Merge Sort in F#

let split l =
  let rec split l left right =
    match l, right with
    | [], _ -> List.rev left, right
    | [_], _ -> List.rev left, right
    | _::_::t, h::right_t -> split t (h::left) right_t
    | _ -> failwith "Error"
  in
    split l [] l


let rec rev_add a b =
  match a with
    | [] -> b
    | h::t -> rev_add t (h::b)


let merge cmp left right =
  let rec merge cmp left right acc =
    match left, right with
    | [], l -> rev_add acc l
    | l, [] -> rev_add acc l
    | left_h::left_t, right_h::right_t ->
        if cmp right_h left_h then
          merge cmp left right_t (right_h::acc)
        else
          merge cmp left_t right (left_h::acc)
  in
    merge cmp left right []


let rec merge_sort cmp l =
  match split l with
  | [], h1 -> h1
  | l1, l2 -> merge cmp (merge_sort cmp l1) (merge_sort cmp l2)