data Tree a = Leaf (a) | Bin (Tree a) (Tree a) deriving (Show)
main :: IO ()
main = print (t1, depth t1)
t1 :: Tree Char
t1 = balance "Patrik"
depth :: Tree a -> Int
depth = cata_f4Tree de
balance :: [a] -> Tree a
balance = ana_f4Tree ba
cata_f4Tree :: (Either a (b, b) -> b) -> Tree a -> b
cata_f4Tree i = i . ((fmap2_f4Tree id (cata_f4Tree i)) . out_f4Tree)
de :: Either a (Int, Int) -> Int
de = either (const 0) (\(m, n) -> 1 + (max m n))
ana_f4Tree :: (a -> Either b (a, a)) -> a -> Tree b
ana_f4Tree o = inn_f4Tree . ((fmap2_f4Tree id (ana_f4Tree o)) . o)
ba :: [a] -> Either a ([a], [a])
ba xs = case xs of
	  ([]) -> error "Can't represent the empty list"
	  (x : ([])) -> Left x
	  xs -> Right (splitAt (div (length xs) 2) xs)
fmap2_f4Tree :: (a -> b) -> (c -> d) -> Either a (c, c) -> Either b (d, d)
fmap2_f4Tree = \p r -> (fmap2_p p r) -+- (fmap2_Prr p r)
out_f4Tree :: Tree a -> Either a (Tree a, Tree a)
out_f4Tree x = case x of
		 (Leaf a) -> Left a
		 (Bin a b) -> Right (a, b)
inn_f4Tree :: Either a (Tree a, Tree a) -> Tree a
inn_f4Tree = either Leaf (uncurry Bin)
(-+-) :: (a -> b) -> (c -> d) -> Either a c -> Either b d
f -+- g = either (Left . f) (Right . g)
fmap2_p :: (a -> b) -> (c -> d) -> a -> b
fmap2_p = \p r -> p
fmap2_Prr :: (a -> b) -> (c -> d) -> (c, c) -> (d, d)
fmap2_Prr = \p r -> (fmap2_r p r) -*- (fmap2_r p r)
(-*-) :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)
f -*- g = \(x, y) -> (f x, g y)
fmap2_r :: (a -> b) -> (c -> d) -> c -> d
fmap2_r = \p r -> r