Imported Upstream snapshot 8.3~beta0+13298

1 files changed, 330 insertions, 0 deletions

diff --git a/plugins/syntax/numbers_syntax.ml b/plugins/syntax/numbers_syntax.ml
new file mode 100644
index 00000000..4375d5e0
--- /dev/null
+++ b/plugins/syntax/numbers_syntax.ml
@@ -0,0 +1,330 @@
+(************************************************************************)
+(*  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*)
+
+(* digit-based syntax for int31, bigN bigZ and bigQ *)
+
+open Bigint
+open Libnames
+open Rawterm
+
+(*** Constants for locating int31 / bigN / bigZ / bigQ constructors ***)
+
+let make_dir l = Names.make_dirpath (List.map Names.id_of_string (List.rev l))
+let make_path dir id = Libnames.make_path (make_dir dir) (Names.id_of_string id)
+
+let make_mind mp id = Names.make_mind mp Names.empty_dirpath (Names.mk_label id)
+let make_mind_mpfile dir id = make_mind (Names.MPfile (make_dir dir)) id
+let make_mind_mpdot dir modname id =
+  let mp = Names.MPdot (Names.MPfile (make_dir dir), Names.mk_label modname)
+  in make_mind mp id
+
+
+(* int31 stuff *)
+let int31_module = ["Coq"; "Numbers"; "Cyclic"; "Int31"; "Int31"]
+let int31_path = make_path int31_module "int31"
+let int31_id = make_mind_mpfile int31_module
+let int31_scope = "int31_scope"
+
+let int31_construct = ConstructRef ((int31_id "int31",0),1)
+
+let int31_0 = ConstructRef ((int31_id "digits",0),1)
+let int31_1 = ConstructRef ((int31_id "digits",0),2)
+
+
+(* bigN stuff*)
+let zn2z_module = ["Coq"; "Numbers"; "Cyclic"; "DoubleCyclic"; "DoubleType"]
+let zn2z_path = make_path zn2z_module "zn2z"
+let zn2z_id = make_mind_mpfile zn2z_module
+
+let zn2z_W0 = ConstructRef ((zn2z_id "zn2z",0),1)
+let zn2z_WW = ConstructRef ((zn2z_id "zn2z",0),2)
+
+let bigN_module = ["Coq"; "Numbers"; "Natural"; "BigN"; "BigN" ]
+let bigN_path = make_path (bigN_module@["BigN"]) "t"
+let bigN_t = make_mind_mpdot bigN_module "BigN" "t_"
+let bigN_scope = "bigN_scope"
+
+(* number of inlined level of bigN (actually the level 0 to n_inlined-1 are inlined) *)
+let n_inlined = of_string "7"
+let bigN_constructor =
+ (* converts a bigint into an int the ugly way *)
+  let rec to_int i =
+    if equal i zero then
+      0
+    else
+      let (quo,rem) = div2_with_rest i in
+      if rem then
+	2*(to_int quo)+1
+      else
+	2*(to_int quo)
+  in
+  fun i ->
+  ConstructRef ((bigN_t,0),
+		if less_than i n_inlined then
+		  (to_int i)+1
+		else
+		  (to_int n_inlined)+1
+	       )
+
+(*bigZ stuff*)
+let bigZ_module = ["Coq"; "Numbers"; "Integer"; "BigZ"; "BigZ" ]
+let bigZ_path = make_path (bigZ_module@["BigZ"]) "t"
+let bigZ_t = make_mind_mpdot bigZ_module "BigZ" "t_"
+let bigZ_scope = "bigZ_scope"
+
+let bigZ_pos = ConstructRef ((bigZ_t,0),1)
+let bigZ_neg = ConstructRef ((bigZ_t,0),2)
+
+
+(*bigQ stuff*)
+let bigQ_module = ["Coq"; "Numbers"; "Rational"; "BigQ"; "BigQ"]
+let bigQ_path = make_path (bigQ_module@["BigQ"]) "t"
+let bigQ_t = make_mind_mpdot bigQ_module "BigQ" "t_"
+let bigQ_scope = "bigQ_scope"
+
+let bigQ_z =  ConstructRef ((bigQ_t,0),1)
+
+
+(*** Definition of the Non_closed exception, used in the pretty printing ***)
+exception Non_closed
+
+(*** Parsing for int31 in digital notation ***)
+
+(* parses a *non-negative* integer (from bigint.ml) into an int31
+   wraps modulo 2^31 *)
+let int31_of_pos_bigint dloc n =
+  let ref_construct = RRef (dloc, int31_construct) in
+  let ref_0 = RRef (dloc, int31_0) in
+  let ref_1 = RRef (dloc, int31_1) in
+  let rec args counter n =
+    if counter <= 0 then
+      []
+    else
+      let (q,r) = div2_with_rest n in
+	(if r then ref_1 else ref_0)::(args (counter-1) q)
+  in
+  RApp (dloc, ref_construct, List.rev (args 31 n))
+
+let error_negative dloc =
+  Util.user_err_loc (dloc, "interp_int31", Pp.str "int31 are only non-negative numbers.")
+
+let interp_int31 dloc n =
+  if is_pos_or_zero n then
+    int31_of_pos_bigint dloc n
+  else
+    error_negative dloc
+
+(* Pretty prints an int31 *)
+
+let bigint_of_int31 =
+  let rec args_parsing args cur =
+    match args with
+      | [] -> cur
+      | (RRef (_,b))::l when b = int31_0 -> args_parsing l (mult_2 cur)
+      | (RRef (_,b))::l when b = int31_1 -> args_parsing l (add_1 (mult_2 cur))
+      | _ -> raise Non_closed
+  in
+  function
+  | RApp (_, RRef (_, c), args) when c=int31_construct -> args_parsing args zero
+  | _ -> raise Non_closed
+
+let uninterp_int31 i =
+  try
+    Some (bigint_of_int31 i)
+  with Non_closed ->
+    None
+
+(* Actually declares the interpreter for int31 *)
+let _ = Notation.declare_numeral_interpreter int31_scope
+  (int31_path, int31_module)
+  interp_int31
+  ([RRef (Util.dummy_loc, int31_construct)],
+   uninterp_int31,
+   true)
+
+
+(*** Parsing for bigN in digital notation ***)
+(* the base for bigN (in Coq) that is 2^31 in our case *)
+let base = pow two (of_string "31")
+
+(* base of the bigN of height N : *)
+let rank n = pow base (pow two n)
+
+(* splits a number bi at height n, that is the rest needs 2^n int31 to be stored
+   it is expected to be used only when the quotient would also need 2^n int31 to be
+   stored *)
+let split_at n bi =
+  euclid bi (rank (sub_1 n))
+
+(* search the height of the Coq bigint needed to represent the integer bi *)
+let height bi =
+  let rec height_aux n =
+    if less_than bi (rank n) then
+      n
+    else
+      height_aux (add_1 n)
+  in
+  height_aux zero
+
+
+(* n must be a non-negative integer (from bigint.ml) *)
+let word_of_pos_bigint dloc hght n =
+  let ref_W0 = RRef (dloc, zn2z_W0) in
+  let ref_WW = RRef (dloc, zn2z_WW) in
+  let rec decomp hgt n =
+    if is_neg_or_zero hgt then
+      int31_of_pos_bigint dloc n
+    else if equal n zero then
+      RApp (dloc, ref_W0, [RHole (dloc, Evd.InternalHole)])
+    else
+      let (h,l) = split_at hgt n in
+      RApp (dloc, ref_WW, [RHole (dloc, Evd.InternalHole);
+			   decomp (sub_1 hgt) h;
+			   decomp (sub_1 hgt) l])
+  in
+  decomp hght n
+
+let bigN_of_pos_bigint dloc n =
+  let ref_constructor i = RRef (dloc, bigN_constructor i) in
+  let result h word = RApp (dloc, ref_constructor h, if less_than h n_inlined then
+				                       [word]
+			                             else
+				                      [Nat_syntax.nat_of_int dloc (sub h n_inlined);
+						       word])
+  in
+  let hght = height n in
+  result hght (word_of_pos_bigint dloc hght n)
+
+let bigN_error_negative dloc =
+  Util.user_err_loc (dloc, "interp_bigN", Pp.str "bigN are only non-negative numbers.")
+
+let interp_bigN dloc n =
+  if is_pos_or_zero n then
+    bigN_of_pos_bigint dloc n
+  else
+    bigN_error_negative dloc
+
+
+(* Pretty prints a bigN *)
+
+let bigint_of_word =
+  let rec get_height rc =
+    match rc with
+    | RApp (_,RRef(_,c), [_;lft;rght]) when c = zn2z_WW ->
+	                                  let hleft = get_height lft in
+					  let hright = get_height rght in
+					  add_1
+					    (if less_than hleft hright then
+						 hright
+					     else
+						 hleft)
+    | _ -> zero
+  in
+  let rec transform hght rc =
+    match rc with
+    | RApp (_,RRef(_,c),_) when c = zn2z_W0-> zero
+    | RApp (_,RRef(_,c), [_;lft;rght]) when c=zn2z_WW-> let new_hght = sub_1 hght in
+	                                                add (mult (rank new_hght)
+                                                          (transform (new_hght) lft))
+	                                            (transform (new_hght) rght)
+    | _ -> bigint_of_int31 rc
+  in
+  fun rc ->
+    let hght = get_height rc in
+    transform hght rc
+
+let bigint_of_bigN rc =
+  match rc with
+  | RApp (_,_,[one_arg]) -> bigint_of_word one_arg
+  | RApp (_,_,[_;second_arg]) -> bigint_of_word second_arg
+  | _ -> raise Non_closed
+
+let uninterp_bigN rc =
+  try
+    Some (bigint_of_bigN rc)
+  with Non_closed ->
+    None
+
+
+(* declare the list of constructors of bigN used in the declaration of the
+   numeral interpreter *)
+
+let bigN_list_of_constructors =
+  let rec build i =
+    if less_than i (add_1 n_inlined) then
+      RRef (Util.dummy_loc, bigN_constructor i)::(build (add_1 i))
+    else
+      []
+  in
+  build zero
+
+(* Actually declares the interpreter for bigN *)
+let _ = Notation.declare_numeral_interpreter bigN_scope
+  (bigN_path, bigN_module)
+  interp_bigN
+  (bigN_list_of_constructors,
+   uninterp_bigN,
+   true)
+
+
+(*** Parsing for bigZ in digital notation ***)
+let interp_bigZ dloc n =
+  let ref_pos = RRef (dloc, bigZ_pos) in
+  let ref_neg = RRef (dloc, bigZ_neg) in
+  if is_pos_or_zero n then
+    RApp (dloc, ref_pos, [bigN_of_pos_bigint dloc n])
+  else
+    RApp (dloc, ref_neg, [bigN_of_pos_bigint dloc (neg n)])
+
+(* pretty printing functions for bigZ *)
+let bigint_of_bigZ = function
+  | RApp (_, RRef(_,c), [one_arg]) when c = bigZ_pos -> bigint_of_bigN one_arg
+  | RApp (_, RRef(_,c), [one_arg]) when c = bigZ_neg ->
+      let opp_val = bigint_of_bigN one_arg in
+      if equal opp_val zero then
+	raise Non_closed
+      else
+	neg opp_val
+  | _ -> raise Non_closed
+
+
+let uninterp_bigZ rc =
+  try
+    Some (bigint_of_bigZ rc)
+  with Non_closed ->
+    None
+
+(* Actually declares the interpreter for bigZ *)
+let _ = Notation.declare_numeral_interpreter bigZ_scope
+  (bigZ_path, bigZ_module)
+  interp_bigZ
+  ([RRef (Util.dummy_loc, bigZ_pos);
+    RRef (Util.dummy_loc, bigZ_neg)],
+   uninterp_bigZ,
+   true)
+
+(*** Parsing for bigQ in digital notation ***)
+let interp_bigQ dloc n =
+  let ref_z = RRef (dloc, bigQ_z) in
+  RApp (dloc, ref_z, [interp_bigZ dloc n])
+
+let uninterp_bigQ rc =
+  try match rc with
+    | RApp (_, RRef(_,c), [one_arg]) when c = bigQ_z ->
+	Some (bigint_of_bigZ one_arg)
+    | _ -> None (* we don't pretty-print yet fractions *)
+  with Non_closed -> None
+
+(* Actually declares the interpreter for bigQ *)
+let _ = Notation.declare_numeral_interpreter bigQ_scope
+  (bigQ_path, bigQ_module)
+  interp_bigQ
+  ([RRef (Util.dummy_loc, bigQ_z)], uninterp_bigQ,
+   true)