{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, FunctionalDependencies, FlexibleContexts, UndecidableInstances, OverlappingInstances, IncoherentInstances #-}

class SubtypeOf a b | a -> b where
  upcast :: a -> b
  downcastSafe :: b -> Maybe a
  downcast :: b -> a
  downcast b = case downcastSafe b of
    Nothing -> error $ "can not downcast the value"
    Just a -> a

class (Ord a) => Rangable t a | t -> a where
  lowLim :: t -> a
  highLim :: t -> a

class Packable t a | t -> a where
  pack :: a -> t
  unpack :: t -> a

class MultipleTo t a | t -> a where
  multiple :: t -> a
  
instance (Num a, Ord a, Rangable range a, Packable range a) => SubtypeOf range a where
  upcast = unpack
  downcastSafe b | b >= (lowLim $ pb) && b <= (highLim $ pb) = Just $ pb
                 | otherwise = Nothing
    where
      pb = pack b

instance (Integral a, Packable range a, MultipleTo range a) => SubtypeOf range a where
  upcast = unpack
  downcastSafe b | b `mod` (multiple pb) == 0 = Just pb
                 | otherwise = Nothing
    where
      pb = pack b

newtype Range1 a = Range1 {unRange1 :: a}
                 deriving Show

instance (Num a, Ord a) => Rangable (Range1 a) a where
  lowLim _ = 0
  highLim _ = 10

instance (Num a, Ord a) => Packable (Range1 a) a where
  pack = Range1
  unpack = unRange1

newtype Range2 a = Range2 {unRange2 :: a}
                   deriving Show

instance (Num a, Ord a) => Rangable (Range2 a) a where
  lowLim _ = -10
  highLim _ = 200

instance (Num a, Ord a) => Packable (Range2 a) a where
  pack = Range2
  unpack = unRange2