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

fun length nil    = 0 |               
    length (a::b) = 1+length b;

fun append nil    b = b |           
    append (h::t) b = h::(append t b);

fun rev nil = nil |                
    rev (a::b) =
       let fun rev2  nil   b = b |
	       rev2 (h::t) b = rev2 t (h::b)
       in
	  rev2 b [a]
       end;

fun map f nil = nil |          
    map f (h::t) = (f h)::(map f t);

fun reduce f zero nil = zero |
    reduce f zero (h::t) = f h (reduce f zero t);

fun to n = let fun up m = if m>n then nil else m::(up(m+1)) 
	   in  up 1
	   end;

reduce (fn a:int=>fn b=>a+b) 0 (to 10);
rev (map factorial (to 4));