fun map (f : 'a -> 'b, xs : 'a list) : 'b list =
 case xs of
 nil => nil
 | (y::ys) => (f (y))::(map (f, ys));
fun zip (xs : 'a list, ys : 'b list) : ('a * 'b) list =
 case (xs, ys) of
 (nil, _) => nil
 | (_, nil) => nil
 | (b::bs, c::cs) => (b, c)::(zip (bs, cs));
fun filter (f : 'a -> bool, xs : 'a list) : 'a list =
 case xs of
 nil => nil
 | (y::ys) =>
 if f (y) then
 y::(filter (f, ys))
 else
 filter (f, ys);
fun foldl (f : 'a * 'b -> 'a, n : 'a, xs : 'b list) : 'a =
 case xs of
 nil => n
 | (y::ys) => foldl (f, f (n, y), ys);
fun upto (x : int, y : int) : int list =
 if x <= y then
 x::(upto (x + 1, y))
 else
 nil;
fun sum (xs : int list) : int = 
 case xs of
 nil => 0
 | (x'::xs') => x' + sum (xs');
 
fun fold (opr: int*int->int, base: int, xs: int list) : int = 
 case xs of
 nil => base
 | (x'::xs') => opr(x', fold(opr, base, xs'));
fun add(x,y) = x+y;
fun foldsum (xs: int list) = fold (add,0, xs);
fun foldr (opr: 'b*'a->'a, base: 'a, xs: 'b list) : 'a = 
 case xs of
 nil => base
 | (x'::xs') => opr(x', foldr(opr, base, xs'));