module Data.Stream
  ( Stream (..)
  , filter, iterate, fromList
  ) where

import Data.Functor.Foldable (Base, Corecursive, Recursive, embed, project, ana)
import Prelude hiding (filter, iterate, head, tail)

data Stream a = Cons { head :: a, tail :: Stream a }

type instance Base (Stream a) = (,) a

instance Recursive (Stream a) where
  project (Cons x xs) = (x, xs)

instance Corecursive (Stream a) where
  embed (x, xs) = Cons x xs

filter :: (a -> Bool) -> Stream a -> Stream a
filter p = ana \case
  Cons x xs
    | p x -> (x, xs)
    | otherwise -> project xs

iterate :: (a -> a) -> a -> Stream a
iterate f = ana \x -> (x, f x)

fromList :: [a] -> Stream a
fromList = ana coalg
  where
    coalg (x : xs) = (x, xs)
    coalg [] = error "Attempted to turn finite list into stream"