(*  sum_examples.ml
 *
 *  Author: W. M. Farmer
 *  Revised: October 13, 2008
 *
 *  Description: Several example implementations of the sum function, which
 *               is the iterated addition represented by the capital sigma
 *               operator.
 *)


let simple_sum m n =
  let accum = ref 0 in
  for i = m to n do
    accum := !accum + i ;
    print_int !accum ;
    print_newline ()
  done;
  !accum ;;

let sum f m n =
  let accum = ref 0 in
  for i = m to n do
    accum := !accum + (f i) ;
    print_int !accum ;
    print_newline ()
  done;
  !accum ;;

let super_sum zero add f m n =
  let accum = ref zero in
  for i = m to n do
    accum := add !accum (f i) ;
  done;
  !accum ;;

let factorial = super_sum 1 ( * ) (function x -> x) 1 ;;

let rec simple_sum_rec m n =
  if m > n 
  then 0
  else m + (simple_sum_rec (m + 1) n) ;;

let rec sum_rec f m n =
  if m > n 
  then 0
  else (f m) + (sum_rec f (m + 1) n) ;;

let rec super_sum_rec zero add f m n =
  if m > n 
  then zero
  else add (f m) (super_sum_rec zero add f (m + 1) n) ;;

let factorial_rec = super_sum_rec 1 ( * ) (function x -> x) 1 ;;