module Stream where

import Numeric.Natural (Natural)

fibInit = (0, 1)
fibGet (_, now) = now
fibNext (prev, now) = (now, prev + now)

-- Abstract type example using nested foralls.
type Stream_A = forall r. (forall s. (s -> Natural) -> (s -> s) -> s -> r) -> r

fibs_A :: Stream_A
fibs_A user = user fibGet fibNext fibInit

-- Abstract type example using existential types. Despite the "forall" word, it
-- means exists.
data Stream_E = forall s. Ctor (s -> Natural) (s -> s) s

fibs_E :: Stream_E
fibs_E = Ctor fibGet fibNext fibInit


foldNat :: (a -> a) -> a -> Natural -> a
foldNat s z n = go n
  where
    go 0 = z
    go n = s (go (n-1))

nth_fibs_A n = fibs_A (\get next init -> get (foldNat next init n))

nth_fibs_E n = case fibs_E of
  Ctor get next init -> get (foldNat next init n)