1 (* Copyright (C) 2002, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
8 * modify it under the terms of the GNU General Public License
9 * as published by the Free Software Foundation; either version 2
10 * of the License, or (at your option) any later version.
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13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
28 (* La tactique Fourier ne fonctionne de manière sûre que si les coefficients
29 des inéquations et équations sont entiers. En attendant la tactique Field.
35 let debug x = print_string ("____ "^x) ; flush stdout;;
37 let debug_pcontext x =
39 List.iter (fun y -> match y with Some(Cic.Name(a),_) -> str := !str ^ a ^ " " | _ ->()) x ;
40 debug ("contesto : "^ (!str) ^ "\n")
43 (******************************************************************************
44 Operations on linear combinations.
46 Opérations sur les combinaisons linéaires affines.
47 La partie homogène d'une combinaison linéaire est en fait une table de hash
48 qui donne le coefficient d'un terme du calcul des constructions,
49 qui est zéro si le terme n'y est pas.
55 The type for linear combinations
57 type flin = {fhom:(Cic.term , rational)Hashtbl.t;fcste:rational}
63 let flin_zero () = {fhom = Hashtbl.create 50;fcste=r0}
69 @return the rational associated with x (coefficient)
73 (Hashtbl.find f.fhom x)
79 Adds c to the coefficient of x
86 let cx = flin_coef f x in
87 Hashtbl.remove f.fhom x;
88 Hashtbl.add f.fhom x (rplus cx c);
97 let flin_add_cste f c =
99 fcste=rplus f.fcste c}
103 @return a empty flin with r1 in fcste
105 let flin_one () = flin_add_cste (flin_zero()) r1;;
110 let flin_plus f1 f2 =
111 let f3 = flin_zero() in
112 Hashtbl.iter (fun x c -> let _=flin_add f3 x c in ()) f1.fhom;
113 Hashtbl.iter (fun x c -> let _=flin_add f3 x c in ()) f2.fhom;
114 flin_add_cste (flin_add_cste f3 f1.fcste) f2.fcste;
120 let flin_minus f1 f2 =
121 let f3 = flin_zero() in
122 Hashtbl.iter (fun x c -> let _=flin_add f3 x c in ()) f1.fhom;
123 Hashtbl.iter (fun x c -> let _=flin_add f3 x (rop c) in ()) f2.fhom;
124 flin_add_cste (flin_add_cste f3 f1.fcste) (rop f2.fcste);
131 let f2 = flin_zero() in
132 Hashtbl.iter (fun x c -> let _=flin_add f2 x (rmult a c) in ()) f.fhom;
133 flin_add_cste f2 (rmult a f.fcste);
137 (*****************************************************************************)
142 @return proiection on string of t
144 let rec string_of_term t =
146 Cic.Cast (t1,t2) -> string_of_term t1
147 |Cic.Const (u,boh) -> UriManager.string_of_uri u
148 |Cic.Var (u) -> UriManager.string_of_uri u
149 | _ -> "not_of_constant"
153 let string_of_constr = string_of_term
159 @raise Failure if conversion is impossible
160 @return rational proiection of t
162 let rec rational_of_term t =
163 (* fun to apply f to the first and second rational-term of l *)
164 let rat_of_binop f l =
165 let a = List.hd l and
166 b = List.hd(List.tl l) in
167 f (rational_of_term a) (rational_of_term b)
169 (* as before, but f is unary *)
170 let rat_of_unop f l =
171 f (rational_of_term (List.hd l))
174 | Cic.Cast (t1,t2) -> (rational_of_term t1)
175 | Cic.Appl (t1::next) ->
178 (match (UriManager.string_of_uri u) with
179 "cic:/Coq/Reals/Rdefinitions/Ropp.con" ->
181 |"cic:/Coq/Reals/Rdefinitions/Rinv.con" ->
182 rat_of_unop rinv next
183 |"cic:/Coq/Reals/Rdefinitions/Rmult.con" ->
184 rat_of_binop rmult next
185 |"cic:/Coq/Reals/Rdefinitions/Rdiv.con" ->
186 rat_of_binop rdiv next
187 |"cic:/Coq/Reals/Rdefinitions/Rplus.con" ->
188 rat_of_binop rplus next
189 |"cic:/Coq/Reals/Rdefinitions/Rminus.con" ->
190 rat_of_binop rminus next
191 | _ -> failwith "not a rational")
192 | _ -> failwith "not a rational")
193 | Cic.Const (u,boh) ->
194 (match (UriManager.string_of_uri u) with
195 "cic:/Coq/Reals/Rdefinitions/R1.con" -> r1
196 |"cic:/Coq/Reals/Rdefinitions/R0.con" -> r0
197 | _ -> failwith "not a rational")
198 | _ -> failwith "not a rational"
202 let rational_of_const = rational_of_term;;
206 let rec flin_of_term t =
207 let fl_of_binop f l =
208 let a = List.hd l and
209 b = List.hd(List.tl l) in
210 f (flin_of_term a) (flin_of_term b)
214 | Cic.Cast (t1,t2) -> (flin_of_term t1)
215 | Cic.Appl (t1::next) ->
220 match (UriManager.string_of_uri u) with
221 "cic:/Coq/Reals/Rdefinitions/Ropp.con" ->
222 flin_emult (rop r1) (flin_of_term (List.hd next))
223 |"cic:/Coq/Reals/Rdefinitions/Rplus.con"->
224 fl_of_binop flin_plus next
225 |"cic:/Coq/Reals/Rdefinitions/Rminus.con"->
226 fl_of_binop flin_minus next
227 |"cic:/Coq/Reals/Rdefinitions/Rmult.con"->
229 let arg1 = (List.hd next) and
230 arg2 = (List.hd(List.tl next))
234 let a = rational_of_term arg1 in
237 let b = (rational_of_term arg2) in
238 (flin_add_cste (flin_zero()) (rmult a b))
241 _ -> (flin_add (flin_zero()) arg2 a)
244 _-> (flin_add (flin_zero()) arg1 (rational_of_term arg2 ))
246 |"cic:/Coq/Reals/Rdefinitions/Rinv.con"->
247 let a=(rational_of_term (List.hd next)) in
248 flin_add_cste (flin_zero()) (rinv a)
249 |"cic:/Coq/Reals/Rdefinitions/Rdiv.con"->
251 let b=(rational_of_term (List.hd(List.tl next))) in
254 let a = (rational_of_term (List.hd next)) in
255 (flin_add_cste (flin_zero()) (rdiv a b))
258 _-> (flin_add (flin_zero()) (List.hd next) (rinv b))
264 | Cic.Const (u,boh) ->
266 match (UriManager.string_of_uri u) with
267 "cic:/Coq/Reals/Rdefinitions/R1.con" -> flin_one ()
268 |"cic:/Coq/Reals/Rdefinitions/R0.con" -> flin_zero ()
272 with _ -> flin_add (flin_zero()) t r1
276 let flin_of_constr = flin_of_term;;
280 Translates a flin to (c,x) list
282 @return something like (c1,x1)::(c2,x2)::...::(cn,xn)
284 let flin_to_alist f =
286 Hashtbl.iter (fun x c -> res:=(c,x)::(!res)) f;
290 (* Représentation des hypothèses qui sont des inéquations ou des équations.
294 The structure for ineq
296 type hineq={hname:Cic.term; (* le nom de l'hypothèse *)
297 htype:string; (* Rlt, Rgt, Rle, Rge, eqTLR ou eqTRL *)
304 (* Transforme une hypothese h:t en inéquation flin<0 ou flin<=0
307 let ineq1_of_term (h,t) =
308 match t with (* match t *)
309 Cic.Appl (t1::next) ->
310 let arg1= List.hd next in
311 let arg2= List.hd(List.tl next) in
312 (match t1 with (* match t1 *)
314 (match UriManager.string_of_uri u with (* match u *)
315 "cic:/Coq/Reals/Rdefinitions/Rlt.con" ->
320 hflin= flin_minus (flin_of_term arg1)
323 |"cic:/Coq/Reals/Rdefinitions/Rgt.con" ->
328 hflin= flin_minus (flin_of_term arg2)
331 |"cic:/Coq/Reals/Rdefinitions/Rle.con" ->
336 hflin= flin_minus (flin_of_term arg1)
339 |"cic:/Coq/Reals/Rdefinitions/Rge.con" ->
344 hflin= flin_minus (flin_of_term arg2)
347 |_->assert false)(* match u *)
348 | Cic.MutInd (u,i,o) ->
349 (match UriManager.string_of_uri u with
350 "cic:/Coq/Init/Logic_Type/eqT.con" ->
353 let arg2= List.hd(List.tl (List.tl next)) in
356 (match UriManager.string_of_uri u with
357 "cic:/Coq/Reals/Rdefinitions/R.con"->
362 hflin= flin_minus (flin_of_term arg1)
369 hflin= flin_minus (flin_of_term arg2)
375 |_-> assert false)(* match t1 *)
376 |_-> assert false (* match t *)
379 let ineq1_of_constr = ineq1_of_term;;
382 (* Applique la méthode de Fourier à une liste d'hypothèses (type hineq)
388 | a::next -> Fourier.print_rational a ; print_string " " ; print_rl next
391 let rec print_sys l =
394 | (a,b)::next -> (print_rl a;
395 print_string (if b=true then "strict\n"else"\n");
400 Hashtbl.iter (fun x y -> print_string ("("^"-"^","^"-"^")")) h
403 let fourier_lineq lineq1 =
405 let hvar=Hashtbl.create 50 in (* la table des variables des inéquations *)
407 Hashtbl.iter (fun x c ->
408 try (Hashtbl.find hvar x;())
409 with _-> nvar:=(!nvar)+1;
410 Hashtbl.add hvar x (!nvar))
414 debug("Il numero di incognite e' "^string_of_int (!nvar+1)^"\n");
415 let sys= List.map (fun h->
416 let v=Array.create ((!nvar)+1) r0 in
417 Hashtbl.iter (fun x c -> v.(Hashtbl.find hvar x)<-c)
419 ((Array.to_list v)@[rop h.hflin.fcste],h.hstrict))
421 debug ("chiamo unsolvable sul sistema di "^ string_of_int (List.length sys) ^"\n");
426 (******************************************************************************
427 Construction de la preuve en cas de succès de la méthode de Fourier,
428 i.e. on obtient une contradiction.
432 let _False = Cic.MutInd (UriManager.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 0 ;;
433 let _not = Cic.Const (UriManager.uri_of_string "cic:/Coq/Init/Logic/not.con") 0;;
434 let _R0 = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R0.con") 0 ;;
435 let _R1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R1.con") 0 ;;
436 let _R = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/R.con") 0 ;;
437 let _Rfourier_eqLR_to_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_eqLR_to_le.con") 0 ;;
438 let _Rfourier_eqRL_to_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_eqRL_to_le.con") 0 ;;
439 let _Rfourier_ge_to_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_ge_to_le.con") 0 ;;
440 let _Rfourier_gt_to_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_gt_to_lt.con") 0 ;;
441 let _Rfourier_le=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le.con") 0 ;;
442 let _Rfourier_le_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le_le.con") 0 ;;
443 let _Rfourier_le_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_le_lt.con") 0 ;;
444 let _Rfourier_lt=Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt.con") 0 ;;
445 let _Rfourier_lt_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt_le.con") 0 ;;
446 let _Rfourier_lt_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_lt_lt.con") 0 ;;
447 let _Rfourier_not_ge_lt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_ge_lt.con") 0 ;;
448 let _Rfourier_not_gt_le = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_gt_le.con") 0 ;;
449 let _Rfourier_not_le_gt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_le_gt.con") 0 ;;
450 let _Rfourier_not_lt_ge = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rfourier_not_lt_ge.con") 0 ;;
451 let _Rinv = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rinv.con") 0 ;;
452 let _Rinv_R1 = Cic.Const(UriManager.uri_of_string "cic:/Coq/Reals/Rbase/Rinv_R1.con" ) 0;;
453 let _Rle = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rle.con") 0 ;;
454 let _Rle_mult_inv_pos = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_mult_inv_pos.con") 0 ;;
455 let _Rle_not_lt = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_not_lt.con") 0 ;;
456 let _Rle_zero_1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_1.con") 0 ;;
457 let _Rle_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_pos_plus1.con") 0 ;;
458 let _Rle_zero_zero = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rle_zero_zero.con") 0 ;;
459 let _Rlt = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rlt.con") 0 ;;
460 let _Rlt_mult_inv_pos = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_mult_inv_pos.con") 0 ;;
461 let _Rlt_not_le = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_not_le.con") 0 ;;
462 let _Rlt_zero_1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_zero_1.con") 0 ;;
463 let _Rlt_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rlt_zero_pos_plus1.con") 0 ;;
464 let _Rminus = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rminus.con") 0 ;;
465 let _Rmult = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rmult.con") 0 ;;
466 let _Rnot_le_le =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_le_le.con") 0 ;;
467 let _Rnot_lt0 = Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_lt0.con") 0 ;;
468 let _Rnot_lt_lt =Cic.Const (UriManager.uri_of_string "cic:/Coq/fourier/Fourier_util/Rnot_lt_lt.con") 0 ;;
469 let _Ropp = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Ropp.con") 0 ;;
470 let _Rplus = Cic.Const (UriManager.uri_of_string "cic:/Coq/Reals/Rdefinitions/Rplus.con") 0 ;;
471 let _sym_eqT = Cic.Const(UriManager.uri_of_string "/Coq/Init/Logic_Type/Equality_is_a_congruence/sym_eqT.con") 0 ;;
472 (*****************************************************************************************************)
473 let is_int x = (x.den)=1
476 (* fraction = couple (num,den) *)
477 let rec rational_to_fraction x= (x.num,x.den)
480 (* traduction -3 -> (Ropp (Rplus R1 (Rplus R1 R1)))
483 let rec int_to_real_aux n =
485 0 -> _R0 (* o forse R0 + R0 ????? *)
486 | _ -> Cic.Appl [ _Rplus ; _R1 ; int_to_real_aux (n-1) ]
491 let x = int_to_real_aux (abs n) in
493 Cic.Appl [ _Ropp ; x ]
499 (* -1/2 -> (Rmult (Ropp R1) (Rinv (Rplus R1 R1)))
502 let rational_to_real x =
503 let (n,d)=rational_to_fraction x in
504 Cic.Appl [ _Rmult ; int_to_real n ; Cic.Appl [ _Rinv ; int_to_real d ] ]
507 (* preuve que 0<n*1/d
512 let tac_zero_inf_pos gl (n,d) =
513 (*let cste = pf_parse_constr gl in*)
514 let tacn=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
515 let tacd=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
517 tacn:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1) ~continuation:!tacn); done;
519 tacd:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1) ~continuation:!tacd); done;
520 (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_mult_inv_pos) ~continuations:[!tacn;!tacd])
522 let tac_zero_inf_pos (n,d) ~status =
523 (*let cste = pf_parse_constr gl in*)
524 let pall str ~status:(proof,goal) t =
525 debug ("tac "^str^" :\n" );
526 let curi,metasenv,pbo,pty = proof in
527 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
528 debug ("th = "^ CicPp.ppterm t ^"\n");
529 debug ("ty = "^ CicPp.ppterm ty^"\n");
532 (fun ~status -> pall "n0" ~status _Rlt_zero_1 ;PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ~status ) in
534 (fun ~status -> pall "d0" ~status _Rlt_zero_1 ;PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ~status ) in
538 tacn:=(Tacticals.then_ ~start:(fun ~status -> pall ("n"^string_of_int i) ~status _Rlt_zero_pos_plus1;PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1 ~status) ~continuation:!tacn); done;
540 tacd:=(Tacticals.then_ ~start:(fun ~status -> pall "d" ~status _Rlt_zero_pos_plus1 ;PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1 ~status) ~continuation:!tacd); done;
544 debug("\nTAC ZERO INF POS\n");
546 (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_mult_inv_pos)
555 (* preuve que 0<=n*1/d
558 let tac_zero_infeq_pos gl (n,d) =
559 (*let cste = pf_parse_constr gl in*)
560 let tacn = ref (if n=0 then
561 (PrimitiveTactics.apply_tac ~term:_Rle_zero_zero )
563 (PrimitiveTactics.apply_tac ~term:_Rle_zero_1 ))
565 let tacd=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
567 tacn:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rle_zero_pos_plus1) ~continuation:!tacn); done;
569 tacd:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1) ~continuation:!tacd); done;
570 (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rle_mult_inv_pos) ~continuations:[!tacn;!tacd])
575 (* preuve que 0<(-n)*(1/d) => False
578 let tac_zero_inf_false gl (n,d) =
579 if n=0 then (PrimitiveTactics.apply_tac ~term:_Rnot_lt0)
581 (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rle_not_lt)
582 ~continuation:(tac_zero_infeq_pos gl (-n,d)))
585 (* preuve que 0<=(-n)*(1/d) => False
588 let tac_zero_infeq_false gl (n,d) =
589 (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_not_le)
590 ~continuation:(tac_zero_inf_pos (-n,d)))
594 (* *********** ********** ******** ??????????????? *********** **************)
596 let apply_type_tac ~cast:t ~applist:al ~status:(proof,goal) =
597 let curi,metasenv,pbo,pty = proof in
598 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
599 let fresh_meta = ProofEngineHelpers.new_meta proof in
601 ProofEngineHelpers.identity_relocation_list_for_metavariable context in
602 let metasenv' = (fresh_meta,context,t)::metasenv in
603 let proof' = curi,metasenv',pbo,pty in
605 PrimitiveTactics.apply_tac ~term:(Cic.Appl ((Cic.Cast (Cic.Meta (fresh_meta,irl),t))::al)) ~status:(proof',goal)
607 proof'',fresh_meta::goals
614 let my_cut ~term:c ~status:(proof,goal)=
615 let curi,metasenv,pbo,pty = proof in
616 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
618 let fresh_meta = ProofEngineHelpers.new_meta proof in
620 ProofEngineHelpers.identity_relocation_list_for_metavariable context in
621 let metasenv' = (fresh_meta,context,c)::metasenv in
622 let proof' = curi,metasenv',pbo,pty in
624 apply_type_tac ~cast:(Cic.Prod(Cic.Name "Anonymous",c,CicSubstitution.lift 1 ty)) ~applist:[Cic.Meta(fresh_meta,irl)] ~status:(proof',goal)
626 (* We permute the generated goals to be consistent with Coq *)
629 | he::tl -> proof'',he::fresh_meta::tl
633 let exact = PrimitiveTactics.exact_tac;;
635 let tac_use h ~status =
636 debug("Inizio TC_USE\n");
639 "Rlt" -> exact ~term:h.hname ~status
640 |"Rle" -> exact ~term:h.hname ~status
641 |"Rgt" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_gt_to_lt)
642 ~continuation:(exact ~term:h.hname)) ~status
643 |"Rge" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_ge_to_le)
644 ~continuation:(exact ~term:h.hname)) ~status
645 |"eqTLR" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_eqLR_to_le)
646 ~continuation:(exact ~term:h.hname)) ~status
647 |"eqTRL" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_eqRL_to_le)
648 ~continuation:(exact ~term:h.hname)) ~status
651 debug("Fine TAC_USE");
659 Cic.Appl ( Cic.Const(u,boh)::next) ->
660 (match (UriManager.string_of_uri u) with
661 "cic:/Coq/Reals/Rdefinitions/Rlt.con" -> true
662 |"cic:/Coq/Reals/Rdefinitions/Rgt.con" -> true
663 |"cic:/Coq/Reals/Rdefinitions/Rle.con" -> true
664 |"cic:/Coq/Reals/Rdefinitions/Rge.con" -> true
665 |"cic:/Coq/Init/Logic_Type/eqT.con" ->
666 (match (List.hd next) with
667 Cic.Const (uri,_) when
668 UriManager.string_of_uri uri =
669 "cic:/Coq/Reals/Rdefinitions/R.con" -> true
675 let list_of_sign s = List.map (fun (x,_,z)->(x,z)) s;;
678 Cic.Appl(Array.to_list a)
681 (* Résolution d'inéquations linéaires dans R *)
682 let rec strip_outer_cast c = match c with
683 | Cic.Cast (c,_) -> strip_outer_cast c
687 let find_in_context id context =
688 let rec find_in_context_aux c n =
690 [] -> failwith (id^" not found in context")
691 | a::next -> (match a with
692 Some (Cic.Name(name),_) when name = id -> n
693 (*? magari al posto di _ qualcosaltro?*)
694 | _ -> find_in_context_aux next (n+1))
696 find_in_context_aux context 1
699 (* mi sembra quadratico *)
700 let rec filter_real_hyp context cont =
703 | Some(Cic.Name(h),Cic.Decl(t))::next -> (
704 let n = find_in_context h cont in
705 [(Cic.Rel(n),t)] @ filter_real_hyp next cont)
706 | a::next -> debug(" no\n"); filter_real_hyp next cont
709 (* lifts everithing at the conclusion level *)
710 let rec superlift c n=
713 | Some(name,Cic.Decl(a))::next -> [Some(name,Cic.Decl(CicSubstitution.lift n a))] @ superlift next (n+1)
714 | Some(name,Cic.Def(a))::next -> [Some(name,Cic.Def(CicSubstitution.lift n a))] @ superlift next (n+1)
715 | _::next -> superlift next (n+1) (*?? ??*)
719 (* fix !!!!!!!!!! this may not work *)
720 let equality_replace a b ~status =
721 let proof,goal = status in
722 let curi,metasenv,pbo,pty = proof in
723 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
724 prerr_endline ("<MY_CUT: " ^ CicPp.ppterm a ^ " <=> " ^ CicPp.ppterm b) ;
725 prerr_endline ("### IN MY_CUT: ") ;
726 prerr_endline ("@ " ^ CicPp.ppterm ty) ;
727 List.iter (function Some (n,Cic.Decl t) -> prerr_endline ("# " ^ CicPp.ppterm t)) context ;
728 prerr_endline ("##- IN MY_CUT ") ;
730 let _eqT_ind = Cic.Const( UriManager.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind.con" ) 0 in
731 (*CSC: codice ad-hoc per questo caso!!! Non funge in generale *)
732 PrimitiveTactics.apply_tac ~term:(Cic.Appl [_eqT_ind;_R;b;Cic.Lambda(Cic.Name "pippo",_R,Cic.Appl [_not; Cic.Appl [_Rlt;_R0;Cic.Rel 1]])]) ~status
734 prerr_endline "EUREKA" ;
738 let tcl_fail a ~status:(proof,goal) =
740 1 -> raise (ProofEngineTypes.Fail "fail-tactical")
745 let assumption_tac ~status:(proof,goal)=
746 let curi,metasenv,pbo,pty = proof in
747 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
749 let tac_list = List.map
750 ( fun x -> num := !num + 1;
752 Some(Cic.Name(nm),t) -> (nm,exact ~term:(Cic.Rel(!num)))
753 | _ -> ("fake",tcl_fail 1)
757 Tacticals.try_tactics ~tactics:tac_list ~status:(proof,goal)
760 (* !!!!! fix !!!!!!!!!! *)
761 let contradiction_tac ~status:(proof,goal)=
763 ~start:(PrimitiveTactics.intros_tac ~name:"bo?" )
764 ~continuation:(Tacticals.then_
765 ~start:(Ring.elim_type_tac ~term:_False)
766 ~continuation:(assumption_tac))
770 (* ********************* TATTICA ******************************** *)
772 let rec fourier ~status:(s_proof,s_goal)=
773 let s_curi,s_metasenv,s_pbo,s_pty = s_proof in
774 let s_metano,s_context,s_ty = List.find (function (m,_,_) -> m=s_goal) s_metasenv in
776 debug ("invoco fourier_tac sul goal "^string_of_int(s_goal)^" e contesto :\n");
777 debug_pcontext s_context;
779 let fhyp = String.copy "new_hyp_for_fourier" in
781 (* here we need to negate the thesis, but to do this we nned to apply the right theoreme,
782 so let's parse our thesis *)
784 let th_to_appl = ref _Rfourier_not_le_gt in
786 Cic.Appl ( Cic.Const(u,boh)::args) ->
787 (match UriManager.string_of_uri u with
788 "cic:/Coq/Reals/Rdefinitions/Rlt.con" -> th_to_appl := _Rfourier_not_ge_lt
789 |"cic:/Coq/Reals/Rdefinitions/Rle.con" -> th_to_appl := _Rfourier_not_gt_le
790 |"cic:/Coq/Reals/Rdefinitions/Rgt.con" -> th_to_appl := _Rfourier_not_le_gt
791 |"cic:/Coq/Reals/Rdefinitions/Rge.con" -> th_to_appl := _Rfourier_not_lt_ge
792 |_-> failwith "fourier can't be applyed")
793 |_-> failwith "fourier can't be applyed"); (* fix maybe strip_outer_cast goes here?? *)
795 (* now let's change our thesis applying the th and put it with hp *)
797 let proof,gl = Tacticals.then_
798 ~start:(PrimitiveTactics.apply_tac ~term:!th_to_appl)
799 ~continuation:(PrimitiveTactics.intros_tac ~name:fhyp)
800 ~status:(s_proof,s_goal) in
801 let goal = if List.length gl = 1 then List.hd gl else failwith "a new goal" in
803 debug ("port la tesi sopra e la nego. contesto :\n");
804 debug_pcontext s_context;
806 (* now we have all the right environment *)
808 let curi,metasenv,pbo,pty = proof in
809 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
812 (* now we want to convert hp to inequations, but first we must lift
813 everyting to thesis level, so that a variable has the save Rel(n)
814 in each hp ( needed by ineq1_of_term ) *)
816 (* ? fix if None ?????*)
817 (* fix change superlift with a real name *)
819 let l_context = superlift context 1 in
820 let hyps = filter_real_hyp l_context l_context in
822 debug ("trasformo in diseq. "^ string_of_int (List.length hyps)^" ipotesi\n");
826 (* transform hyps into inequations *)
828 List.iter (fun h -> try (lineq:=(ineq1_of_term h)@(!lineq))
833 debug ("applico fourier a "^ string_of_int (List.length !lineq)^" disequazioni\n");
835 let res=fourier_lineq (!lineq) in
836 let tac=ref Ring.id_tac in
838 (print_string "Tactic Fourier fails.\n";flush stdout;failwith "fourier_tac fails")
841 match res with (*match res*)
844 (* in lc we have the coefficient to "reduce" the system *)
846 print_string "Fourier's method can prove the goal...\n";flush stdout;
848 debug "I coeff di moltiplicazione rit sono: ";
852 (fun (h,c) -> if c<>r0 then (lutil:=(h,c)::(!lutil);
853 (* DBG *)Fourier.print_rational(c);print_string " "(* DBG *))
855 (List.combine (!lineq) lc);
857 print_string (" quindi lutil e' lunga "^string_of_int (List.length (!lutil))^"\n");
859 (* on construit la combinaison linéaire des inéquation *)
861 (match (!lutil) with (*match (!lutil) *)
864 debug ("elem di lutil ");Fourier.print_rational c1;print_string "\n";
866 let s=ref (h1.hstrict) in
868 (* let t1=ref (mkAppL [|parse "Rmult";parse (rational_to_real c1);h1.hleft|]) in
869 let t2=ref (mkAppL [|parse "Rmult";parse (rational_to_real c1);h1.hright|]) in
872 let t1 = ref (Cic.Appl [_Rmult;rational_to_real c1;h1.hleft] ) in
873 let t2 = ref (Cic.Appl [_Rmult;rational_to_real c1;h1.hright]) in
875 List.iter (fun (h,c) ->
876 s:=(!s)||(h.hstrict);
877 t1:=(Cic.Appl [_Rplus;!t1;Cic.Appl [_Rmult;rational_to_real c;h.hleft ] ]);
878 t2:=(Cic.Appl [_Rplus;!t2;Cic.Appl [_Rmult;rational_to_real c;h.hright] ]))
881 let ineq=Cic.Appl [(if (!s) then _Rlt else _Rle);!t1;!t2 ] in
882 let tc=rational_to_real cres in
885 (* ora ho i termini che descrivono i passi di fourier per risolvere il sistema *)
887 debug "inizio a costruire tac1\n";
889 let tac1=ref ( fun ~status ->
890 debug "Sotto tattica t1\n";
892 (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_lt)
893 ~continuations:[tac_use h1;tac_zero_inf_pos (rational_to_fraction c1)] ~status)
895 (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le)
896 ~continuations:[tac_use h1;tac_zero_inf_pos (rational_to_fraction c1)] ~status))
901 List.iter (fun (h,c) ->
905 tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac
906 ~term:_Rfourier_lt_lt)
907 ~continuations:[!tac1;tac_use h;
909 (rational_to_fraction c)]))
913 tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac
914 ~term:_Rfourier_lt_le)
915 ~continuations:[!tac1;tac_use h;
917 (rational_to_fraction c)]))
924 tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_lt)
925 ~continuations:[!tac1;tac_use h;
927 (rational_to_fraction c)]))
931 tac1:=(Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_le)
932 ~continuations:[!tac1;tac_use h;
934 (rational_to_fraction c)]))
938 s:=(!s)||(h.hstrict))
939 lutil;(*end List.iter*)
941 let tac2= if sres then
942 tac_zero_inf_false goal (rational_to_fraction cres)
944 tac_zero_infeq_false goal (rational_to_fraction cres)
946 tac:=(Tacticals.thens ~start:(my_cut ~term:ineq)
947 ~continuations:[Tacticals.then_ (* ?????????????????????????????? *)
948 ~start:(fun ~status:(proof,goal as status) ->
949 let curi,metasenv,pbo,pty = proof in
950 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
951 PrimitiveTactics.change_tac ~what:ty ~with_what:(Cic.Appl [ _not; ineq]) ~status)
952 ~continuation:(Tacticals.then_
953 ~start:(PrimitiveTactics.apply_tac
954 ~term:(if sres then _Rnot_lt_lt else _Rnot_le_le))
955 ~continuation:Ring.id_tac
957 ~continuation:(Tacticals.thens
958 ~start:(equality_replace (Cic.Appl [_Rminus;!t2;!t1] ) tc)
959 ~continuations:[tac2;(Tacticals.thens
960 ~start:(equality_replace (Cic.Appl[_Rinv;_R1]) _R1)
962 (* en attendant Field, ça peut aider Ring de remplacer 1/1 par 1 ... *)
963 [Tacticals.try_tactics
964 (* ???????????????????????????? *)
965 ~tactics:[ "ring", Ring.ring_tac ; "id", Ring.id_tac]
968 ~start:(PrimitiveTactics.apply_tac ~term:_sym_eqT)
969 ~continuation:(PrimitiveTactics.apply_tac ~term:_Rinv_R1)
973 ] (* end continuations before comment *)
978 tac:=(Tacticals.thens ~start:(PrimitiveTactics.cut_tac ~term:_False)
979 ~continuations:[Tacticals.then_
980 (* ???????????????????????????????
982 ~start:(PrimitiveTactics.intros_tac ~name:(String.copy "??"))
983 (* ????????????????????????????? *)
985 ~continuation:contradiction_tac;!tac])
988 |_-> assert false)(*match (!lutil) *)
989 |_-> assert false); (*match res*)
991 debug ("finalmente applico tac\n");
992 (!tac ~status:(proof,goal))
996 let fourier_tac ~status:(proof,goal) = fourier ~status:(proof,goal);;