fun buildList(n) = if n <= 0 then [0] else n::buildList(n-1);
fun inList([],_) = false |
inList(L, n:int) = if hd(L) = n then true else inList(tl(L), n);

fun summe_und_uebertr(c, x, y, base) = 
	let
		val system = buildList(base - 1);
		val sum = c + x + y
	in
		if inList(system, c) andalso inList(system, x) andalso inList(system, y)
		then SOME (sum div base, sum mod base)
		else NONE
	end;
	
fun dual_summe_und_uebertr(c, x1, x2) = summe_und_uebertr(c, x1, x2, 2);

dual_summe_und_uebertr(1,1,1);
dual_summe_und_uebertr(1,0,1);
dual_summe_und_uebertr(0,0,0);
dual_summe_und_uebertr(1,1,4);
dual_summe_und_uebertr(0,~65,1);
dual_summe_und_uebertr(0,0,123);
dual_summe_und_uebertr(7,1,1);

fun dez_summe_und_uebertr(c, x1, x2) = summe_und_uebertr(c, x1, x2, 10);

dez_summe_und_uebertr(0,7,8);
dez_summe_und_uebertr(0,2,3);
dez_summe_und_uebertr(1,23,3);
dez_summe_und_uebertr(1,4,3);
dez_summe_und_uebertr(1,9,9);
dez_summe_und_uebertr(1,9,~9);

fun hex_summe_und_uebertr(c, x1, x2) = summe_und_uebertr(c, x1, x2, 16);

hex_summe_und_uebertr(0,7,8);
hex_summe_und_uebertr(0,2,3);
hex_summe_und_uebertr(1,23,3);
hex_summe_und_uebertr(1,4,3);
hex_summe_und_uebertr(1,9,9);
hex_summe_und_uebertr(1,9,~9);

fun fillList([], 0) = [0] |
	fillList(L, n) = if length(L) >= n then L else fillList(L@[0], n);
	
fun summa(f, l1:int list, l2:int list, c:int, s) = 
	if null(l1) then SOME(s)
	else 
		let
			val t = f(c, hd(rev(l1)), hd(rev(l2)))
		in
			if isSome(t)
			then summa(f, rev(tl(rev(l1))), rev(tl(rev(l2))), hd(valOf(t)), s @ [hd(rev(valOf(t)))] )
			else NONE
		end;
	
fun summe(f, l1, l2) = 
	let
		val mlen = Int.max(length l1, length l2);
		val m1 = fillList(l1, mlen);
		val m2 = fillList(l2, mlen);
		val r = summa(f, m1, m2, 0, [])
	in
		if r = SOME([]) then SOME([0]) else r
	end;