(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

open Coqast
open Ast
open Pp
open Util
open Names
open Pcoq
open Extend
open Topconstr
open Libnames

(**********************************************************************)
(* Parsing with Grammar                                               *)
(**********************************************************************)

let get_r_sign loc =
  let mkid id =
    mkRefC (Qualid (loc,Libnames.make_short_qualid id))
  in
  ((mkid (id_of_string "R0"),
    mkid (id_of_string "R1"),
    mkid (id_of_string "Rplus"),
    mkid (id_of_string "Rmult"),
    mkid (id_of_string "NRplus"),
    mkid (id_of_string "NRmult")))

let get_r_sign_ast loc =
  let mkid id =
    Termast.ast_of_ref (Nametab.locate (Libnames.make_short_qualid id))
  in
  ((mkid (id_of_string "R0"),
    mkid (id_of_string "R1"),
    mkid (id_of_string "Rplus"), 
    mkid (id_of_string "Rmult"),
    mkid (id_of_string "NRplus"),
    mkid (id_of_string "NRmult")))

(* We have the following interpretation:
  [| 0 |] = 0
  [| 1 |] = 1
  [| 2 |] = 1 + 1
  [| 3 |] = 1 + (1 + 1)
  [| 2n |] = 2 * [| n |]         for n >= 2
  [| 2n+1 |] = 1 + 2 * [| n |]   for n >= 2
  [| -n |] = - [| n |]           for n >= 0
*)

let int_decomp n = 
let div2 k = 
let x = k mod 2 in
let y = k - x in (x,y/2) in
let rec list_ch m =
if m< 2 then [m]
else let (x1,x2) = div2 m in x1::(list_ch x2)
in list_ch n

let _ = if !Options.v7 then
let r_of_int n dloc =
  let (a0,a1,plus,mult,_,_) = get_r_sign dloc in
  let list_ch = int_decomp n in
  let a2 = mkAppC (plus, [a1; a1]) in
  let rec mk_r l =
    match l with
    | [] -> failwith "Error r_of_int"
    | [a] -> if a=1 then a1 else a0
    | [a;b] -> if a==1 then mkAppC (plus, [a1; a2]) else a2
    | a::l' -> if a=1 then mkAppC (plus, [a1; mkAppC (mult, [a2; mk_r l'])]) else mkAppC (mult, [a2; mk_r l'])
  in mk_r list_ch
in
let r_of_string s dloc = 
  r_of_int (int_of_string s) dloc
in
let rsyntax_create name =
  let e =
    Pcoq.create_constr_entry (Pcoq.get_univ "rnatural") name in
  Pcoq.Gram.Unsafe.clear_entry e;
  e
in
let rnumber = rsyntax_create "rnumber"
in
let _ = 
  Gram.extend rnumber None
    [None, None,
     [[Gramext.Stoken ("INT", "")],
      Gramext.action r_of_string]]
in ()

(**********************************************************************)
(* Old ast printing                                                   *)
(**********************************************************************)

exception Non_closed_number

let _ = if !Options.v7 then
let int_of_r p =
  let (a0,a1,plus,mult,_,_) = get_r_sign_ast dummy_loc in
  let rec int_of_r_rec p = 
    match p with
  | Node (_,"APPLIST", [b;a;c]) when alpha_eq(b,plus) & alpha_eq(a,a1) & alpha_eq(c,a1) -> 2
  | Node (_,"APPLIST", [b;a;c]) when alpha_eq(b,plus) & alpha_eq(a,a1) ->
      (match c with
      |	Node (_,"APPLIST", [e;d;f]) when alpha_eq(e,mult) -> 1 + int_of_r_rec c
      |	Node (_,"APPLIST", [e;d;f]) when alpha_eq(e,plus) & alpha_eq(d,a1) & alpha_eq(f,a1) -> 3
      |	_ -> raise Non_closed_number)
  | Node (_,"APPLIST", [b;a;c]) when alpha_eq(b,mult) ->
      (match a with
      |	Node (_,"APPLIST", [e;d;f]) when alpha_eq(e,plus) & alpha_eq(d,a1) & alpha_eq(f,a1) ->
	  (match c with
	  | g when alpha_eq(g,a1) -> raise Non_closed_number
	  | g when alpha_eq(g,a0) -> raise Non_closed_number
	  | _ -> 2 * int_of_r_rec c)
      |	_ -> raise Non_closed_number)
  | a when alpha_eq(a,a0) -> 0
  | a when alpha_eq(a,a1) -> 1
  | _ -> raise Non_closed_number in
  try 
    Some (int_of_r_rec p)
  with
    Non_closed_number -> None
in
let replace_plus p = 
  let (_,_,_,_,astnrplus,_) = get_r_sign_ast dummy_loc in
  ope ("REXPR",[ope("APPLIST",[astnrplus;p])])
in
let replace_mult p = 
  let (_,_,_,_,_,astnrmult) = get_r_sign_ast dummy_loc in
  ope ("REXPR",[ope("APPLIST",[astnrmult;p])])
in
let rec r_printer_odd std_pr p =
  let (_,a1,plus,_,_,_) = get_r_sign_ast dummy_loc in
  match (int_of_r (ope("APPLIST",[plus;a1;p]))) with
    | Some i -> str (string_of_int i)
    | None -> std_pr (replace_plus p)
in
let rec r_printer_odd_outside std_pr p =
  let (_,a1,plus,_,_,_) = get_r_sign_ast dummy_loc in
  match (int_of_r (ope("APPLIST",[plus;a1;p]))) with
    | Some i -> str"``" ++ str (string_of_int i) ++ str"``"
    | None -> std_pr (replace_plus p)
in
let rec r_printer_even std_pr p =
  let (_,a1,plus,mult,_,_) = get_r_sign_ast dummy_loc in
  match (int_of_r (ope("APPLIST",[mult;(ope("APPLIST",[plus;a1;a1]));p]))) with
    | Some i -> str (string_of_int i)
    | None -> std_pr (replace_mult p)
in
let rec r_printer_even_outside std_pr p =
  let (_,a1,plus,mult,_,_) = get_r_sign_ast dummy_loc in
  match (int_of_r (ope("APPLIST",[mult;(ope("APPLIST",[plus;a1;a1]));p]))) with
    | Some i -> str"``" ++ str (string_of_int i) ++ str"``"
    | None -> std_pr (replace_mult p)
in
let _ = Esyntax.Ppprim.add ("r_printer_odd", r_printer_odd) in
let _ = Esyntax.Ppprim.add ("r_printer_odd_outside", r_printer_odd_outside) in
let _ = Esyntax.Ppprim.add ("r_printer_even", r_printer_even) in
let _ = Esyntax.Ppprim.add ("r_printer_even_outside", r_printer_even_outside)
in ()

(**********************************************************************)
(* Parsing R via scopes                                               *)
(**********************************************************************)

open Libnames
open Rawterm
open Bignat

let make_dir l = make_dirpath (List.map id_of_string (List.rev l))
let rdefinitions = make_dir ["Coq";"Reals";"Rdefinitions"]

(* TODO: temporary hack *)
let make_path dir id = Libnames.encode_kn dir (id_of_string id)

let glob_R = ConstRef (make_path rdefinitions "R")
let glob_R1 = ConstRef (make_path rdefinitions "R1")
let glob_R0 = ConstRef (make_path rdefinitions "R0")
let glob_Ropp = ConstRef (make_path rdefinitions "Ropp")
let glob_Rplus = ConstRef (make_path rdefinitions "Rplus")
let glob_Rmult = ConstRef (make_path rdefinitions "Rmult")

(* V7 *)
let r_of_posint dloc n =
  let ref_R0 = RRef (dloc, glob_R0) in
  let ref_R1 = RRef (dloc, glob_R1) in
  let ref_Rplus = RRef (dloc, glob_Rplus) in
  let ref_Rmult = RRef (dloc, glob_Rmult) in
  let a2 = RApp(dloc, ref_Rplus, [ref_R1; ref_R1]) in
  let list_ch = int_decomp n in
  let rec mk_r l =
    match l with
    | [] -> failwith "Error r_of_posint"
    | [a] -> if a=1 then ref_R1 else ref_R0
    | a::[b] -> if a==1 then RApp (dloc, ref_Rplus, [ref_R1; a2]) else a2
    | a::l' -> if a=1 then RApp (dloc, ref_Rplus, [ref_R1; RApp (dloc, ref_Rmult, [a2; mk_r l'])]) else RApp (dloc, ref_Rmult, [a2; mk_r l'])
  in mk_r list_ch

(* int_of_string o bigint_to_string : temporary hack ... *)
(* utiliser les bigint de caml ? *)
let r_of_int2 dloc z =
  match z with
  | NEG n -> RApp (dloc, RRef(dloc,glob_Ropp), [r_of_posint dloc (int_of_string (bigint_to_string (POS n)))]) 
  | POS n -> r_of_posint dloc (int_of_string (bigint_to_string z))

(* V8 *)
let two = mult_2 one
let three = add_1 two
let four = mult_2 two

(* Unary representation of strictly positive numbers *)
let rec small_r dloc n =
  if is_one n then RRef (dloc, glob_R1)
  else RApp(dloc,RRef (dloc,glob_Rplus),
            [RRef (dloc, glob_R1);small_r dloc (sub_1 n)])

let r_of_posint dloc n =
  let r1 = RRef (dloc, glob_R1) in
  let r2 = small_r dloc two in
  let rec r_of_pos n =
    if less_than n four then small_r dloc n
    else
      let (q,r) = div2_with_rest n in
      let b = RApp(dloc,RRef(dloc,glob_Rmult),[r2;r_of_pos q]) in
      if r then RApp(dloc,RRef(dloc,glob_Rplus),[r1;b]) else b in
  if is_nonzero n then r_of_pos n else RRef(dloc,glob_R0)

let r_of_int dloc z =
  match z with
  | NEG n -> RApp (dloc, RRef(dloc,glob_Ropp), [r_of_posint dloc n]) 
  | POS n -> r_of_posint dloc n

(**********************************************************************)
(* Printing R via scopes                                              *)
(**********************************************************************)

let bignat_of_r =
(* for numbers > 1 *)
let rec bignat_of_pos = function
  (* 1+1 *)
  | RApp (_,RRef (_,p), [RRef (_,o1); RRef (_,o2)])
      when p = glob_Rplus & o1 = glob_R1 & o2 = glob_R1 -> two
  (* 1+(1+1) *)
  | RApp (_,RRef (_,p1), [RRef (_,o1);
      RApp(_,RRef (_,p2),[RRef(_,o2);RRef(_,o3)])])
      when p1 = glob_Rplus & p2 = glob_Rplus &
           o1 = glob_R1 & o2 = glob_R1 & o3 = glob_R1 -> three
  (* (1+1)*b *)
  | RApp (_,RRef (_,p), [a; b]) when p = glob_Rmult ->
      if bignat_of_pos a <> two then raise Non_closed_number;
      mult_2 (bignat_of_pos b)
  (* 1+(1+1)*b *)
  | RApp (_,RRef (_,p1), [RRef (_,o); RApp (_,RRef (_,p2),[a;b])])
      when p1 = glob_Rplus & p2 = glob_Rmult & o = glob_R1  -> 
      if bignat_of_pos a <> two then raise Non_closed_number;
        add_1 (mult_2 (bignat_of_pos b))
  | _ -> raise Non_closed_number
in
let bignat_of_r = function
  | RRef (_,a) when a = glob_R0 -> zero
  | RRef (_,a) when a = glob_R1 -> one
  | r -> bignat_of_pos r
in
bignat_of_r

let bigint_of_r = function
  | RApp (_,RRef (_,o), [a]) when o = glob_Ropp -> NEG (bignat_of_r a)
  | a -> POS (bignat_of_r a)

let uninterp_r p =
  try
    Some (bigint_of_r p)
  with Non_closed_number ->
    None

let _ = Symbols.declare_numeral_interpreter "R_scope"
  (glob_R,["Coq";"Reals";"Rdefinitions"])
  ((if !Options.v7 then r_of_int2 else r_of_int),None)
  ([RRef(dummy_loc,glob_Ropp);RRef(dummy_loc,glob_R0);
    RRef(dummy_loc,glob_Rplus);RRef(dummy_loc,glob_Rmult);RRef(dummy_loc,glob_R1)],
    uninterp_r,
    None)

(************************************************************************)
(* Old ast printers via scope *)

let _ = if !Options.v7 then
let bignat_of_pos p =
  let (_,one,plus,_,_,_) = get_r_sign_ast dummy_loc in
  let rec transl = function
    | Node (_,"APPLIST",[p; o; a]) when alpha_eq(p,plus) & alpha_eq(o,one)
        -> add_1(transl a)
    | a when alpha_eq(a,one) -> Bignat.one
    | _ -> raise Non_closed_number
  in transl p
in
let bignat_option_of_pos p =
  try 
    Some (bignat_of_pos p)
  with Non_closed_number -> 
    None
in
let r_printer_Rplus1 p =
  match bignat_option_of_pos p with
    | Some n -> Some (str (Bignat.to_string (add_1 n)))
    | None -> None
in
let r_printer_Ropp p =
  match bignat_option_of_pos p with
    | Some n -> Some (str "-" ++ str (Bignat.to_string n))
    | None -> None
in
let r_printer_R1 _ =
  Some (int 1)
in
let r_printer_R0 _ =
  Some (int 0)
in
(* Declare pretty-printers for integers *)
let _ =
  Esyntax.declare_primitive_printer "r_printer_Ropp" "R_scope" (r_printer_Ropp)
in let _ =
  Esyntax.declare_primitive_printer "r_printer_Rplus1" "R_scope" (r_printer_Rplus1)
in let _ =
  Esyntax.declare_primitive_printer "r_printer_R1" "R_scope" (r_printer_R1)
in let _ =
  Esyntax.declare_primitive_printer "r_printer_R0" "R_scope" r_printer_R0
in ()