module Cardinal
where

data Cardinal = F
              | B
              | L
              | R
              | T
              | D
              | Sum Cardinal Cardinal
              | Difference Cardinal Cardinal
              | Product Cardinal Cardinal
              | ScalarProduct Double Cardinal
                deriving (Show, Eq)

instance Num Cardinal where
    x + y = Sum x y
    x - y = Difference x y
    x * y = Sum x y
    negate x = ScalarProduct (-1) x
    abs x = x
    signum x = x
    fromInteger _ = F -- Whatever.