Stream is a Comonad

stream.hs

module Main where

class Functor w => Comonad w where
    extract :: w a -> a
    duplicate :: w a -> w (w a)
    extend :: (w a -> b) -> w a -> w b

data Stream a = Cons a (Stream a)

instance Functor Stream where
    fmap f (Cons x xs) = Cons (f x) (fmap f xs)

instance Comonad Stream where
    extract (Cons x _) = x
    duplicate xs@(Cons _ xs') = Cons xs (duplicate xs')
    extend f xs@(Cons _ xs') = Cons (f xs) (extend f xs')

replicateS :: (a -> a) -> a -> Stream a
replicateS f t = Cons t (replicateS f (f t))

sumS :: Num a => Int -> Stream a -> a
sumS n (Cons a as) = if n <= 0 then 0 else a + sumS (n - 1) as

showS :: Stream Int -> Stream String
showS s = extend (\(Cons x _) -> show x) s

advanceS :: Stream a -> Stream a
advanceS (Cons a as) = as

extractS' :: [a] -> Int -> Stream a -> [a]
extractS' acc 0 s = acc
extractS' acc n s = extractS' (extract s:acc) (n-1) (advanceS s)

extractS n s = extractS' [] n s

main = print $ extractS 20 (showS (replicateS (*2) 1))