import Prelude hiding((.), id)
import Control.Arrow
import Control.Category

newtype Stream a b = Stream { runStream :: [a] -> [b] }

instance Category Stream where
  id = Stream (id)
  (.) (Stream (f)) (Stream (g)) = Stream (f . g)

instance Arrow Stream where
  arr f = Stream (map f)
  first (Stream f) = Stream (unzip >>> first f >>> uncurry zip)

instance ArrowLoop Stream where
  loop (Stream f) = Stream $ \iL ->
    let (oL,sL) = unzip $ f $ zip iL sL in
    oL

delay x = Stream (x:)

stream ~(x:xs) = x:stream xs

mul = arr (uncurry (*))

facStream = loop (mul >>> (arr id &&& delay 1))