reasoning about _⇔_ -- -- NOTE: we don’t use Relation.Binary.IsEquivalence here, since we’re reasoning -- about a heterogeneous equivalence relation (i.e., the types of the operands -- of _⇔_, which are themselves types, can be of different lev...
algebraic-stack_agda0000_doc_4324
{-# OPTIONS --rewriting #-} module Properties.StrictMode where import Agda.Builtin.Equality.Rewrite open import Agda.Builtin.Equality using (_≡_; refl) open import FFI.Data.Either using (Either; Left; Right; mapL; mapR; mapLR; swapLR; cond) open import FFI.Data.Maybe using (Maybe; just; nothing) open import Luau.Heap...
algebraic-stack_agda0000_doc_4325
------------------------------------------------------------------------ -- The Agda standard library -- -- An inductive definition of the heterogeneous suffix relation ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.List.Relation.Binary.Suffix.H...
algebraic-stack_agda0000_doc_4326
module PredicateName where open import OscarPrelude record PredicateName : Set where constructor ⟹_⟩ field name : Nat open PredicateName public instance EqPredicateName : Eq PredicateName Eq._==_ EqPredicateName _ = decEq₁ (cong name) ∘ (_≟_ on name $ _)
algebraic-stack_agda0000_doc_4327
{-# OPTIONS --copatterns --sized-types #-} open import Size open import Function open import Relation.Binary open import Relation.Binary.PropositionalEquality as P open ≡-Reasoning open import Algebra.Structures using (IsCommutativeSemiring; IsCommutativeMonoid) open import Data.Nat open import Data.Nat.Properties u...
algebraic-stack_agda0000_doc_4328
module _ where open import Agda.Builtin.Reflection open import Agda.Builtin.Unit open import Agda.Builtin.Nat open import Agda.Builtin.Equality variable A : Set super-tac : Term → TC ⊀ super-tac hole = unify hole (lit (nat 101)) solver : Nat → Term → TC ⊀ solver n hole = unify hole (lit (nat (n + 1))) foo : {@(...
algebraic-stack_agda0000_doc_4329
{-# OPTIONS --safe #-} module Cubical.Algebra.NatSolver.HornerForms where open import Cubical.Foundations.Prelude open import Cubical.Data.Nat hiding (isZero) open import Cubical.Data.FinData open import Cubical.Data.Vec open import Cubical.Data.Bool using (Bool; true; false; if_then_else_) private variable ℓ ...
algebraic-stack_agda0000_doc_4330
module Basic.Compiler.SplitCode where open import Basic.Compiler.Code open import Basic.AST open import Basic.BigStep open import Utils.Monoid open import Data.Vec hiding (_++_; [_]; _∷ʳ_) open import Data.Bool renaming (if_then_else_ to ifBool_then_else_) open import Data.Nat open import Data.List hiding ([_]) open...
algebraic-stack_agda0000_doc_4331
-- Andreas, 2016-05-13 Issue 1973 reported by Nisse -- Problems with parameters to overloaded projections -- {-# OPTIONS -v tc.proj.amb:100 #-} -- {-# OPTIONS -v tc.deftype:100 #-} record R₁ : Set₁ where field f : Set open R₁ public postulate F : ∀ {a} → Set a → Set a module M (_ : Set₁) where record R₂...
algebraic-stack_agda0000_doc_4332
module Category.Monad.Reader {i}{I : Set i} where open import Category.Applicative.Indexed open import Category.Monad open import Category.Monad.Predicate open import Relation.Unary open import Relation.Unary.PredicateTransformer open import Data.Product open import Data.Unit open import Function open import Level Re...
algebraic-stack_agda0000_doc_4333
-- Andreas, 2019-03-25, issue #3647, reported and bisected by nad. -- Regression introduced in refactoring a78d7f54e447cadf039da81b50ff40c81aa93909. {-# OPTIONS --allow-unsolved-metas #-} -- {-# OPTIONS -v 90 #-} postulate A : Set P : A → Set Q : A → A → Set Q _ x = P x record R (P : A → Set) : Set where fie...
algebraic-stack_agda0000_doc_4334
module Test where open import IO using (run; putStrLn) import IO.Primitive as Prim using (IO) open import Data.Nat.Show as Nat using (show) open import Data.Unit using (⊀) open import Vector main : Prim.IO ⊀ main = run (putStrLn (Nat.show (length gravity₂)))
algebraic-stack_agda0000_doc_4335
module Logic.Linear where open import Data.Nat using (ℕ; zero; suc) open import Data.Fin using (Fin; zero; suc) open import Data.Vec using (Vec; []; _∷_; _++_; map) open import Data.Empty using (⊥) -- Operator precedences. infix 10 _^⊥ e?_ e!_ infixl 9 _⊗_ _&_ infixl 8 _⊕_ _⅋_ infixl 7 _⊾_ infixl 6 _≡_ -- Primitive ...
algebraic-stack_agda0000_doc_4322
-- Andreas, 2017-01-12, issue #2386 -- Should be rejected: data Eq (A : Set) : (x y : A) → Set where refl : (x y : A) → Eq A x y {-# BUILTIN EQUALITY Eq #-} -- Expected error: -- Wrong type of constructor of BUILTIN EQUALITY -- when checking the pragma BUILTIN EQUALITY Eq
algebraic-stack_agda0000_doc_6368
module Numeral.Real where open import Data.Tuple open import Logic import Lvl open import Numeral.Natural open import Numeral.Natural.Oper open import Numeral.Rational open import Numeral.Rational.Oper open import Relator.Equals open import Type open import Type.Quotient -- TODO: This will not work, but it is th...
algebraic-stack_agda0000_doc_6369
------------------------------------------------------------------------------ -- The division program is correct ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism #...
algebraic-stack_agda0000_doc_6370
module Data.Num.Bij.Properties where open import Data.Num.Bij renaming (_+B_ to _+_; _*B_ to _*_) open import Data.List open import Relation.Binary.PropositionalEquality as PropEq using (_≡_; _≢_; refl; cong; sym; trans) open PropEq.≡-Reasoning --------------------------------------------------------------------...
algebraic-stack_agda0000_doc_6371
{-# OPTIONS --safe #-} module Cubical.Algebra.OrderedCommMonoid.Properties where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Structure open import Cubical.Foundations.HLevels open import Cubical.Foundations.SIP using (TypeWithStr) open import Cubical.Data.Sigma open import Cubical.Algebra...
algebraic-stack_agda0000_doc_6372
{-# OPTIONS --allow-unsolved-metas #-} -- {-# OPTIONS -v tc.conv.elim:100 #-} module Issue814 where record IsMonoid (M : Set) : Set where field unit : M _*_ : M → M → M record Monoid : Set₁ where field carrier : Set is-mon : IsMonoid carrier record Structure (Struct : Set₁) (HasS...
algebraic-stack_agda0000_doc_6374
open import Nat open import Prelude open import List open import core open import judgemental-erase module moveerase where -- type actions don't change the term other than moving the cursor -- around moveeraset : {t t' : τ̂} {ÎŽ : direction} → (t + move ÎŽ +> t') → (t ◆t) == (t' ◆t) movee...
algebraic-stack_agda0000_doc_6375
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Data.Bool.Properties where open import Cubical.Core.Everything open import Cubical.Functions.Involution open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.Isomorphism open import Cubical.Found...
algebraic-stack_agda0000_doc_6376
-- There were some serious bugs in the termination checker -- which were hidden by the fact that it didn't go inside -- records. They should be fixed now. module Issue222 where record R (A : Set) : Set where module M (a : A) where -- Bug.agda:4,17-18 -- Panic: unbound variable A -- when checking that the expressio...
algebraic-stack_agda0000_doc_6377
-- {-# OPTIONS -v scope.decl.trace:50 #-} data D : Set where D : Set
algebraic-stack_agda0000_doc_6378
-- A Simple selection of modules with some renamings to -- make my (your) life easier when starting a new agda module. -- -- This includes standard functionality to work on: -- 1. Functions, -- 2. Naturals, -- 3. Products and Coproducts (projections and injections are p1, p2, i1, i2). -- 4. Finite Types (zero and s...
algebraic-stack_agda0000_doc_6379
module Control.Monad.Free.Quotiented where open import Prelude open import Data.List hiding (map) open import Data.Fin.Sigma open import Algebra postulate uip : isSet A -------------------------------------------------------------------------------- -- Some functors ------------------------------------------------...
algebraic-stack_agda0000_doc_6380
------------------------------------------------------------------------ -- Container combinators ------------------------------------------------------------------------ {-# OPTIONS --sized-types #-} module Indexed-container.Combinators where open import Equality.Propositional open import Logical-equivalence using ...
algebraic-stack_agda0000_doc_6381
module Lib.Vec where open import Common.Nat renaming (zero to Z; suc to S) open import Lib.Fin open import Common.Unit import Common.List -- using (List ; [] ; _∷_) data Vec (A : Set) : Nat -> Set where _∷_ : forall {n} -> A -> Vec A n -> Vec A (S n) [] : Vec A Z infixr 30 _++_ _++_ : {A : Set}{m n : Nat} ->...
algebraic-stack_agda0000_doc_6382
{-# OPTIONS --without-K #-} module Agda.Builtin.Nat where open import Agda.Builtin.Bool data Nat : Set where zero : Nat suc : (n : Nat) → Nat {-# BUILTIN NATURAL Nat #-} infix 4 _==_ _<_ infixl 6 _+_ _-_ infixl 7 _*_ _+_ : Nat → Nat → Nat zero + m = m suc n + m = suc (n + m) {-# BUILTIN NATPLUS _+_ #-} _...
algebraic-stack_agda0000_doc_6383
{-# OPTIONS --allow-unsolved-metas #-} open import Agda.Builtin.List open import Agda.Builtin.Nat infixl 6 _∷ʳ_ _∷ʳ_ : {A : Set} → List A → A → List A [] ∷ʳ x = x ∷ [] (hd ∷ tl) ∷ʳ x = hd ∷ tl ∷ʳ x infixl 5 _∷ʳ′_ data InitLast {A : Set} : List A → Set where [] : InitLast [] _∷ʳ′_ : (xs : List A) (x :...
algebraic-stack_agda0000_doc_6373
{-# OPTIONS --rewriting #-} module Properties.Subtyping where open import Agda.Builtin.Equality using (_≡_; refl) open import FFI.Data.Either using (Either; Left; Right; mapLR; swapLR; cond) open import FFI.Data.Maybe using (Maybe; just; nothing) open import Luau.Subtyping using (_<:_; _≮:_; Tree; Language; ¬Language...
algebraic-stack_agda0000_doc_12928
{-# OPTIONS --cubical-compatible #-} module Issue1025 where data _≡_ {A : Set} (x : A) : A → Set where refl : x ≡ x postulate mySpace : Set postulate myPoint : mySpace data Foo : myPoint ≡ myPoint → Set where foo : Foo refl test : {e : myPoint ≡ myPoint} → (a : Foo e) → (i : a ≡ a) → i ≡ refl test foo refl = {...
algebraic-stack_agda0000_doc_12929
------------------------------------------------------------------------ -- The Agda standard library -- -- Non empty trie, basic type and operations ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe --sized-types #-} open import Relation.Binary using (StrictTotal...
algebraic-stack_agda0000_doc_12930
module Basic where open import Prelude data List (A : Set) : Set data List A where nil : List A cons : A -> List A -> List A append : {A : Set} -> List A -> List A -> List A append nil ys = ys append (cons x xs) ys = cons x (append xs ys) record Equiv {A : Set} (R : A -> A -> Set) : Set record Equiv {A} R wh...
algebraic-stack_agda0000_doc_12931
{- This file contains: - An implementation of the free groupoid (a free group that has no limitiations over the high dimensional path structure). An intermediate construction used to calculate the fundamental group of a Bouquet. -} {-# OPTIONS --safe #-} module Cubical.HITs.FreeGroupoid.Base where open import ...
algebraic-stack_agda0000_doc_12932
{-# OPTIONS --without-K --exact-split #-} module encode-decode where import 05-identity-types open 05-identity-types public record Lift {i j : Level} (A : UU i) : UU (i ⊔ j) where field raise : A module Coprod where code-left : {i j : Level} {A : UU i} {B : UU j} → A → (coprod A B) → (UU i) code-left a₀ (...
algebraic-stack_agda0000_doc_12933
------------------------------------------------------------------------------ -- Properties of the mirror function ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-universe-polymorphism...
algebraic-stack_agda0000_doc_12934
module UnequalTerms where data Zero : Set where data One : Set where one : One err1 : Zero err1 = one err2 : One -> One err2 = \(x : Zero) -> one
algebraic-stack_agda0000_doc_12935
-- Andreas, 2015-02-26 -- {-# OPTIONS -v interaction:100 #-} data D : Set where c : D goal : D goal = {! !} -- C-c C-r gave a parse error here, as there was a (single) space. g1 : D g1 = {! !} g2 : D g2 = {! !} -- works now
algebraic-stack_agda0000_doc_12936
------------------------------------------------------------------------ -- The Agda standard library -- -- Code related to vector equality over propositional equality that -- makes use of heterogeneous equality ------------------------------------------------------------------------ {-# OPTIONS --with-K --safe #-} m...
algebraic-stack_agda0000_doc_12937
{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Relation.Binary.Construct.Constant where open import Cubical.Core.Everything open import Cubical.Foundations.Prelude open import Cubical.Foundations.HLevels using (hProp) open import Cubical.Relation.Binary open import Cubical.Structures.Carrier -----...
algebraic-stack_agda0000_doc_12939
{-# OPTIONS --cubical #-} module Numeral.Natural.Equiv.Path where open import Data.Boolean.Equiv.Path open import Functional open import Logic.Propositional open import Numeral.Natural.Oper.Comparisons open import Numeral.Natural open import Relator.Equals.Proofs.Equivalence using () renaming ([≡]-equiv to Id-equiv ;...
algebraic-stack_agda0000_doc_12940
module List.Order.Bounded {A : Set}(_≀_ : A → A → Set) where open import Bound.Total A open import Bound.Total.Order _≀_ open import Data.List data _≀*_ : List A → Bound → Set where lenx : {t : Bound} → [] ≀* t lecx : {t : Bound}{x : A}{xs : List A} → LeB (val x) t → xs ≀* t → (x ∷ xs) ≀* t data _*≀_ : Bound → ...