int列表的累计和

Question

我为累积总和实现了以下功能：

fun cumsum_reverse (xs: int list) = 
  if null xs then [0]
  else
    let val tl_cumsum = cumsum_reverse (tl xs)
    in
      hd xs + hd tl_cumsum :: tl_cumsum
    end

fun reverse (first: int list, second: int list) =
  if null first
  then
    second
  else
    reverse (tl first, hd first :: second)

fun cumsum (xs: int list) = 
  tl(reverse(cumsum_reverse(reverse(xs, [])), []))

测试用例：

val test = cumsum[1,4,20] = [1,5,25]

有没有办法只使用一个函数来实现它？