(* initial version of the Rational structure that shows how we can group
   a type, its constructors, and some functions into a single unit. *)

module Rational =
struct
    type rational = Whole of int | Fraction of int * int

    let add(r1, r2) =
        match (r1, r2) with
        | (Whole i, Whole j)                   -> Whole(i + j)
        | (Whole i, Fraction(a, b))            -> Fraction(i * b + a, b)
        | (Fraction(a, b), Whole(i))           -> Fraction(i * b + a, b)
        | (Fraction(a1, b1), Fraction(a2, b2)) ->
            Fraction(a1 * b2 + a2 * b1, b1 * b2)

   let to_string(r) =
       match r with
       | Whole i        -> string_of_int(i)
       | Fraction(a, b) -> string_of_int(a) ^ "/" ^ string_of_int(b)
end