module JoinList where

data JoinList m a = Empty
                  | Single m a
                  | Append m (JoinList m a) (JoinList m a)
  deriving (Eq, Show)

-- Exercise 1

tag :: Monoid m => JoinList m a -> m
tag Empty = mempty
tag Single m _ = m
tag Append m _ _ = m

(+++) :: Monoid m => JoinList m a -> JoinList m a -> JoinList m a
(+++) jl1 jl2 = mappend jl1 jl2

-- Exercise 2

indexJ :: (Sized b, Monoid b) => Int -> JoinList b a -> Maybe a
indexJ _ Empty = Nothing
indexJ n (Single _ a)
       | n == 0 = Just a
       | otherwise = Nothing
indexJ n (Append m jl1 jl2)
       | n < 0 || n >= m = Nothing
       | n < tag1 = indexJ n jl1
       | n >= tag1 = indexJ (n - tag1) jl2
       where tag1 = tag jl1

dropJ :: (Sized b, Monoid b) => Int -> JoinList b a -> JoinList b a
dropJ _ Empty = Empty
dropJ n jl
      | n <= 0 = jl
dropJ n (Single _ _)
      | n >= 1 = Empty
dropJ n (Append m jl1 jl2)
      | n >= m = Empty
      | n >= tag1 = jl2
      where tag1 = tag jl1