List.purs

module Test.Example.List where

import Prelude

import Effect (Effect)
import Effect.Console (log, logShow)

import Data.Functor.Mu (Mu)
import Data.TacitString (TacitString)
import Matryoshka (class Corecursive, Algebra, Coalgebra, ana, cata, embed, hylo)

data ListF a t = Nil | Cons a t

derive instance functorListF :: Functor (ListF a)

instance showListF :: Show a => Show (ListF a TacitString) where
  show Nil = "Nil"
  show (Cons h t) = show h <> " : " <> show t

nil :: forall a t. Corecursive t (ListF a) => t
nil = embed Nil

cons :: forall a t. Corecursive t (ListF a) => a -> t -> t
cons h t = embed (Cons h t)

prod :: Algebra (ListF Int) Int
prod Nil = 1
prod (Cons h t) = h * t

count :: Coalgebra (ListF Int) Int
count n
  | n <= 0 = Nil
  | otherwise = Cons n (n - 1)

fac :: Int -> Int
fac = hylo prod count

type List a = Mu (ListF a)

listExample :: Effect Unit
listExample = do
  log "list example"
  let someList = cons 1 (cons 2 (cons 3 (cons 4 nil)))
  logShow $ cata prod (someList :: List Int)
  logShow (ana count 4 :: List Int)
  logShow (fac 6)