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|
(************************************************************************)
(* 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 Pp
open Util
open Names
open Pcoq
open Topconstr
open Libnames
exception Non_closed_number
(**********************************************************************)
(* Parsing R via scopes *)
(**********************************************************************)
open Libnames
open Rawterm
open Bigint
let make_dir l = make_dirpath (List.map id_of_string (List.rev l))
let rdefinitions = make_dir ["Coq";"Reals";"Rdefinitions"]
let make_path dir id = Libnames.make_path dir (id_of_string id)
let r_path = make_path rdefinitions "R"
(* TODO: temporary hack *)
let make_path dir id = Libnames.encode_con dir (id_of_string id)
let r_kn = make_path rdefinitions "R"
let glob_R = ConstRef r_kn
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")
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 equal 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 n <> zero then r_of_pos n else RRef(dloc,glob_R0)
let r_of_int dloc z =
if is_strictly_neg z then
RApp (dloc, RRef(dloc,glob_Ropp), [r_of_posint dloc (neg z)])
else
r_of_posint dloc z
(**********************************************************************)
(* 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 ->
let n = bignat_of_r a in
if n = zero then raise Non_closed_number;
neg n
| a -> bignat_of_r a
let uninterp_r p =
try
Some (bigint_of_r p)
with Non_closed_number ->
None
let _ = Notation.declare_numeral_interpreter "R_scope"
(r_path,["Coq";"Reals";"Rdefinitions"])
r_of_int
([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,
false)
|
