------------------------------------------------------------------------
-- The Agda standard library
--
-- M-types (the dual of W-types)
------------------------------------------------------------------------
{-# OPTIONS --cubical-compatible --sized-types #-}
module Codata.Sized.M where
open import Size using (Size; ∞)
open import Level using (Level; _⊔_)
open import Codata.Sized.Thunk using (Thunk; force)
open import Data.Product.Base hiding (map)
open import Data.Container.Core as C hiding (map)
data M {s p} (C : Container s p) (i : Size) : Set (s ⊔ p) where
inf : ⟦ C ⟧ (Thunk (M C) i) → M C i
module _ {s p} {C : Container s p} where
head : ∀ {i} → M C i → Shape C
head (inf (x , f)) = x
tail : (x : M C ∞) → Position C (head x) → M C ∞
tail (inf (x , f)) = λ p → f p .force
-- map
module _ {s₁ s₂ p₁ p₂} {C₁ : Container s₁ p₁} {C₂ : Container s₂ p₂}
(m : C₁ ⇒ C₂) where
map : ∀ {i} → M C₁ i → M C₂ i
map (inf t) = inf (⟪ m ⟫ (C.map (λ t → λ where .force → map (t .force)) t))
-- unfold
module _ {s p ℓ} {C : Container s p} (open Container C)
{S : Set ℓ} (alg : S → ⟦ C ⟧ S) where
unfold : S → ∀ {i} → M C i
unfold seed = let (x , next) = alg seed in
inf (x , λ p → λ where .force → unfold (next p))
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