module Cardinal
where

data Cardinal = F
              | B
              | L
              | R
              | D
              | T
              | FL
              | FR
              | FD
              | FT
              | BL
              | BR
              | BD
              | BT
              | LD
              | LT
              | RD
              | RT
              | FLD
              | FLT
              | FRD
              | FRT
              | BLD
              | BLT
              | BRD
              | BRT
              | I
              | Scalar Double
              | Sum Cardinal Cardinal
              | Difference Cardinal Cardinal
              | Product Cardinal Cardinal
              | Quotient Cardinal Cardinal
                deriving (Show, Eq)

instance Num Cardinal where
    x + y = Sum x y
    x - y = Difference x y
    x * y = Product x y
    negate x = Product (Scalar (-1)) x
    abs x = x
    signum x = x
    fromInteger x = Scalar (fromIntegral x)

instance Fractional Cardinal where
    x / y   = Quotient x y
    recip x = Quotient (Scalar 1) x
    fromRational x = Scalar (fromRational x)