counting inversions in sml in O(n*log(n)) time

gistfile1.sml

fun count_and_sort [] = ([],0)
  | count_and_sort [x] = ([x],0)
  | count_and_sort xs =
      let 
      fun count_and_sort_split_inversions([],ys,acc,sum) = (List.rev(acc) @ ys,sum)
        | count_and_sort_split_inversions(xs,[],acc,sum) = (List.rev(acc) @ xs,sum)
        | count_and_sort_split_inversions(x :: xs, y :: ys,acc,sum) = 
            if x < y
            then count_and_sort_split_inversions(xs, y :: ys, x :: acc, sum)
            else count_and_sort_split_inversions(x :: xs, ys, y :: acc, sum + List.length(x :: xs))
        val len = List.length xs
        val (left,right) = splitAt(xs,len div 2)
        val (a,x) =  count_and_sort left
        val (b,y) = count_and_sort right
        val (c,z) = count_and_sort_split_inversions (left,right,[],0)
        in
          (c, x + y + z)
        end