(* Largest palindrome number which is the product of two 3-digit numbers *)
(* Upper bound: 999 x 999 = 998001 *)
(* Largest palindrome: 997799 *)

fun pop (x::[]) = (x, [])
  | pop (x::xs) = let val (y, ys) = pop xs in (y, x::ys) end
  | pop     []  = raise Empty;

fun palindrome     []  = true
  | palindrome (x::[]) = true
  | palindrome (x::xs) =
      let val (y, ys) = pop xs in
        x = y andalso palindrome ys
      end

fun itol n = if n < 10 then [n] else (n mod 10) :: itol (n div 10);

fun find_factors _ 999 = NONE
  | find_factors n j =
      if n mod j = 0 andalso n div j < 999
        then SOME (j, n div j)
        else find_factors n (j + 1)

fun find_pal n = if palindrome (itol n) then
    let val factors = find_factors n 100 in
      (case factors of
            NONE        => find_pal (n - 1) (* palindrome, but insufficient *)
          | SOME (x, y) => (x, y, n)) (* bingo! *)
    end else find_pal (n - 1); (* not palindrome *)