如何使用纯函数式编程在ocaml中创建非上下文解析器？

type expr = 
  | Int of int
  | Add of expr * expr
  | Sub of expr * expr
  | Mul of expr * expr
  | Div of expr * expr

let rec parse_expr input =
  let rec parse_int input =
    match input with
    | c::cs when Char.is_digit c ->
      let num = int_of_string (String.make 1 c) in
      parse_int_helper (num, cs)
    | _ -> failwith "Expected integer"
  and parse_int_helper (acc, input) =
    match input with
    | c::cs when Char.is_digit c ->
      let num = acc * 10 + int_of_string (String.make 1 c) in
      parse_int_helper (num, cs)
    | _ -> Int acc
  in
  let rec parse_add_sub input =
    let left = parse_int input in
    match input with
    | '+'::cs -> let right = parse_add_sub cs in Add (left, right)
    | '-'::cs -> let right = parse_add_sub cs in Sub (left, right)
    | _ -> left
  in
  let rec parse_mul_div input =
    let left = parse_add_sub input in
    match input with
    | '*'::cs -> let right = parse_mul_div cs in Mul (left, right)
    | '/'::cs -> let right = parse_mul_div cs in Div (left, right)
    | _ -> left
  in
  parse_mul_div input

let parse input =
  let tokens = String.split_on_char ' ' input in
  List.fold_left (fun acc token -> acc ^ " " ^ token) "" tokens |> parse_expr