type t =
  | Int of int
  | Ident of string
  | Plus
  | Minus
  | Asterisk
  | Slash
  | Carret
  | Percent
  | LParen
  | RParen

let tokens = ref [
  "+", Plus;
  "-", Minus;
  "*", Asterisk;
  "/", Slash;
  "^", Carret;
  "%", Percent;
  "(", LParen;
  ")", RParen;
]

let expect_token str tok seq =
  let rec aux ts seq =
    match ts (), seq () with
    | Seq.Nil, _ -> Some seq
    | Seq.Cons _, Seq.Nil -> None
    | Seq.Cons (a, ts), Seq.Cons (b, seq) ->
      if a = b then aux ts seq else None
  in
  let str = String.to_seq str in
  aux str seq |> Option.map (fun s -> tok, s)

let find_token seq =
  !tokens |> List.find_map
    (fun (s, t) -> expect_token s t seq)

let to_string = function
  | Int n -> string_of_int n
  | Ident s -> s
  | t ->
    begin match List.find_opt (fun (_, tok) -> t = tok) !tokens with
      | None -> failwith "Token.to_string"
      | Some (s, _) -> s
    end