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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Pp
open Errors
open Util
open Names
open Bigint
exception Non_closed_number
(**********************************************************************)
(* Parsing positive via scopes *)
(**********************************************************************)
open Globnames
open Glob_term
let binnums = ["Coq";"Numbers";"BinNums"]
let make_dir l = DirPath.make (List.rev_map Id.of_string l)
let make_path dir id = Libnames.make_path (make_dir dir) (Id.of_string id)
let positive_path = make_path binnums "positive"
(* TODO: temporary hack *)
let make_kn dir id = Globnames.encode_mind dir id
let positive_kn = make_kn (make_dir binnums) (Id.of_string "positive")
let glob_positive = IndRef (positive_kn,0)
let path_of_xI = ((positive_kn,0),1)
let path_of_xO = ((positive_kn,0),2)
let path_of_xH = ((positive_kn,0),3)
let glob_xI = ConstructRef path_of_xI
let glob_xO = ConstructRef path_of_xO
let glob_xH = ConstructRef path_of_xH
let pos_of_bignat dloc x =
let ref_xI = GRef (dloc, glob_xI, None) in
let ref_xH = GRef (dloc, glob_xH, None) in
let ref_xO = GRef (dloc, glob_xO, None) in
let rec pos_of x =
match div2_with_rest x with
| (q,false) -> GApp (dloc, ref_xO,[pos_of q])
| (q,true) when not (Bigint.equal q zero) -> GApp (dloc,ref_xI,[pos_of q])
| (q,true) -> ref_xH
in
pos_of x
let error_non_positive dloc =
user_err_loc (dloc, "interp_positive",
str "Only strictly positive numbers in type \"positive\".")
let interp_positive dloc n =
if is_strictly_pos n then pos_of_bignat dloc n
else error_non_positive dloc
(**********************************************************************)
(* Printing positive via scopes *)
(**********************************************************************)
let rec bignat_of_pos = function
| GApp (_, GRef (_,b,_),[a]) when Globnames.eq_gr b glob_xO -> mult_2(bignat_of_pos a)
| GApp (_, GRef (_,b,_),[a]) when Globnames.eq_gr b glob_xI -> add_1(mult_2(bignat_of_pos a))
| GRef (_, a, _) when Globnames.eq_gr a glob_xH -> Bigint.one
| _ -> raise Non_closed_number
let uninterp_positive p =
try
Some (bignat_of_pos p)
with Non_closed_number ->
None
(************************************************************************)
(* Declaring interpreters and uninterpreters for positive *)
(************************************************************************)
let _ = Notation.declare_numeral_interpreter "positive_scope"
(positive_path,binnums)
interp_positive
([GRef (Loc.ghost, glob_xI, None);
GRef (Loc.ghost, glob_xO, None);
GRef (Loc.ghost, glob_xH, None)],
uninterp_positive,
true)
(**********************************************************************)
(* Parsing N via scopes *)
(**********************************************************************)
let n_kn = make_kn (make_dir binnums) (Id.of_string "N")
let glob_n = IndRef (n_kn,0)
let path_of_N0 = ((n_kn,0),1)
let path_of_Npos = ((n_kn,0),2)
let glob_N0 = ConstructRef path_of_N0
let glob_Npos = ConstructRef path_of_Npos
let n_path = make_path binnums "N"
let n_of_binnat dloc pos_or_neg n =
if not (Bigint.equal n zero) then
GApp(dloc, GRef (dloc,glob_Npos,None), [pos_of_bignat dloc n])
else
GRef (dloc, glob_N0, None)
let error_negative dloc =
user_err_loc (dloc, "interp_N", str "No negative numbers in type \"N\".")
let n_of_int dloc n =
if is_pos_or_zero n then n_of_binnat dloc true n
else error_negative dloc
(**********************************************************************)
(* Printing N via scopes *)
(**********************************************************************)
let bignat_of_n = function
| GApp (_, GRef (_,b,_),[a]) when Globnames.eq_gr b glob_Npos -> bignat_of_pos a
| GRef (_, a,_) when Globnames.eq_gr a glob_N0 -> Bigint.zero
| _ -> raise Non_closed_number
let uninterp_n p =
try Some (bignat_of_n p)
with Non_closed_number -> None
(************************************************************************)
(* Declaring interpreters and uninterpreters for N *)
let _ = Notation.declare_numeral_interpreter "N_scope"
(n_path,binnums)
n_of_int
([GRef (Loc.ghost, glob_N0, None);
GRef (Loc.ghost, glob_Npos, None)],
uninterp_n,
true)
(**********************************************************************)
(* Parsing Z via scopes *)
(**********************************************************************)
let z_path = make_path binnums "Z"
let z_kn = make_kn (make_dir binnums) (Id.of_string "Z")
let glob_z = IndRef (z_kn,0)
let path_of_ZERO = ((z_kn,0),1)
let path_of_POS = ((z_kn,0),2)
let path_of_NEG = ((z_kn,0),3)
let glob_ZERO = ConstructRef path_of_ZERO
let glob_POS = ConstructRef path_of_POS
let glob_NEG = ConstructRef path_of_NEG
let z_of_int dloc n =
if not (Bigint.equal n zero) then
let sgn, n =
if is_pos_or_zero n then glob_POS, n else glob_NEG, Bigint.neg n in
GApp(dloc, GRef (dloc,sgn,None), [pos_of_bignat dloc n])
else
GRef (dloc, glob_ZERO, None)
(**********************************************************************)
(* Printing Z via scopes *)
(**********************************************************************)
let bigint_of_z = function
| GApp (_, GRef (_,b,_),[a]) when Globnames.eq_gr b glob_POS -> bignat_of_pos a
| GApp (_, GRef (_,b,_),[a]) when Globnames.eq_gr b glob_NEG -> Bigint.neg (bignat_of_pos a)
| GRef (_, a, _) when Globnames.eq_gr a glob_ZERO -> Bigint.zero
| _ -> raise Non_closed_number
let uninterp_z p =
try
Some (bigint_of_z p)
with Non_closed_number -> None
(************************************************************************)
(* Declaring interpreters and uninterpreters for Z *)
let _ = Notation.declare_numeral_interpreter "Z_scope"
(z_path,binnums)
z_of_int
([GRef (Loc.ghost, glob_ZERO, None);
GRef (Loc.ghost, glob_POS, None);
GRef (Loc.ghost, glob_NEG, None)],
uninterp_z,
true)
|
