(* --- recursive functions --- *)

(* From Section 1.12 *)


fun factorial(0) = 1
  | factorial(n) = n * factorial(n-1);


(* Ex 1.12.4. Homemade multiply  *)
fun multiply(x, 0) = 0
  | multiply(x, y) = x + multiply(x, y-1);


(* Ex 1.12.6.  Summation. *)
fun sum(1) = 1
  | sum(n) = n + sum(n-1);


(* For the assignment *)

(* Ex 1.11.4 *)
fun divideAll(a, b) = ( ??, ??, ??);


(* interpret the first int as numerator and second as denominator *)
datatype rational = Fraction of int * int;



fun gcd(a, 0) = a
  | gcd(a, b) = gcd(b, a mod b);

fun add(Fraction(a, b), Fraction(c, d)) = 
  let 
      val numerator = a * d + c * b;
      val denominator = b * d;
      val divisor = gcd(numerator, denominator);
  in
     Fraction(numerator div divisor, denominator div divisor)
  end;