From 2dbe106c09b60690b87e31e58d505b1f4e05b57f Mon Sep 17 00:00:00 2001
From: aspiwack
Date: Fri, 11 May 2007 17:00:58 +0000
Subject: Processor integers + Print assumption (see coqdev mailing list for
 the details).

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9821 85f007b7-540e-0410-9357-904b9bb8a0f7
---
 parsing/g_intsyntax.ml | 266 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 266 insertions(+)
 create mode 100644 parsing/g_intsyntax.ml

(limited to 'parsing/g_intsyntax.ml')

diff --git a/parsing/g_intsyntax.ml b/parsing/g_intsyntax.ml
new file mode 100644
index 0000000000..e1cbbb7e05
--- /dev/null
+++ b/parsing/g_intsyntax.ml
@@ -0,0 +1,266 @@
+(************************************************************************)
+(*  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 $ $ i*)
+
+(* digit-based syntax for int31 and bigint *)
+
+open Bigint
+open Libnames
+open Rawterm
+
+(* arnaud : plan : 
+  - path des modules int31 et bigint dans des variables
+  - nom des constructeurs dans des variables
+  - nom des scopes dans des variables
+  - fonction qui cree les int31 en fonction d'un entier (ce sont des bigint de coq)
+    <= div2 with rest 31 fois, dans un tableau d'args preconstruit
+  - fonction qui cree un bigint de hauteur n (en appelant deux fois la fonction 
+    a la hauteur n-1 (sauf dans les cas ou il y a du 0))
+  /!\ attention aux nombres negatifs  *)
+
+(*** Constants for locating the int31 and bigN ***)
+
+
+
+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)
+
+(* copied on g_zsyntax.ml, where it is said to be a temporary hack*)
+(* takes a path an identifier in the form of a string list and a string, 
+   returns a kernel_name *)
+let make_kn dir id = Libnames.encode_kn (make_dir dir) (Names.id_of_string id)
+
+
+(* int31 stuff *)
+let int31_module = ["Coq"; "Ints"; "Int31"]
+let int31_path = make_path int31_module "int31"
+let int31_id = make_kn int31_module
+
+
+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)
+
+
+(* bigint stuff*)
+let zn2z_module = ["Coq"; "Ints"; "Basic_type"]
+let zn2z_path = make_path zn2z_module "zn2z"
+let zn2z_id = make_kn zn2z_module
+
+let zn2z_W0 = ConstructRef ((zn2z_id "zn2z",0),1)
+let zn2z_WW = ConstructRef ((zn2z_id "zn2z",0),2)
+
+let bigN_module = ["Coq"; "Ints"; "BigN"]
+let bigN_path = make_path bigN_module "bigN"
+(* big ugly hack *)
+let bigN_id id = (Obj.magic ((Names.MPdot ((Names.MPfile (make_dir bigN_module)), 
+                             Names.mk_label "BigN")),
+              [], Names.id_of_string id) : Names.kernel_name)
+
+(* number of inlined level of bigN (actually the level 0 to n_inlined-1 are inlined) *)
+let n_inlined = of_string "13"
+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_id "t_",0),
+		if less_than i n_inlined then
+		  (to_int i)+1
+		else
+		  (to_int n_inlined)+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
+				                      [RHole (dloc, Evd.InternalHole);
+						       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 "bogN 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
+					  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-> add (mult (rank hght)
+                                                          (transform (sub_1 hght) lft))
+	                                            (transform (sub_1 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)
-- 
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