-- The data type of rational numbers

module Rat (Rat, rat, numerator, denominator, addR, mulR)
 where

-- A rational number consists of a numerator and a denominator:
data Rat = Rat Int Int
 deriving Eq

-- A nice Show instance
instance Show Rat where
  show (Rat n d) = show n ++ "/" ++ show d

-- A constructor for rational numbers:
rat :: Int -> Int -> Rat
rat n d = let g = gcd n d in posDenomRat (div n g) (div d g)
 where posDenomRat x y = if y<0 then Rat (0 - x) (abs y)
                                else Rat x y

-- Selector operations for rational numbers:
numerator :: Rat -> Int
numerator (Rat n _) = n

denominator :: Rat -> Int
denominator (Rat _ d) = d

-- Operations on rational numbers:
addR :: Rat -> Rat -> Rat
addR (Rat n1 d1) (Rat n2 d2) = rat (n1*d2 + n2*d1) (d1*d2)

mulR :: Rat -> Rat -> Rat
mulR (Rat n1 d1) (Rat n2 d2) = rat (n1*n2) (d1*d2)