bsc-leon-vatthauer/slides/code-examples/reverse.agda

{-# OPTIONS --guardedness #-}
open import Codata.Musical.Colist hiding (_++_)
open import Codata.Musical.Colist.Bisimilarity
open import Codata.Musical.Notation
open import Data.Nat
open import Data.Nat.Show renaming (show to showℕ)
open import Function.Base
open import Relation.Binary.PropositionalEquality
open import Data.String using (String; _++_)

module reverse where
  data Delay (A : Set) : Set where
    now : A → Delay A
    later : ∞ (Delay A) → Delay A

  foldl : ∀ {A B : Set} → (A → B → A) → A → Colist B → Delay A
  foldl c n [] = now n
  foldl c n (x ∷ xs) = later (♯ foldl c (c n x) (♭ xs))

  -- reversing possibly infinite lists
  reverse : ∀ {A : Set} → Colist A → Delay (Colist A)
  reverse {A} = reverseAcc []
    where
      reverseAcc : Colist A → Colist A → Delay (Colist A)
      reverseAcc = foldl (λ xs x → x ∷ (♯ xs)) -- 'flip _∷_' with extra steps

  run_for_steps : ∀ {A : Set} → Delay A → ℕ → Delay A
  run now   x for n     steps = now x
  run later x for zero  steps = later x
  run later x for suc n steps = run ♭ x for n steps


  fin-colist : Colist ℕ
  fin-colist = 1 ∷ ♯ (2 ∷ ♯ (3 ∷ ♯ []))

  inf-colist : Colist ℕ
  inf-colist = 1 ∷ ♯ inf-colist

  -- run reverse fin-colist for 5 steps
  -- run reverse inf-colist for 1000 steps