bin.hs

data NatE = NZero | NDouble NatG
    deriving Show
data NatO = NSucc NatE
    deriving Show
type NatG = Either NatE NatO

toInt0 :: NatE -> Int
toInt0 NZero = 0
toInt0 (NDouble n) = 2 * (toInt n)

toInt1 :: NatO -> Int
toInt1 (NSucc n) = 1 + toInt0 n


incE :: NatE -> NatO
incE g = NSucc g

incO :: NatO -> NatE
incO (NSucc NZero) = NDouble $ Right $ NSucc NZero
incO (NSucc (NDouble (Left e))) = NDouble $ Right $ incE e
incO (NSucc (NDouble (Right o))) = NDouble $ Left $ incO o

toInt :: NatG -> Int
toInt n = either toInt0 toInt1 n

toNatG :: Int -> NatG 
toNatG 0 = Left $ NZero
toNatG n = case (toNatG (n-1)) of
                Left e -> Right $ incE e
                Right o -> Left $ incO o