open Lam
open Types
open Proof

(* fonction d'affichage *)
let rec string_of_ty = function
  TVar s -> s
  | Arr(t1, t2) ->
    let s1 = string_of_ty t1 in
    let s2 = string_of_ty t2 in
    "(" ^ s1 ^ " -> " ^ s2 ^ ")"
  | Bot -> "False"

let rec string_of_expr = function
  Fun ((s, t), e) ->
    let s_ty = string_of_ty t in
    let s_e = string_of_expr e in
    "fun (" ^ s ^ " : " ^ s_ty ^ ") => (" ^ s_e ^ ")"
  | App (e1, e2) ->
    "("^(string_of_expr e1)^" "^(string_of_expr e2)^")"
  | Var (s) -> s
  | Exf (e, t) ->
    let s_e = string_of_expr e in
    let s_ty = string_of_ty t in
    "exf (" ^ s_e ^ " : " ^ s_ty ^ ")"


let print_ty t =
  print_string (string_of_ty t)

let print_expr e =
  print_string (string_of_expr e)

let print_goal ((_, ty, c) : goal) : unit =
  let rec print_hyps (c : context) : unit = match c with
    [] -> ()
    | (id, _, ty)::q -> print_string (id^" : "^(string_of_ty ty)^"\n"); print_hyps q
  in print_hyps c;
  print_ty ty;
  print_string "\n==========\n"

let affiche_val _ = print_string "TODO"