Binary tree that allows lazy reading from disk (if used with bytestring-mmap)

gistfile1.txt

data BTree a 
    = Null
    | Leaf a
    | Node a (BTree a) (BTree a)
    deriving (Show)

-- makeTree :: [a] -> BTree a
-- makeTree xs = 

instance Binary a => Binary (BTree a) where
    put Null         = putWord8 0
    put (Leaf a)     = putWord8 1 >> put a
    put (Node a l r) = do
        putWord8 2
        put a
        put (encode l)
        put r
    get = do
        w <- getWord8
        case w of
            0 -> return Null
            1 -> fmap Leaf get
            2 -> do
                x <- get
                ls  <- get
                r   <- get
                return (Node x (decode ls) r)

empty :: BTree a
empty = Null

insert :: Ord a => BTree a -> a -> BTree a
insert Null x = Leaf x
insert l@(Leaf y) x =
    case x `compare` y of
        LT -> Node y (Leaf x) Null
        GT -> Node y Null (Leaf x)
        EQ -> l
insert n@(Node y l r) x =
    case x `compare` y of
        LT -> Node y (insert l x) r
        GT -> Node y l (insert r x)
        EQ -> n

toList :: BTree a -> [a]
toList t = go t []
    where
        go Null xs         = xs
        go (Leaf x) xs     = x:xs
        go (Node x l r) xs = go l $ x : go r xs