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module Codata.Sized.Covec.Bisimilarity where
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open import Level using (_⊔_)
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- open import Size
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- open import Codata.Sized.Thunk
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+ open import Size using (Size; ∞)
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+ open import Codata.Sized.Thunk using (Thunk; Thunk^R; force)
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open import Codata.Sized.Conat hiding (_⊔_)
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- open import Codata.Sized.Covec
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+ open import Codata.Sized.Covec using (Covec; _∷_; [])
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open import Relation.Binary.Definitions
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using (Reflexive; Symmetric; Transitive; Sym; Trans)
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open import Relation.Binary.PropositionalEquality.Core as ≡ using (_≡_)
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module Codata.Sized.Covec.Effectful where
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- open import Codata.Sized.Conat
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- open import Codata.Sized.Covec
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- open import Effect.Functor
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- open import Effect.Applicative
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+ open import Codata.Sized.Conat using (Conat; zero; suc)
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+ open import Codata.Sized.Covec using (Covec; _∷_; []; map; replicate; ap)
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+ open import Effect.Functor using (RawFunctor)
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+ open import Effect.Applicative using (RawApplicative)
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functor : ∀ {ℓ i n} → RawFunctor {ℓ} (λ A → Covec A n i)
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functor = record { _<$>_ = map }
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module Codata.Sized.Covec.Instances where
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- open import Codata.Sized.Covec.Effectful
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+ open import Codata.Sized.Covec.Effectful using (functor; applicative)
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instance
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covecFunctor = functor
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module Codata.Sized.Covec.Properties where
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- open import Size
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+ open import Size using (Size; ∞)
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open import Codata.Sized.Thunk using (Thunk; force)
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- open import Codata.Sized.Conat
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- open import Codata.Sized.Covec
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+ open import Codata.Sized.Conat using (zero; suc)
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+ open import Codata.Sized.Covec using (Covec; _∷_; []; map)
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open import Codata.Sized.Covec.Bisimilarity
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open import Function.Base using (id; _∘_)
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- open import Relation.Binary.PropositionalEquality.Core as ≡
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+ open import Relation.Binary.PropositionalEquality.Core as ≡ using (_≡_)
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-- Functor laws
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module Codata.Sized.Cowriter.Bisimilarity where
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open import Level using (Level; _⊔_)
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- open import Size
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- open import Codata.Sized.Thunk
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- open import Codata.Sized.Cowriter
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+ open import Size using (Size; ∞)
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+ open import Codata.Sized.Thunk using (Thunk; Thunk^R; force)
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+ open import Codata.Sized.Cowriter using (Cowriter; _∷_;[_])
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open import Relation.Binary.Core using (REL; Rel)
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open import Relation.Binary.Bundles using (Setoid)
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open import Relation.Binary.Structures using (IsEquivalence)
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open import Relation.Binary.Definitions
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using (Reflexive; Symmetric; Transitive; Sym; Trans)
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open import Relation.Binary.PropositionalEquality.Core as ≡ using (_≡_)
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- import Relation.Binary.PropositionalEquality.Properties as ≡
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+ import Relation.Binary.PropositionalEquality.Properties as ≡ using (setoid)
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private
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variable
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module Codata.Sized.Delay.Bisimilarity where
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- open import Size
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- open import Codata.Sized.Thunk
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- open import Codata.Sized.Delay
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- open import Level
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+ open import Size using (Size; ∞)
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+ open import Codata.Sized.Thunk using (Thunk; Thunk^R; force)
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+ open import Codata.Sized.Delay using (Delay; now; later)
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+ open import Level using (_⊔_)
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open import Relation.Binary.Definitions
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using (Reflexive; Symmetric; Transitive; Sym; Trans)
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open import Relation.Binary.PropositionalEquality.Core as ≡ using (_≡_)
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module Codata.Sized.Delay.Effectful where
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open import Codata.Sized.Delay
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+ using (Delay; now; never; later; map; bind; zipWith; alignWith)
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open import Function.Base using (id)
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- open import Effect.Choice
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- open import Effect.Empty
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- open import Effect.Functor
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+ open import Effect.Choice using (RawChoice)
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+ open import Effect.Empty using (RawEmpty)
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+ open import Effect.Functor using (RawFunctor)
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open import Effect.Applicative
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- open import Effect.Monad
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+ using (RawApplicative; RawApplicativeZero; RawAlternative)
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+ open import Effect.Monad using (RawMonad; RawMonadZero)
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open import Data.These using (leftMost)
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functor : ∀ {i ℓ} → RawFunctor {ℓ} (λ A → Delay A i)
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import Data.Sum.Base as Sum
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import Data.Nat.Base as ℕ
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open import Codata.Sized.Thunk using (Thunk; force)
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- open import Codata.Sized.Conat
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+ open import Codata.Sized.Conat using (Conat; zero; suc; infinity; _⊔_; toℕ)
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open import Codata.Sized.Conat.Bisimilarity as Coℕ using (zero ; suc)
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open import Codata.Sized.Delay
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- open import Codata.Sized.Delay.Bisimilarity
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+ open import Codata.Sized.Delay.Bisimilarity using (now; later; _⊢_≈_)
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open import Function.Base using (id; _∘′_)
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open import Relation.Binary.PropositionalEquality.Core as ≡ using (_≡_)
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module Codata.Sized.M.Bisimilarity where
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- open import Level
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- open import Size
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- open import Codata.Sized.Thunk
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- open import Codata.Sized.M
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- open import Data.Container.Core
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+ open import Level using (_⊔_)
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+ open import Size using (Size; ∞)
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+ open import Codata.Sized.Thunk using (Thunk; Thunk^R; force)
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+ open import Codata.Sized.M using (M; inf)
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+ open import Data.Container.Core using (Container)
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open import Data.Container.Relation.Binary.Pointwise using (Pointwise; _,_)
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open import Data.Product.Base using (_,_)
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open import Function.Base using (_∋_)
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module Codata.Sized.M.Properties where
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- open import Level
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- open import Size
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+ open import Level using (_⊔_)
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+ open import Size using (Size; ∞)
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open import Codata.Sized.Thunk using (Thunk; force)
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- open import Codata.Sized.M
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- open import Codata.Sized.M.Bisimilarity
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+ open import Codata.Sized.M using (M; inf; map; unfold)
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+ open import Codata.Sized.M.Bisimilarity using (Bisim; inf)
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open import Data.Container.Core as C hiding (map)
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- import Data.Container.Morphism as Mp
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+ import Data.Container.Morphism as Mp using (id; _∘_)
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open import Data.Product.Base as Product using (_,_)
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open import Data.Product.Properties hiding (map-cong)
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open import Function.Base using (_$′_; _∘′_)
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- import Relation.Binary.PropositionalEquality.Core as ≡
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- import Relation.Binary.PropositionalEquality.Properties as ≡
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-
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+ import Relation.Binary.PropositionalEquality.Core as ≡ using (_≡_; refl; subst)
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+ import Relation.Binary.PropositionalEquality.Properties as ≡ using (setoid)
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open import Data.Container.Relation.Binary.Pointwise using (_,_)
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import Data.Container.Relation.Binary.Equality.Setoid as EqSetoid
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