class Bitwise a where
      (&) :: a -> a -> a
      (^|^) :: a -> a -> a
      (^) :: a -> a -> a

data Bit = Zero | One deriving (Show, Eq)

instance Bitwise Bit where
  (&) One One = One
  (&) _ _ = Zero
  (^|^) Zero Zero = Zero
  (^|^) _ _ = One
  (^) One Zero = One
  (^) Zero One = One
  (^) _ _ = Zero

zero :: Bit
zero = Zero

one :: Bit
one = One