100 Doors Problem in SML

100doors.sml

(* 100 doors *)
fun listOf 0 _ = []
 |  listOf n e = e::(listOf (n-1) e);

fun invert x = not x;

fun flip _ _ [] = []
 |  flip 0 _  _ = []
 |  flip s n (h::t) = if (s=n) then (invert h)::(flip s 1 t) else h::(flip s (n+1) t);

 fun flipThrough 100 (h::t) = (h::t)
  |  flipThrough n   (h::t) = flipThrough (n+1) (flip n 1 (h::t));

fun onehundreddoors () = let
                       fun answer [] _ = []
                        |  answer (h::t) n = if h then n::(answer t (n+1)) else answer t (n+1);
                  in answer (flipThrough 1 (listOf 100 false)) 1 end;