type term =
  | Var of int
  | App of term * term
  | Lam of term
;;

let mk_app x y = App(x, y);;
let mk_lam x = Lam x;;
let mk_var x = Var x;;

exception ParsingError of string;;

let isAlphaNum c = let n = Char.code c in 48 <= n && n <= 122 ;;
let isSpace c = c = ' ' || c = '\n' || c = '\t' ;;

let rec index_of x =
  function
  | [] -> raise (Failure "index_of: Not Found")
  | h::t -> if x = h then 0 else 1 + index_of x t
;;
(* FIXME *)
let mk_var' (bound, free) x =
  if List.mem x bound
  then free, mk_var (index_of x bound)
  else if List.mem x free
       then free, mk_var (List.length bound + index_of x free)
       else (free @ [x]), mk_var (List.length bound + List.length free)
;;

let mk_app' = function
  | [] ->  raise (ParsingError "bug")
  | t :: ts -> List.fold_left mk_app t ts
;;

let explode s =
  let rec aux i l =
    if i < 0 then l else aux (i - 1) (s.[i] :: l)
  in aux (String.length s - 1) []
;;

let implode l =
  let res = String.create (List.length l) in
  let rec aux i = function
    | [] -> res
    | c :: l -> res.[i] <- c; aux (i + 1) l in
  aux 0 l
;;

let rec strip_spaces = function
  | c::cs when isSpace c -> strip_spaces cs
  | cs -> cs
;;

let read_var s =
  let rec aux = function
  | [] -> None, []
  | c::cs as x -> if isAlphaNum c
    then match aux cs with
         | (Some x), cs' -> Some (c :: x), cs'
         | None, cs' -> (Some [c]), cs'
    else None, x
  in match aux s with
    | None, y -> None, y
    | Some x, y -> Some (implode x), y
;;

let read_var' (bound, free as vars) s =
  match read_var s with
  | Some varname, cs ->
    let free, v = mk_var' vars varname in
    Some [v], cs, (bound, free)
  | _, _ -> raise (ParsingError ("Can't read variable"))
;;

let rec read_smt vars =
  let check_if_lambda cs = match read_var cs with
    | None, _ -> false
    | Some x, cs -> match strip_spaces cs with
      | [] -> false
      | c::_ -> c = '.'
  in let read_lambda (bound, free) cs = (
    match read_var (strip_spaces cs) with
      | Some varname, cs ->
      let vars' = (varname::bound, free) in
      (match strip_spaces cs with
        | [] -> raise (ParsingError "manca dopo variabile lambda")
        | c::cs -> (if c = '.' then (match read_smt vars' cs with
          | None, _, _ -> raise (ParsingError "manca corpo lambda")
          | Some [x], y, (_, free) -> Some [mk_lam x], y, (bound, free)
          | Some _, _, _ -> raise (ParsingError "???")
          ) else raise (ParsingError "manca . nel lambda")
        ))
      | _, _ -> assert false
 ) in let rec aux vars cs =
  match strip_spaces cs with
  | [] -> None, [], vars
  | c::_ as x ->
      let tms, cs, vars = (
           if c = '(' then read_pars vars x
      else if c = ')' then (None, x, vars)
      else if check_if_lambda x then read_lambda vars x
      else read_var' vars x) in
      match tms with
      | Some [tm] -> (
        match aux vars cs with
          | None, cs, vars -> Some [tm], cs, vars
          | Some ts, cs, vars -> Some (tm :: ts), cs, vars
        )
      | Some _ -> raise (ParsingError "bug")
      | None -> None, x, vars
  in fun cs -> match aux vars cs with
    | None, cs, vars -> None, cs, vars
    | Some ts, cs, vars -> Some [mk_app' ts], cs, vars
and read_pars vars = function
  | [] -> None, [], vars
  | c::cs -> if c = '(' then (
    let tm, cs, vars = read_smt vars cs in
    let cs = strip_spaces cs in
    match cs with
      | [] -> None, [], vars
      | c::cs -> if c = ')' then tm, cs, vars else raise (ParsingError ") mancante")
    ) else raise (ParsingError "???")
;;

let parse x =
  match read_smt ([],[]) (explode x) with
  | Some [y], [], _ -> y
  | _, _, _ -> raise (ParsingError "???")
;;

let var_zero = "ω";; (* w is an invalid variable name *)

let parse_many strs =
  let f (x, y) z = match read_smt y (explode z) with
  | Some[tm], [], vars -> (tm :: x, vars)
  | _, _, _ -> raise (ParsingError "???")
  in let aux = List.fold_left f ([], ([], [var_zero])) (* index zero is reserved *)
  in let (tms, (_, free)) = aux strs
  in (List.rev tms, free)
;;

(**********************************************************************

let rec string_of_term = function
  | Tvar n -> string_of_int n
  | Tapp(t1, t2) -> "(" ^ string_of_term t1 ^ " " ^ string_of_term t2 ^ ")"
  | Tlam(t1) -> "(\\" ^ string_of_term t1 ^ ")"
;;

let _ = prerr_endline (">>>" ^ string_of_term (parse "(\\x. x y z z1 k) z1 z j"));;


**********************************************************************)