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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 *)
-(************************************************************************)
-
-(*i $Id$ i*)
-
-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)