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-- Minimal implicational modal logic, vector-based de Bruijn approach, initial encoding module Vi.BoxMp where open import Lib using (Nat; suc; _+_; Fin; fin; Vec; []; _,_; proj; VMem; mem) -- Types infixr 0 _=>_ data Ty : Set where UNIT : Ty _=>_ : Ty -> Ty -> Ty BOX : Ty -> Ty -- Contex...
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------------------------------------------------------------------------ -- The Agda standard library -- -- This module is DEPRECATED. Please use the -- Relation.Binary.Construct.Closure.ReflexiveTransitive module directly ------------------------------------------------------------------------ {-# OPTIONS --without-K...
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------------------------------------------------------------------------ -- The Agda standard library -- -- This module is DEPRECATED. Please use -- Data.List.Relation.Binary.Lex.Core directly. ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Data.List...
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module Issue2487-1 where postulate get-out-of-jail : {A : Set} -> A
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{-# OPTIONS --without-K #-} module overloading.level where open import sum open import equality.core open import overloading.bundle open import function.isomorphism open import hott.level.core open import sets.unit open Bundle bundle-structure-iso : ∀ {i j}{Base : Set i} (Struct : Base → Set ...
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module Data.Fin.Subset.Properties.Cardinality where open import Data.Nat as ℕ using (ℕ) open import Data.Nat.Properties as NP open import Data.Empty using (⊥-elim) open import Data.Fin open import Data.Fin.Subset open import Data.Fin.Subset.Properties open import Data.Vec using (_∷_; []) open import Data.Vec.Any usi...
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module _ where open import Agda.Builtin.Nat open import Imports.ImportedDisplayForms postulate T : Nat → Set foo : (a : Nat) → T (a + a) foo a = {!!}
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open import Oscar.Prelude open import Oscar.Class.HasEquivalence open import Oscar.Class.Smap open import Oscar.Class.Surjextensionality open import Oscar.Class.Symmetry open import Oscar.Class.Symmetrical open import Oscar.Class.Transitivity open import Oscar.Data.ProductIndexEquivalence open import Oscar.Data.Surjex...
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{-# OPTIONS --cubical --no-import-sorts --safe #-} module Cubical.Algebra.AbGroup.Base where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Equiv open import Cubical.Foundations.Equiv.HalfAdjoint open import Cubical.Foundations.HLevels open import Cubical.Foundations.Isomorphism open import Cu...
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{-# OPTIONS --cubical #-} module Type.Cubical.Path.Category{ℓ} where open import Data.Tuple as Tuple using (_,_) open import Data open import Functional open import Function.Axioms open import Logic.Propositional open import Structure.Category open import Structure.Categorical.Properties open import Structure.Operato...
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open import Agda.Builtin.Bool f : Bool → Bool f x = let y = x in {!!}
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{-# OPTIONS --cubical --safe #-} module Cubical.HITs.Ints.QuoInt where open import Cubical.HITs.Ints.QuoInt.Base public -- open import Cubical.HITs.Ints.QuoInt.Properties public
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{-# OPTIONS --without-K --exact-split #-} module dn-sheaves where import rings open rings public {- We postulate a propositional resizing axiom -} raise-UU-Prop : (l : Level) → UU-Prop lzero → UU-Prop l raise-UU-Prop l (pair P is-prop-P) = pair ( raise l P) ( is-prop-is-equiv' P ( map-raise l P)...
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-- MIT License -- Copyright (c) 2021 Luca Ciccone and Luca Padovani -- Permission is hereby granted, free of charge, to any person -- obtaining a copy of this software and associated documentation -- files (the "Software"), to deal in the Software without -- restriction, including without limitation the rights to use...
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module Algebra.Dioid.Bool where open import Algebra.Dioid data Bool : Set where true : Bool false : Bool data _≡_ : (x y : Bool) -> Set where reflexivity : ∀ {x : Bool} -> x ≡ x symmetry : ∀ {x y : Bool} -> x ≡ y -> y ≡ x transitivity : ∀ {x y z : Bool} -> x ≡ y -> y ...
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9. Copyright (c) 2020, 2021, Oracle and/or its affiliates. Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl -} open import LibraBFT.Prelude open import LibraBFT.Lemmas open import Lib...
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module Identity where data _==_ {A : Set}(x : A) : A -> Set where refl : x == x elim== : {A : Set}(x : A)(C : (y : A) -> x == y -> Set) -> C x refl -> (y : A) -> (p : x == y) -> C y p elim== x C Cx .x refl = Cx elim==₁ : {A : Set}(x : A)(C : (y : A) -> x == y -> Set1) -> C x refl -> (y : A) -> (p : x ...
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{-# OPTIONS --no-auto-inline #-} module Haskell.Prim.Num where open import Agda.Builtin.Nat as Nat hiding (_+_; _-_; _*_; _<_; _==_) open import Agda.Builtin.Int using (pos; negsuc) open import Agda.Builtin.FromNat open import Agda.Builtin.FromNeg open import Agda.Builtin.Unit open import Haskell.Prim open import Ha...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Some derivable properties ------------------------------------------------------------------------ open import Algebra module Algebra.Properties.Lattice {l₁ l₂} (L : Lattice l₁ l₂) where open Lattice L open im...
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{-# OPTIONS --without-K --safe #-} -- Some of the obvious properties of cartesian functors module Categories.Functor.Cartesian.Properties where open import Level open import Data.Product using (Σ ; _,_) open import Categories.Category open import Categories.Category.Cartesian.Structure open import Categories.Functor...
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-- Andreas, 2012-05-24, issue reported by Nisse {-# OPTIONS --allow-unsolved-metas #-} -- {-# OPTIONS -v tc.meta:50 #-} module Issue658 where import Common.Level postulate A : Set P : A → Set Q : (x : A) → P x → Set p : (x : A) → P x record R : Set where field a : A r : R r = {!!} postulate q : Q (...
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{- Byzantine Fault Tolerant Consensus Verification in Agda, version 0.9. Copyright (c) 2020 Oracle and/or its affiliates. Licensed under the Universal Permissive License v 1.0 as shown at https://opensource.oracle.com/licenses/upl -} open import LibraBFT.Prelude open import LibraBFT.Hash open import LibraBFT.Ab...
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{-# OPTIONS --without-K --safe #-} -- Pi combinators inspired by duals and traced monoidal categories module PiPointedFracTrace where open import Data.Unit open import Data.Sum open import Data.Product open import Relation.Binary.PropositionalEquality open import PiPointedFrac -------------------------------------...
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module McK-B where open import CS410-Prelude open import CS410-Nat open import CS410-Vec data Bit : Set where O I : Bit exp2 : Nat -> Nat exp2 zero = 1 exp2 (suc n) = exp2 n +N exp2 n WordNZ : Nat -> Set data Word (n : Nat) : Set where O : Word n [_] : WordNZ n -> Word n WordNZ zero = One WordNZ (suc n) ...
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module IdentP where data Bool : Set where false : Bool true : Bool f : {A : Set} → A → A → A f x y = x g : Bool → Bool g false = true g true = true
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-- Andreas, 2018-09-03, issue #3207 -- -- Error message for disabled Prop. {-# OPTIONS --no-prop #-} test = Prop
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module Fin where open import Prelude open import Star open import Modal open import Nat Fin : Nat -> Set Fin = Any (\_ -> True) fzero : {n : Nat} -> Fin (suc n) fzero = done _ • ε fsuc : {n : Nat} -> Fin n -> Fin (suc n) fsuc i = step • i
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module HasDecidableSalvation where open import OscarPrelude open import HasSalvation record HasDecidableSalvation (A : Set) : Set₁ where field ⦃ hasSalvation ⦄ : HasSalvation A ▷?_ : (x : A) → Dec $ ▷ x open HasDecidableSalvation ⦃ … ⦄ public {-# DISPLAY HasDecidableSalvation.▷?_ _ = ▷?_ #-}
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{- A couple of general facts about equivalences: - if f is an equivalence then (cong f) is an equivalence ([equivCong]) - if f is an equivalence then pre- and postcomposition with f are equivalences ([preCompEquiv], [postCompEquiv]) - if f is an equivalence then (Σ[ g ] section f g) and (Σ[ g ] retract f g) are contr...
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module List where import Prelude import Equiv import Datoid import Nat open Prelude open Equiv open Datoid open Nat data List (a : Set) : Set where nil : List a _::_ : a -> List a -> List a map : {a b : Set} -> (a -> b) -> List a -> List b map f nil = nil map f (x :: xs) = f ...
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interleaved mutual data CoNat : Set record ∞CoNat : Set constructor zero : CoNat record ∞CoNat where coinductive field force : CoNat constructor suc : ∞CoNat → ?
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------------------------------------------------------------------------------ -- Inductive PA properties using the induction principle ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-u...
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-- Andreas, 2014-03-27 fixed issue {-# OPTIONS --copatterns --sized-types #-} open import Common.Size record R (i : Size) : Set where inductive constructor c field j : Size< i r : R j data ⊥ : Set where elim : (i : Size) → R i → ⊥ elim i (c j r) = elim j r -- elim should be rejected by termination c...
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module Rationals.Properties where open import Nats renaming (_*_ to _:*:_) open import Rationals open import Data.Empty open import Data.Product open import Equality ------------------------------------------------------------------------ -- internal stuffs private a*b÷b=a : ∀ a b → a :*: b ÷ b →ℕ ≡ (a , refl) ...
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module RandomAccessList.Standard.Core where open import BuildingBlock.BinaryLeafTree using (BinaryLeafTree; Node; Leaf) open import Data.Nat open import Data.Nat.Etc -- parameterized by the level of the least significant digit data 0-1-RAL (A : Set) : ℕ → Set where [] : ∀ {n} → ...
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------------------------------------------------------------------------------ -- Test the consistency of PA.Axiomatic.Standard.Base ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS --no-univ...
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-- Box modality: cofree presheaf on a family module SOAS.Abstract.Box {T : Set} where open import SOAS.Common open import SOAS.Context open import SOAS.Sorting open import SOAS.Variable open import SOAS.Families.Core {T} open import SOAS.Families.Isomorphism open import SOAS.Families.BCCC using (_×ₘ_; _+ₘ_; _⇨_; _⇨̣_...
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-- 2011-10-04 Andreas {-# OPTIONS --experimental-irrelevance #-} module TerminationOnIrrelevant where data ⊥ : Set where data Empty : Set where c : Empty → Empty d : Empty → Empty d (c x) = x f : .Empty → ⊥ f (c x) = f x g : .Empty → ⊥ g (c x) = g x data _≡_ {A : Set}(a : A) : A → Set where refl : a ≡ a -- t...
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module RepeatedVariableInPattern where K : Set -> Set K A A = A
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module Categories.Functor.CartesianClosed where open import Categories.Category using (Category; _[_∘_]; _[_,_]) open import Categories.Category.Cartesian using (Cartesian) open import Categories.Category.Cartesian.Bundle using (CartesianCategory) open import Categories.Category.CartesianClosed using (CartesianClosed)...
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module Issue2937.WithUnicode where foo : _ → _ → Set foo bar x = λ x → foo (bar x {!!}) x
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-- Left ℤ-multiplication on groups and some of its properties {-# OPTIONS --safe --experimental-lossy-unification #-} module Cubical.Algebra.Group.ZAction where open import Cubical.Foundations.Prelude open import Cubical.Foundations.Isomorphism open import Cubical.Foundations.Equiv open import Cubical.Data.Sigma open...
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------------------------------------------------------------------------ -- The Agda standard library -- -- Monad syntax for the TC monad ------------------------------------------------------------------------ {-# OPTIONS --without-K --safe #-} module Reflection.TypeChecking.MonadSyntax where open import Agda.Built...
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{-# OPTIONS --without-K --rewriting #-} open import HoTT open import homotopy.HSpace open import homotopy.EM1HSpace open import homotopy.EilenbergMacLane1 using (EM₁-level₁) open import lib.types.TwoSemiCategory open import lib.two-semi-categories.FundamentalCategory module homotopy.EM1HSpaceAssoc where module EM₁HS...
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module Vec where open import Basics open import Ix open import All open import Cutting open import Tensor data Vec (X : Set) : Nat -> Set where [] : Vec X zero _,-_ : forall {n} -> X -> Vec X n -> Vec X (suc n) _+V_ : forall {X n m} -> Vec X n -> Vec X m -> Vec X (n +N m) [] +V ys = ys (x ,- xs) +V ys = x...
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------------------------------------------------------------------------------ -- Test the consistency of FOTC.Relation.Binary.Bisimilarity.Type ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIO...
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{-# OPTIONS --without-K --safe #-} module Math.NumberTheory.Product.Nat where -- agda-stdlib open import Data.Nat.Properties -- agda-misc open import Math.NumberTheory.Product.Generic open MonoidProduct *-1-monoid public
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open import Prelude module Implicits.Syntax.Context where open import Implicits.Syntax.Type open import Data.List.All open import Data.Vec open import Data.List Ctx : ℕ → ℕ → Set Ctx ν n = Vec (Type ν) n ICtx : ℕ → Set ICtx ν = List (Type ν) -- wellformed implicit contexts _⊢OK : ∀ {ν} → ICtx ν → Set Δ ⊢OK = All (...
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------------------------------------------------------------------------------ -- Distributive laws on a binary operation (Stanovský example) ------------------------------------------------------------------------------ {-# OPTIONS --exact-split #-} {-# OPTIONS --no-sized-types #-} {-# OPTIONS ...
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{-# OPTIONS --safe --warning=error --without-K #-} open import Sets.EquivalenceRelations open import LogicalFormulae open import Setoids.Setoids open import Rings.Definition open import Modules.Definition open import Numbers.Naturals.Semiring open import Numbers.Naturals.Order open import Lists.Lists open import Vecto...
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{-# OPTIONS --rewriting #-} -- 2014-05-27 Jesper and Andreas postulate A B : Set R : A → B → Set {-# BUILTIN REWRITE R #-}
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{-# OPTIONS --without-K --exact-split --rewriting --overlapping-instances #-} open import lib.Basics open import lib.NConnected open import lib.NType2 open import lib.types.Truncation open import Coequalizers.Definition open import Coequalizers.Misc open import Graphs.Definition open import Util.Misc module Groups...
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module CTL.Proof where open import CTL.Proof.AG public open import CTL.Proof.EG public
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module ReflectionExposeConstraints where open import Agda.Builtin.Reflection open import Agda.Builtin.List open import Agda.Builtin.Nat open import Agda.Builtin.Unit open import Agda.Builtin.Equality _>>=_ : ∀ {a b} {A : Set a} {B : Set b} → TC A → (A → TC B) → TC B _>>=_ = bindTC _ifMeta_ : {A : Set} → Term → (Meta...
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open import Relation.Unary open import Relation.Ternary.Separation module Relation.Ternary.Separation.Monad.Free {ℓ} {A : Set ℓ} {{r : RawSep A}} (Cmd : Pred A ℓ) (δ : ∀ {Φ} → Cmd Φ → Pred A ℓ) where open import Level open import Function open import Data.Unit open import Data.Product open import Relation.U...
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module PLRTree.Complete.Correctness.Alternative {A : Set} where open import BTree.Complete.Alternative {A} open import BTree.Complete.Alternative.Properties {A} open import BTree.Equality {A} open import PLRTree {A} open import PLRTree.Complete {A} renaming (Complete to Complete' ; _⋗_ to _⋗'_ ; _⋘_ to _⋘'_ ; _⋙_ to ...
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-- Andreas, 2012-02-13: polarity info must be correct {-# OPTIONS --sized-types --show-implicit #-} -- {-# OPTIONS -v tc.size.solve:20 -v tc.conv.size:20 #-} -- {-# OPTIONS -v tc.polarity.set:10 -v tc.conv.term.shortcut:20 #-} module WrongPolarity where open import Common.Size data ⊥ : Set where data Sink (A : Set...
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module DescStrat where open import StratSigma data Desc42 : Set43 where id42 : Desc42 const42 : Set42 -> Desc42 prod42 : Desc42 -> Desc42 -> Desc42 sigma42 : (S : Set42) -> (S -> Desc42) -> Desc42 pi42 : (S : Set42) -> (S -> Desc42) -> Desc42 [|_|]42_ : Desc42 -> Set42 -> Set42 [| id42 |]42 Z ...
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module CombinatoryLogic.Semantics where open import Relation.Binary using (Rel) open import CombinatoryLogic.Syntax -- Kapitel 1, Abschnitt C, §5 (Axiome) data Axiom : Combinator → Set where Q : Axiom (Π ∙ (W ∙ (C ∙ Q))) B : Axiom (C ∙ (B ∙ B ∙ (B ∙ B ∙ B)) ∙ B == B ∙ (B ∙ B) ∙ B) C : Axiom (C ∙ (B ∙ B ∙ (B ∙ ...
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open import Prelude open import dynamics-core open import progress-checks module finality where finality : Σ[ d ∈ ihexp ] (d final × (Σ[ d' ∈ ihexp ] (d ↦ d'))) → ⊥ finality (π1 , π2 , π3 , π4) = final-not-step π2 (π3 , π4) -- a slight restatement of the above, generalizing it to the -- multistep judgement ...
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postulate A : Set record R : Set where constructor c field f : A open R {{...}} works : {{_ : R}} → A works = f works' : {{_ : R}} → Set → A works' B = f test : {{_ : R}} → A test {{_}} = f -- No variable of type R was found in scope. -- when checking that the expression f has type A test1 : {{_ : R}} → Set...
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module monad where open import eq record Monad (M : Set → Set) : Set₁ where field return : ∀{A : Set} → A → M A bind : ∀{A B : Set} → M A → (A → M B) → M B monad-left-id : ∀{A B : Set}{a : A}{f : A → M B} → bind (return a) f ≡ f a monad-right-id : ∀{A : Set}{c : M A} → bind c...
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------------------------------------------------------------------------ -- Higher lenses with erased proofs ------------------------------------------------------------------------ -- At the time of writing there are counterparts in this file of more -- or less everything in Lens.Non-dependent.Higher, except for part...
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{-# OPTIONS --cubical --safe #-} module Cubical.HITs.Cylinder.Base where open import Cubical.Core.Everything open import Cubical.Foundations.Everything open import Cubical.HITs.PropositionalTruncation import Cubical.Data.Everything as Data open Data hiding (inl; inr) open import Cubical.HITs.Interval -- Cylinder...
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module Editor where open import Agda.Builtin.FromNat open import BasicIO open import Data.Bool open import Data.Char open import Data.List hiding (_++_) open import Data.String open import Data.Unit open import Function open import Int open import Terminal readTimeout : Int readTimeout = 0 readMinChars : Int readMin...
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{-# OPTIONS --cubical --safe #-} module Cubical.Foundations.UnivalenceId where open import Cubical.Core.Glue renaming ( isEquiv to isEquivPath ; _≃_ to EquivPath ; equivFun to equivFunPath ) open import Cubical.Core.Id open import Cubical.Foundations.Prelude public hiding (...
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module Ual.Void where data ⊥ : Set where ¬ : Set → Set ¬ p = p → ⊥
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module Arity where open import OscarPrelude record Arity : Set where constructor ⟨_⟩ field arity : Nat open Arity public instance EqArity : Eq Arity Eq._==_ EqArity _ = decEq₁ (cong arity) ∘ (_≟_ on arity $ _)
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open import Common.Reflect open import Common.Prelude data Z : Set where zero : Z foo : QName → Bool → Bool foo (quote Nat.zero) b = {!b!} foo _ _ = false
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open import Oscar.Prelude open import Oscar.Class open import Oscar.Class.Leftunit open import Oscar.Class.Reflexivity open import Oscar.Class.Transitivity open import Oscar.Class.Transleftidentity module Oscar.Class.Transleftidentity.ToLeftunit where module _ {𝔬} {𝔒 : Ø 𝔬} {𝔯} {_∼_ : 𝔒 → 𝔒 → Ø 𝔯} {ℓ} {...
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------------------------------------------------------------------------ -- A map function for the substitutions ------------------------------------------------------------------------ open import Data.Universe.Indexed module deBruijn.Substitution.Function.Map {i u e} {Uni : IndexedUniverse i u e} where import Ax...
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{-# OPTIONS --sized-types #-} module SList.Properties (A : Set) where open import Data.List open import List.Permutation.Base A open import SList lemma-unsize-size : (xs : List A) → xs ∼ unsize A (size A xs) lemma-unsize-size [] = ∼[] lemma-unsize-size (x ∷ xs) = ∼x /head /head (lemma-unsize-size xs)
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open import Relation.Unary using ( ∅ ; _∪_ ) open import Web.Semantic.DL.Concept using ( Concept ) open import Web.Semantic.DL.Role using ( Role ) open import Web.Semantic.DL.Signature using ( Signature ) open import Web.Semantic.Util using ( Subset ; ⁅_⁆ ) module Web.Semantic.DL.TBox where infixl 5 _⊑₁_ _⊑₂_ infixr ...
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module GUIgeneric.GUIFeatures where open import GUIgeneric.Prelude open import GUIgeneric.GUIDefinitions renaming (add to add'; add' to add) open import GUIgeneric.GUI open import GUIgeneric.GUIExampleLib open import StateSizedIO.GUI.WxGraphicsLibLevel3 open Interfaceˢ public -- Components -- frameAndOKButton : ...
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{-# OPTIONS --allow-unsolved-metas #-} {- 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 Haskell.Modules.RWS open i...
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------------------------------------------------------------------------ -- From the Agda standard library -- -- Sizes for Agda's sized types ------------------------------------------------------------------------ module Common.Size where open import Agda.Builtin.Size public renaming (ω to ∞; SizeU to SizeUniv)
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module cfg1 where open import Level renaming ( suc to succ ; zero to Zero ) open import Data.Nat hiding ( _≟_ ) -- open import Data.Fin -- open import Data.Product open import Data.List open import Data.Maybe -- open import Data.Bool using ( Bool ; true ; false ; _∧_ ; _∨_ ) open import Relation.Binary.Propositional...
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open import Agda.Builtin.Equality variable A B : Set f g : A postulate F : Set → Set map : (A → B) → F A → F B lemma : (x : F A) → map (λ x → f (g x)) x ≡ map f (map g x) → F A lemma {A = A} {f = f} {g = g} x _ = x
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------------------------------------------------------------------------ -- Coinductive higher lenses with erased "proofs" ------------------------------------------------------------------------ {-# OPTIONS --guardedness #-} import Equality.Path as P module Lens.Non-dependent.Higher.Coinductive.Erased {e⁺} (eq : ...
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{-# OPTIONS --warning=error --without-K --safe #-} open import LogicalFormulae open import Categories.Definition open import Categories.Functor.Definition module Categories.Functor.Lemmas where functorCompose : {a b c d e f : _} {B : Category {a} {b}} {C : Category {c} {d}} {D : Category {e} {f}} → (Functor C D) → (...
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{-# OPTIONS --without-K #-} module Pi0Examples where open import PiU using (U; ZERO; ONE; PLUS; TIMES) open import PiLevel0 using (_⟷_; unite₊l; uniti₊l; unite₊r; uniti₊r; swap₊; assocl₊; assocr₊; unite⋆l; uniti⋆l; unite⋆r; uniti⋆r; swap⋆; assocl⋆; assocr⋆; absorbr; absorbl; factorzr; fac...
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import Lvl open import Data.Boolean open import Type module Data.List.Sorting.MergeSort {ℓ} {T : Type{ℓ}} (_≤?_ : T → T → Bool) where open import Data.List open import Data.List.Functions as List open import Data.List.Relation.Membership as Membership using (_∈_ ; use ; skip) open import Data.List.Relation.Membe...
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{- This file contains basic theory about subgroups. The definition is the same as the first definition of subgroups in: https://www.cs.bham.ac.uk/~mhe/HoTT-UF-in-Agda-Lecture-Notes/HoTT-UF-Agda.html#subgroups-sip -} {-# OPTIONS --safe #-} module Cubical.Algebra.Group.Subgroup where open import Cubical.Foundations....
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module CompleteSemantics.Iemhoff where open import Syntax public -- Introspective brilliant Kripke models. record Model : Set₁ where infix 3 _⊩ᵅ_ field World : Set _≤_ : World → World → Set refl≤ : ∀ {w} → w ≤ w trans≤ : ∀ {w w′ w″} → w ≤ w′ → w′ ≤ w″ → w ≤ w″ _R_ : World → Worl...
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module sum-thms where open import eq open import sum open import list open import product inj₁-inj : ∀{ℓ ℓ'}{A : Set ℓ}{B : Set ℓ'}{x : A}{x'} → inj₁{ℓ}{ℓ'}{A}{B} x ≡ inj₁ x' → x ≡ x' inj₁-inj refl = refl
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module MultiSorted.Context {s} (Sort : Set s) where -- An attempt to define more structured context -- that directly support the cartesian structure data Context : Set s where ctx-empty : Context ctx-slot : Sort → Context ctx-concat : Context → Context → Context -- the variables in a context data var : Contex...
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{-# OPTIONS --prop #-} open import Agda.Primitive record LiftP {ℓ ℓ'}(A : Prop ℓ) : Prop (ℓ ⊔ ℓ') where constructor liftP field unliftP : A open LiftP public unliftP' : {ℓ ℓ' ℓ'' : Level} {A : Prop ℓ}{B : Set ℓ''}(f : A → B) → LiftP {ℓ}{ℓ'} A → B unliftP' f (liftP x) = f x
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{-# OPTIONS --cubical --no-import-sorts #-} module Cubical.Codata.Everything where open import Cubical.Codata.EverythingSafe public --- Modules making assumptions that might be incompatible with other -- flags or make use of potentially unsafe features. -- Assumes --guardedness open import Cubical.Codata.Stream pub...
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module Automaton.Pushdown where
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module Naturals where open import Library open import Categories open import Functors open Fun record NatT {a b c d}{C : Cat {a}{b}}{D : Cat {c}{d}}(F G : Fun C D) : Set (a ⊔ b ⊔ c ⊔ d) where constructor natural open Cat field cmp : ∀ {X} → Hom D (OMap F X) (OMap G X) nat : ∀{X Y}{f : Hom C X Y} → ...
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module PushProdPull where open import Categories.Category open import Categories.Category.Cartesian.Bundle open import Categories.Category.CartesianClosed.Canonical open import Categories.Category.Core open import Categories.Category.Product open import Categories.Diagram.Pullback open import Categories.Diagram.Pushou...
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module Esterel.Lang.Properties where open import Esterel.Lang open import Relation.Binary.PropositionalEquality open import Relation.Unary open import Relation.Nullary using (¬_ ; Dec ; yes ; no) open import Esterel.Environment open import Esterel.Variable.Signal as Signal open import Esterel.Variable.Shared as Shared...
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------------------------------------------------------------------------ -- Safe modules that use --erased-cubical and --guardedness ------------------------------------------------------------------------ {-# OPTIONS --safe --erased-cubical --guardedness #-} module README.Safe.Cubical.Erased.Guardedness where -- M-...
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module OpenModule where module A where postulate X : Set -- Both open import and open module applies the directives -- to the "open" rather than to the module. open import Nat hiding (zero) renaming (Nat to N) open module B = A renaming (X to Y) Test : Set Test = Y → B.X → N → Nat.Nat zero : N zero = Nat.zero ...
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-- The category of contexts and renamings module SOAS.ContextMaps.CategoryOfRenamings {T : Set} where open import SOAS.Common open import SOAS.Context {T} open import SOAS.Variable open import SOAS.ContextMaps.Combinators (ℐ {T}) open import Categories.Functor.Bifunctor open import Categories.Object.Initial open imp...
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{-# OPTIONS --universe-polymorphism #-} module Categories.Support.SetoidPi where open import Level open import Function as Fun using (_on_) open import Relation.Binary as B using () renaming (_=[_]⇒_ to _=[_]⇒₀_; _⇒_ to _⊆_) open import Relation.Binary.PropositionalEquality as PE using (_≡_) open import Relation.Bina...
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{-# OPTIONS --without-K --safe #-} -- This module provides the basic expression type for polynomials. module Polynomial.Expr where open import Data.Nat using (ℕ) open import Data.Fin using (Fin) infixl 6 _⊕_ infixl 7 _⊗_ infixr 8 _⊛_ data Expr {ℓ} (A : Set ℓ) (n : ℕ) : Set ℓ where Κ : A → Expr A n Ι : Fin ...
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-- 2012-09-25 Andreas, reported by Nicolas Pouillard {-# OPTIONS --sized-types #-} module Issue700 where import Common.Level open import Common.Size postulate Size< : Size → Set {-# BUILTIN SIZELT Size< #-} postulate A : Set data T (i : Size) : Set where c : (j : Size< i) → T j → T _ bug : ∀ i → T i → A bug ...
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-- {-# OPTIONS -v term:30 #-} {-# OPTIONS --copatterns #-} module ColistMutual where mutual data CoList (A : Set) : Set where [] : CoList A _∷_ : (x : A)(xs : ∞CoList A) → CoList A record ∞CoList (A : Set) : Set where coinductive field out : CoList A open ∞CoList mutual repeat : {A : Set}(a...
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-- Saturated sets. module SAT3 where open import Library open import Terms open import Substitution open import Reduction open import SN open import SN.AntiRename -- Kripke predicates on well-typed terms. TmSet : (a : Ty) → Set₁ TmSet a = {Γ : Cxt} (t : Tm Γ a) → Set _⊆_ : ∀{a} (𝑨 𝑨′ : TmSet a) → Set 𝑨 ⊆ 𝑨′ = ...
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