module Stream (
      Stream(..)
    , append
    , empty
    , fromList
    , infinite
    , merge
  ) where

import Tree (Tree(..), Structure(..))

data Stream a = Stream [(a, Stream a)] deriving Show

instance Functor Stream where
  fmap f (Stream pairs) =
    Stream $ (\(a, stream) -> (f a, fmap f stream)) <$> pairs

instance Tree Stream where
  getStructure (Stream []) = Leaf
  getStructure (Stream pairs) =
    Node $ (\(s, stream) -> (s, getStructure stream)) <$> pairs

empty :: Stream a
empty = fromList []

append :: Stream a -> Stream a -> Stream a
append (Stream []) b = b
append (Stream pairs) b =
  Stream $ (\(a, stream) -> (a, stream `append` b)) <$> pairs

fromList :: [a] -> Stream a
fromList [] = Stream []
fromList (pair:pairs) = Stream [(pair, fromList pairs)]

infinite :: a -> Stream a
infinite a = Stream [(a, infinite a)]

merge :: Eq a => Stream a -> Stream a -> Stream a
merge (Stream aPairs) (Stream bPairs) = Stream $ foldl mergeOrAdd aPairs bPairs
  where
    openAt _ l [] = (l, [])
    openAt p up l@(x:xs) = if p x then (up, l) else openAt p (x:up) xs
    zipUp ([], l) = l
    zipUp (x:xs, l) = zipUp (xs, x:l)
    mergeOrAdd accumulator (b, bStream) = zipUp $
      case openAt ((== b) . fst) [] accumulator of
        (up, []) -> (up, [(b, bStream)])
        (up, (x, xStream):down) -> (up, (x, merge xStream bStream):down)