(* various recursive and tail recursive factorial functions *)

(* define an exception *)

exception negative of int;

(* simple recursive version *)

fun fact1 n = if (n = 0) then 1 else n * fact1(n-1);

(* recursive value definition using a 'fn' lambda expression *)

val rec fact5 = fn n => if (n=0) then 1 else n * fact5(n-1);

(* recursive version using argument pattern matching *)

fun fact2 0 = 1
  | fact2 n = n * fact2(n-1);

(* recursive version with check for negative value of n *)

fun fact3 n = case (n < 0) of 
	        true  => raise negative n
	      |	false => if (n=0) then 1 else n * fact3(n-1);

(* tail recursive version using a let *)

fun fact4 n =
   let fun fact (0,m) = m 
	 | fact (n,m) = fact (n-1, m*n)
   in
     if (n >= 0) then fact(n,1) else raise negative(n)
   end;