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.
12 * HELM is distributed in the hope that it will be useful,
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/.
27 (******************** OTHER USEFUL TACTICS **********************)
29 let rewrite_tac ~term:equality ~status:(proof,goal) =
31 let module U = UriManager in
32 let curi,metasenv,pbo,pty = proof in
33 let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
34 let eq_ind_r,ty,t1,t2 =
35 match CicTypeChecker.type_of_aux' metasenv context equality with
36 C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
37 when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
40 (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind_r.con",[])
43 | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
44 when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
47 (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind_r.con",[])
52 (ProofEngineTypes.Fail
53 "Rewrite: the argument is not a proof of an equality")
56 let gty' = CicSubstitution.lift 1 gty in
57 let t1' = CicSubstitution.lift 1 t1 in
59 ProofEngineReduction.replace_lifting
60 ~equality:ProofEngineReduction.alpha_equivalence
61 ~what:t1' ~with_what:(C.Rel 1) ~where:gty'
63 C.Lambda (C.Name "dummy_for_rewrite", ty, gty'')
65 prerr_endline ("#### Sintetizzato: " ^ CicPp.ppterm pred);
66 let fresh_meta = ProofEngineHelpers.new_meta proof in
68 ProofEngineHelpers.identity_relocation_list_for_metavariable context in
69 let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in
72 PrimitiveTactics.exact_tac
74 [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
75 ~status:((curi,metasenv',pbo,pty),goal)
77 assert (List.length goals = 0) ;
82 let rewrite_simpl_tac ~term ~status =
83 Tacticals.then_ ~start:(rewrite_tac ~term)
85 (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~term:None)
89 (******************** THE FOURIER TACTIC ***********************)
91 (* La tactique Fourier ne fonctionne de manière sûre que si les coefficients
92 des inéquations et équations sont entiers. En attendant la tactique Field.
98 let debug x = print_string ("____ "^x) ; flush stdout;;
100 let debug_pcontext x =
102 List.iter (fun y -> match y with Some(Cic.Name(a),_) -> str := !str ^
103 a ^ " " | _ ->()) x ;
104 debug ("contesto : "^ (!str) ^ "\n")
107 (******************************************************************************
108 Operations on linear combinations.
110 Opérations sur les combinaisons linéaires affines.
111 La partie homogène d'une combinaison linéaire est en fait une table de hash
112 qui donne le coefficient d'un terme du calcul des constructions,
113 qui est zéro si le terme n'y est pas.
119 The type for linear combinations
121 type flin = {fhom:(Cic.term , rational)Hashtbl.t;fcste:rational}
125 @return an empty flin
127 let flin_zero () = {fhom = Hashtbl.create 50;fcste=r0}
133 @return the rational associated with x (coefficient)
137 (Hashtbl.find f.fhom x)
143 Adds c to the coefficient of x
150 let cx = flin_coef f x in
151 Hashtbl.remove f.fhom x;
152 Hashtbl.add f.fhom x (rplus cx c);
161 let flin_add_cste f c =
163 fcste=rplus f.fcste c}
167 @return a empty flin with r1 in fcste
169 let flin_one () = flin_add_cste (flin_zero()) r1;;
174 let flin_plus f1 f2 =
175 let f3 = flin_zero() in
176 Hashtbl.iter (fun x c -> let _=flin_add f3 x c in ()) f1.fhom;
177 Hashtbl.iter (fun x c -> let _=flin_add f3 x c in ()) f2.fhom;
178 flin_add_cste (flin_add_cste f3 f1.fcste) f2.fcste;
184 let flin_minus f1 f2 =
185 let f3 = flin_zero() in
186 Hashtbl.iter (fun x c -> let _=flin_add f3 x c in ()) f1.fhom;
187 Hashtbl.iter (fun x c -> let _=flin_add f3 x (rop c) in ()) f2.fhom;
188 flin_add_cste (flin_add_cste f3 f1.fcste) (rop f2.fcste);
195 let f2 = flin_zero() in
196 Hashtbl.iter (fun x c -> let _=flin_add f2 x (rmult a c) in ()) f.fhom;
197 flin_add_cste f2 (rmult a f.fcste);
201 (*****************************************************************************)
206 @raise Failure if conversion is impossible
207 @return rational proiection of t
209 let rec rational_of_term t =
210 (* fun to apply f to the first and second rational-term of l *)
211 let rat_of_binop f l =
212 let a = List.hd l and
213 b = List.hd(List.tl l) in
214 f (rational_of_term a) (rational_of_term b)
216 (* as before, but f is unary *)
217 let rat_of_unop f l =
218 f (rational_of_term (List.hd l))
221 | Cic.Cast (t1,t2) -> (rational_of_term t1)
222 | Cic.Appl (t1::next) ->
225 (match (UriManager.string_of_uri u) with
226 "cic:/Coq/Reals/Rdefinitions/Ropp.con" ->
228 |"cic:/Coq/Reals/Rdefinitions/Rinv.con" ->
229 rat_of_unop rinv next
230 |"cic:/Coq/Reals/Rdefinitions/Rmult.con" ->
231 rat_of_binop rmult next
232 |"cic:/Coq/Reals/Rdefinitions/Rdiv.con" ->
233 rat_of_binop rdiv next
234 |"cic:/Coq/Reals/Rdefinitions/Rplus.con" ->
235 rat_of_binop rplus next
236 |"cic:/Coq/Reals/Rdefinitions/Rminus.con" ->
237 rat_of_binop rminus next
238 | _ -> failwith "not a rational")
239 | _ -> failwith "not a rational")
240 | Cic.Const (u,boh) ->
241 (match (UriManager.string_of_uri u) with
242 "cic:/Coq/Reals/Rdefinitions/R1.con" -> r1
243 |"cic:/Coq/Reals/Rdefinitions/R0.con" -> r0
244 | _ -> failwith "not a rational")
245 | _ -> failwith "not a rational"
249 let rational_of_const = rational_of_term;;
253 let rec flin_of_term t =
254 let fl_of_binop f l =
255 let a = List.hd l and
256 b = List.hd(List.tl l) in
257 f (flin_of_term a) (flin_of_term b)
261 | Cic.Cast (t1,t2) -> (flin_of_term t1)
262 | Cic.Appl (t1::next) ->
267 match (UriManager.string_of_uri u) with
268 "cic:/Coq/Reals/Rdefinitions/Ropp.con" ->
269 flin_emult (rop r1) (flin_of_term (List.hd next))
270 |"cic:/Coq/Reals/Rdefinitions/Rplus.con"->
271 fl_of_binop flin_plus next
272 |"cic:/Coq/Reals/Rdefinitions/Rminus.con"->
273 fl_of_binop flin_minus next
274 |"cic:/Coq/Reals/Rdefinitions/Rmult.con"->
276 let arg1 = (List.hd next) and
277 arg2 = (List.hd(List.tl next))
281 let a = rational_of_term arg1 in
284 let b = (rational_of_term arg2) in
285 (flin_add_cste (flin_zero()) (rmult a b))
288 _ -> (flin_add (flin_zero()) arg2 a)
291 _-> (flin_add(flin_zero()) arg1 (rational_of_term arg2))
293 |"cic:/Coq/Reals/Rdefinitions/Rinv.con"->
294 let a=(rational_of_term (List.hd next)) in
295 flin_add_cste (flin_zero()) (rinv a)
296 |"cic:/Coq/Reals/Rdefinitions/Rdiv.con"->
298 let b=(rational_of_term (List.hd(List.tl next))) in
301 let a = (rational_of_term (List.hd next)) in
302 (flin_add_cste (flin_zero()) (rdiv a b))
305 _-> (flin_add (flin_zero()) (List.hd next) (rinv b))
311 | Cic.Const (u,boh) ->
313 match (UriManager.string_of_uri u) with
314 "cic:/Coq/Reals/Rdefinitions/R1.con" -> flin_one ()
315 |"cic:/Coq/Reals/Rdefinitions/R0.con" -> flin_zero ()
319 with _ -> flin_add (flin_zero()) t r1
323 let flin_of_constr = flin_of_term;;
327 Translates a flin to (c,x) list
329 @return something like (c1,x1)::(c2,x2)::...::(cn,xn)
331 let flin_to_alist f =
333 Hashtbl.iter (fun x c -> res:=(c,x)::(!res)) f;
337 (* Représentation des hypothèses qui sont des inéquations ou des équations.
341 The structure for ineq
343 type hineq={hname:Cic.term; (* le nom de l'hypothèse *)
344 htype:string; (* Rlt, Rgt, Rle, Rge, eqTLR ou eqTRL *)
351 (* Transforme une hypothese h:t en inéquation flin<0 ou flin<=0
354 let ineq1_of_term (h,t) =
355 match t with (* match t *)
356 Cic.Appl (t1::next) ->
357 let arg1= List.hd next in
358 let arg2= List.hd(List.tl next) in
359 (match t1 with (* match t1 *)
361 (match UriManager.string_of_uri u with (* match u *)
362 "cic:/Coq/Reals/Rdefinitions/Rlt.con" ->
367 hflin= flin_minus (flin_of_term arg1)
370 |"cic:/Coq/Reals/Rdefinitions/Rgt.con" ->
375 hflin= flin_minus (flin_of_term arg2)
378 |"cic:/Coq/Reals/Rdefinitions/Rle.con" ->
383 hflin= flin_minus (flin_of_term arg1)
386 |"cic:/Coq/Reals/Rdefinitions/Rge.con" ->
391 hflin= flin_minus (flin_of_term arg2)
394 |_->assert false)(* match u *)
395 | Cic.MutInd (u,i,o) ->
396 (match UriManager.string_of_uri u with
397 "cic:/Coq/Init/Logic_Type/eqT.con" ->
400 let arg2= List.hd(List.tl (List.tl next)) in
403 (match UriManager.string_of_uri u with
404 "cic:/Coq/Reals/Rdefinitions/R.con"->
409 hflin= flin_minus (flin_of_term arg1)
416 hflin= flin_minus (flin_of_term arg2)
422 |_-> assert false)(* match t1 *)
423 |_-> assert false (* match t *)
426 let ineq1_of_constr = ineq1_of_term;;
429 (* Applique la méthode de Fourier à une liste d'hypothèses (type hineq)
435 | a::next -> Fourier.print_rational a ; print_string " " ; print_rl next
438 let rec print_sys l =
441 | (a,b)::next -> (print_rl a;
442 print_string (if b=true then "strict\n"else"\n");
447 Hashtbl.iter (fun x y -> print_string ("("^"-"^","^"-"^")")) h
450 let fourier_lineq lineq1 =
452 let hvar=Hashtbl.create 50 in (* la table des variables des inéquations *)
454 Hashtbl.iter (fun x c ->
455 try (Hashtbl.find hvar x;())
456 with _-> nvar:=(!nvar)+1;
457 Hashtbl.add hvar x (!nvar))
461 debug("Il numero di incognite e' "^string_of_int (!nvar+1)^"\n");
462 let sys= List.map (fun h->
463 let v=Array.create ((!nvar)+1) r0 in
464 Hashtbl.iter (fun x c -> v.(Hashtbl.find hvar x)<-c)
466 ((Array.to_list v)@[rop h.hflin.fcste],h.hstrict))
468 debug ("chiamo unsolvable sul sistema di "^
469 string_of_int (List.length sys) ^"\n");
474 (*****************************************************************************
475 Construction de la preuve en cas de succès de la méthode de Fourier,
476 i.e. on obtient une contradiction.
480 let _eqT = Cic.MutInd(UriManager.uri_of_string
481 "cic:/Coq/Init/Logic_Type/eqT.ind") 0 [] ;;
482 let _False = Cic.MutInd (UriManager.uri_of_string
483 "cic:/Coq/Init/Logic/False.ind") 0 [] ;;
484 let _not = Cic.Const (UriManager.uri_of_string
485 "cic:/Coq/Init/Logic/not.con") [];;
486 let _R0 = Cic.Const (UriManager.uri_of_string
487 "cic:/Coq/Reals/Rdefinitions/R0.con") [] ;;
488 let _R1 = Cic.Const (UriManager.uri_of_string
489 "cic:/Coq/Reals/Rdefinitions/R1.con") [] ;;
490 let _R = Cic.Const (UriManager.uri_of_string
491 "cic:/Coq/Reals/Rdefinitions/R.con") [] ;;
492 let _Rfourier_eqLR_to_le=Cic.Const (UriManager.uri_of_string
493 "cic:/Coq/fourier/Fourier_util/Rfourier_eqLR_to_le.con") [] ;;
494 let _Rfourier_eqRL_to_le=Cic.Const (UriManager.uri_of_string
495 "cic:/Coq/fourier/Fourier_util/Rfourier_eqRL_to_le.con") [] ;;
496 let _Rfourier_ge_to_le =Cic.Const (UriManager.uri_of_string
497 "cic:/Coq/fourier/Fourier_util/Rfourier_ge_to_le.con") [] ;;
498 let _Rfourier_gt_to_lt =Cic.Const (UriManager.uri_of_string
499 "cic:/Coq/fourier/Fourier_util/Rfourier_gt_to_lt.con") [] ;;
500 let _Rfourier_le=Cic.Const (UriManager.uri_of_string
501 "cic:/Coq/fourier/Fourier_util/Rfourier_le.con") [] ;;
502 let _Rfourier_le_le =Cic.Const (UriManager.uri_of_string
503 "cic:/Coq/fourier/Fourier_util/Rfourier_le_le.con") [] ;;
504 let _Rfourier_le_lt =Cic.Const (UriManager.uri_of_string
505 "cic:/Coq/fourier/Fourier_util/Rfourier_le_lt.con") [] ;;
506 let _Rfourier_lt=Cic.Const (UriManager.uri_of_string
507 "cic:/Coq/fourier/Fourier_util/Rfourier_lt.con") [] ;;
508 let _Rfourier_lt_le =Cic.Const (UriManager.uri_of_string
509 "cic:/Coq/fourier/Fourier_util/Rfourier_lt_le.con") [] ;;
510 let _Rfourier_lt_lt =Cic.Const (UriManager.uri_of_string
511 "cic:/Coq/fourier/Fourier_util/Rfourier_lt_lt.con") [] ;;
512 let _Rfourier_not_ge_lt = Cic.Const (UriManager.uri_of_string
513 "cic:/Coq/fourier/Fourier_util/Rfourier_not_ge_lt.con") [] ;;
514 let _Rfourier_not_gt_le = Cic.Const (UriManager.uri_of_string
515 "cic:/Coq/fourier/Fourier_util/Rfourier_not_gt_le.con") [] ;;
516 let _Rfourier_not_le_gt = Cic.Const (UriManager.uri_of_string
517 "cic:/Coq/fourier/Fourier_util/Rfourier_not_le_gt.con") [] ;;
518 let _Rfourier_not_lt_ge = Cic.Const (UriManager.uri_of_string
519 "cic:/Coq/fourier/Fourier_util/Rfourier_not_lt_ge.con") [] ;;
520 let _Rinv = Cic.Const (UriManager.uri_of_string
521 "cic:/Coq/Reals/Rdefinitions/Rinv.con") [] ;;
522 let _Rinv_R1 = Cic.Const(UriManager.uri_of_string
523 "cic:/Coq/Reals/Rbase/Rinv_R1.con" ) [] ;;
524 let _Rle = Cic.Const (UriManager.uri_of_string
525 "cic:/Coq/Reals/Rdefinitions/Rle.con") [] ;;
526 let _Rle_mult_inv_pos = Cic.Const (UriManager.uri_of_string
527 "cic:/Coq/fourier/Fourier_util/Rle_mult_inv_pos.con") [] ;;
528 let _Rle_not_lt = Cic.Const (UriManager.uri_of_string
529 "cic:/Coq/fourier/Fourier_util/Rle_not_lt.con") [] ;;
530 let _Rle_zero_1 = Cic.Const (UriManager.uri_of_string
531 "cic:/Coq/fourier/Fourier_util/Rle_zero_1.con") [] ;;
532 let _Rle_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string
533 "cic:/Coq/fourier/Fourier_util/Rle_zero_pos_plus1.con") [] ;;
534 let _Rle_zero_zero = Cic.Const (UriManager.uri_of_string
535 "cic:/Coq/fourier/Fourier_util/Rle_zero_zero.con") [] ;;
536 let _Rlt = Cic.Const (UriManager.uri_of_string
537 "cic:/Coq/Reals/Rdefinitions/Rlt.con") [] ;;
538 let _Rlt_mult_inv_pos = Cic.Const (UriManager.uri_of_string
539 "cic:/Coq/fourier/Fourier_util/Rlt_mult_inv_pos.con") [] ;;
540 let _Rlt_not_le = Cic.Const (UriManager.uri_of_string
541 "cic:/Coq/fourier/Fourier_util/Rlt_not_le.con") [] ;;
542 let _Rlt_zero_1 = Cic.Const (UriManager.uri_of_string
543 "cic:/Coq/fourier/Fourier_util/Rlt_zero_1.con") [] ;;
544 let _Rlt_zero_pos_plus1 = Cic.Const (UriManager.uri_of_string
545 "cic:/Coq/fourier/Fourier_util/Rlt_zero_pos_plus1.con") [] ;;
546 let _Rminus = Cic.Const (UriManager.uri_of_string
547 "cic:/Coq/Reals/Rdefinitions/Rminus.con") [] ;;
548 let _Rmult = Cic.Const (UriManager.uri_of_string
549 "cic:/Coq/Reals/Rdefinitions/Rmult.con") [] ;;
550 let _Rnot_le_le =Cic.Const (UriManager.uri_of_string
551 "cic:/Coq/fourier/Fourier_util/Rnot_le_le.con") [] ;;
552 let _Rnot_lt0 = Cic.Const (UriManager.uri_of_string
553 "cic:/Coq/fourier/Fourier_util/Rnot_lt0.con") [] ;;
554 let _Rnot_lt_lt =Cic.Const (UriManager.uri_of_string
555 "cic:/Coq/fourier/Fourier_util/Rnot_lt_lt.con") [] ;;
556 let _Ropp = Cic.Const (UriManager.uri_of_string
557 "cic:/Coq/Reals/Rdefinitions/Ropp.con") [] ;;
558 let _Rplus = Cic.Const (UriManager.uri_of_string
559 "cic:/Coq/Reals/Rdefinitions/Rplus.con") [] ;;
561 (******************************************************************************)
563 let is_int x = (x.den)=1
566 (* fraction = couple (num,den) *)
567 let rec rational_to_fraction x= (x.num,x.den)
570 (* traduction -3 -> (Ropp (Rplus R1 (Rplus R1 R1)))
573 let rec int_to_real_aux n =
575 0 -> _R0 (* o forse R0 + R0 ????? *)
577 | _ -> Cic.Appl [ _Rplus ; _R1 ; int_to_real_aux (n-1) ]
582 let x = int_to_real_aux (abs n) in
584 Cic.Appl [ _Ropp ; x ]
590 (* -1/2 -> (Rmult (Ropp R1) (Rinv (Rplus R1 R1)))
593 let rational_to_real x =
594 let (n,d)=rational_to_fraction x in
595 Cic.Appl [ _Rmult ; int_to_real n ; Cic.Appl [ _Rinv ; int_to_real d ] ]
598 (* preuve que 0<n*1/d
601 let tac_zero_inf_pos (n,d) ~status =
602 (*let cste = pf_parse_constr gl in*)
603 let pall str ~status:(proof,goal) t =
604 debug ("tac "^str^" :\n" );
605 let curi,metasenv,pbo,pty = proof in
606 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
607 debug ("th = "^ CicPp.ppterm t ^"\n");
608 debug ("ty = "^ CicPp.ppterm ty^"\n");
611 (fun ~status -> pall "n0" ~status _Rlt_zero_1 ;
612 PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ~status ) in
614 (fun ~status -> pall "d0" ~status _Rlt_zero_1 ;
615 PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ~status ) in
619 tacn:=(Tacticals.then_ ~start:(fun ~status -> pall ("n"^string_of_int i)
620 ~status _Rlt_zero_pos_plus1;
621 PrimitiveTactics.apply_tac ~term:_Rlt_zero_pos_plus1 ~status)
622 ~continuation:!tacn);
625 tacd:=(Tacticals.then_ ~start:(fun ~status -> pall "d"
626 ~status _Rlt_zero_pos_plus1 ;PrimitiveTactics.apply_tac
627 ~term:_Rlt_zero_pos_plus1 ~status) ~continuation:!tacd);
632 debug("TAC ZERO INF POS\n");
634 (Tacticals.thens ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_mult_inv_pos)
643 (* preuve que 0<=n*1/d
646 let tac_zero_infeq_pos gl (n,d) ~status =
647 (*let cste = pf_parse_constr gl in*)
648 debug("inizio tac_zero_infeq_pos\n");
651 (PrimitiveTactics.apply_tac ~term:_Rle_zero_zero )
653 (PrimitiveTactics.apply_tac ~term:_Rle_zero_1 )
656 let tacd=ref (PrimitiveTactics.apply_tac ~term:_Rlt_zero_1 ) in
658 tacn:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
659 ~term:_Rle_zero_pos_plus1) ~continuation:!tacn);
662 tacd:=(Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
663 ~term:_Rlt_zero_pos_plus1) ~continuation:!tacd);
666 (Tacticals.thens ~start:(PrimitiveTactics.apply_tac
667 ~term:_Rle_mult_inv_pos) ~continuations:[!tacn;!tacd]) ~status in
668 debug("fine tac_zero_infeq_pos\n");
674 (* preuve que 0<(-n)*(1/d) => False
677 let tac_zero_inf_false gl (n,d) ~status=
678 debug("inizio tac_zero_inf_false\n");
680 (debug "1\n";let r =(PrimitiveTactics.apply_tac ~term:_Rnot_lt0 ~status) in
684 (debug "2\n";let r = (Tacticals.then_ ~start:(
685 fun ~status:(proof,goal as status) ->
686 let curi,metasenv,pbo,pty = proof in
687 let metano,context,ty =List.find (function (m,_,_) -> m=goal) metasenv in
688 debug("!!!!!!!!!1: unify "^CicPp.ppterm _Rle_not_lt^" with "
689 ^ CicPp.ppterm ty ^"\n");
690 let r = PrimitiveTactics.apply_tac ~term:_Rle_not_lt ~status in
691 debug("!!!!!!!!!2\n");
694 ~continuation:(tac_zero_infeq_pos gl (-n,d))) ~status in
700 (* preuve que 0<=n*(1/d) => False ; n est negatif
703 let tac_zero_infeq_false gl (n,d) ~status:(proof,goal as status)=
704 debug("stat tac_zero_infeq_false\n");
706 let curi,metasenv,pbo,pty = proof in
707 let metano,context,ty =List.find (function (m,_,_) -> m=goal) metasenv in
709 debug("faccio fold di " ^ CicPp.ppterm
713 [_Rmult ; int_to_real n ; Cic.Appl [_Rinv ; int_to_real d]]
716 debug("apply di _Rlt_not_le a "^ CicPp.ppterm ty ^"\n");
717 (*CSC: Patch to undo the over-simplification of RewriteSimpl *)
720 (ReductionTactics.fold_tac ~also_in_hypotheses:false
725 [_Rmult ; int_to_real n ; Cic.Appl [_Rinv ; int_to_real d]]
730 (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac ~term:_Rlt_not_le)
731 ~continuation:(tac_zero_inf_pos (-n,d))) ~status in
732 debug("end tac_zero_infeq_false\n");
735 Tacticals.id_tac ~status
740 (* *********** ********** ******** ??????????????? *********** **************)
742 let apply_type_tac ~cast:t ~applist:al ~status:(proof,goal) =
743 let curi,metasenv,pbo,pty = proof in
744 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
745 let fresh_meta = ProofEngineHelpers.new_meta proof in
747 ProofEngineHelpers.identity_relocation_list_for_metavariable context in
748 let metasenv' = (fresh_meta,context,t)::metasenv in
749 let proof' = curi,metasenv',pbo,pty in
751 PrimitiveTactics.apply_tac ~term:(Cic.Appl ((Cic.Cast (Cic.Meta
752 (fresh_meta,irl),t))::al)) ~status:(proof',goal)
754 proof'',fresh_meta::goals
761 let my_cut ~term:c ~status:(proof,goal)=
762 let curi,metasenv,pbo,pty = proof in
763 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
765 let fresh_meta = ProofEngineHelpers.new_meta proof in
767 ProofEngineHelpers.identity_relocation_list_for_metavariable context in
768 let metasenv' = (fresh_meta,context,c)::metasenv in
769 let proof' = curi,metasenv',pbo,pty in
771 apply_type_tac ~cast:(Cic.Prod(Cic.Name "Anonymous",c,
772 CicSubstitution.lift 1 ty)) ~applist:[Cic.Meta(fresh_meta,irl)]
773 ~status:(proof',goal)
775 (* We permute the generated goals to be consistent with Coq *)
778 | he::tl -> proof'',he::fresh_meta::tl
782 let exact = PrimitiveTactics.exact_tac;;
784 let tac_use h ~status:(proof,goal as status) =
785 debug("Inizio TC_USE\n");
786 let curi,metasenv,pbo,pty = proof in
787 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
788 debug ("hname = "^ CicPp.ppterm h.hname ^"\n");
789 debug ("ty = "^ CicPp.ppterm ty^"\n");
793 "Rlt" -> exact ~term:h.hname ~status
794 |"Rle" -> exact ~term:h.hname ~status
795 |"Rgt" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
796 ~term:_Rfourier_gt_to_lt)
797 ~continuation:(exact ~term:h.hname)) ~status
798 |"Rge" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
799 ~term:_Rfourier_ge_to_le)
800 ~continuation:(exact ~term:h.hname)) ~status
801 |"eqTLR" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
802 ~term:_Rfourier_eqLR_to_le)
803 ~continuation:(exact ~term:h.hname)) ~status
804 |"eqTRL" -> (Tacticals.then_ ~start:(PrimitiveTactics.apply_tac
805 ~term:_Rfourier_eqRL_to_le)
806 ~continuation:(exact ~term:h.hname)) ~status
809 debug("Fine TAC_USE\n");
817 Cic.Appl ( Cic.Const(u,boh)::next) ->
818 (match (UriManager.string_of_uri u) with
819 "cic:/Coq/Reals/Rdefinitions/Rlt.con" -> true
820 |"cic:/Coq/Reals/Rdefinitions/Rgt.con" -> true
821 |"cic:/Coq/Reals/Rdefinitions/Rle.con" -> true
822 |"cic:/Coq/Reals/Rdefinitions/Rge.con" -> true
823 |"cic:/Coq/Init/Logic_Type/eqT.con" ->
824 (match (List.hd next) with
825 Cic.Const (uri,_) when
826 UriManager.string_of_uri uri =
827 "cic:/Coq/Reals/Rdefinitions/R.con" -> true
833 let list_of_sign s = List.map (fun (x,_,z)->(x,z)) s;;
836 Cic.Appl(Array.to_list a)
839 (* Résolution d'inéquations linéaires dans R *)
840 let rec strip_outer_cast c = match c with
841 | Cic.Cast (c,_) -> strip_outer_cast c
845 let find_in_context id context =
846 let rec find_in_context_aux c n =
848 [] -> failwith (id^" not found in context")
849 | a::next -> (match a with
850 Some (Cic.Name(name),_) when name = id -> n
851 (*? magari al posto di _ qualcosaltro?*)
852 | _ -> find_in_context_aux next (n+1))
854 find_in_context_aux context 1
857 (* mi sembra quadratico *)
858 let rec filter_real_hyp context cont =
861 | Some(Cic.Name(h),Cic.Decl(t))::next -> (
862 let n = find_in_context h cont in
863 [(Cic.Rel(n),t)] @ filter_real_hyp next cont)
864 | a::next -> debug(" no\n"); filter_real_hyp next cont
867 (* lifts everithing at the conclusion level *)
868 let rec superlift c n=
871 | Some(name,Cic.Decl(a))::next -> [Some(name,Cic.Decl(
872 CicSubstitution.lift n a))] @ superlift next (n+1)
873 | Some(name,Cic.Def(a))::next -> [Some(name,Cic.Def(
874 CicSubstitution.lift n a))] @ superlift next (n+1)
875 | _::next -> superlift next (n+1) (*?? ??*)
879 let equality_replace a b ~status =
880 debug("inizio EQ\n");
881 let module C = Cic in
882 let proof,goal = status in
883 let curi,metasenv,pbo,pty = proof in
884 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
885 let a_eq_b = C.Appl [ _eqT ; _R ; a ; b ] in
886 let fresh_meta = ProofEngineHelpers.new_meta proof in
888 ProofEngineHelpers.identity_relocation_list_for_metavariable context in
889 let metasenv' = (fresh_meta,context,a_eq_b)::metasenv in
890 debug("chamo rewrite tac su"^CicPp.ppterm (C.Meta (fresh_meta,irl)));
892 rewrite_simpl_tac ~term:(C.Meta (fresh_meta,irl))
893 ~status:((curi,metasenv',pbo,pty),goal)
895 let new_goals = fresh_meta::goals in
896 debug("fine EQ -> goals : "^string_of_int( List.length new_goals) ^" = "
897 ^string_of_int( List.length goals)^"+ meta\n");
901 let tcl_fail a ~status:(proof,goal) =
903 1 -> raise (ProofEngineTypes.Fail "fail-tactical")
908 let assumption_tac ~status:(proof,goal)=
909 let curi,metasenv,pbo,pty = proof in
910 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
912 let tac_list = List.map
913 ( fun x -> num := !num + 1;
915 Some(Cic.Name(nm),t) -> (nm,exact ~term:(Cic.Rel(!num)))
916 | _ -> ("fake",tcl_fail 1)
920 Tacticals.try_tactics ~tactics:tac_list ~status:(proof,goal)
923 (* !!!!! fix !!!!!!!!!! *)
924 let contradiction_tac ~status:(proof,goal)=
926 ~start:(PrimitiveTactics.intros_tac ~name:"bo?" )
927 ~continuation:(Tacticals.then_
928 ~start:(Ring.elim_type_tac ~term:_False)
929 ~continuation:(assumption_tac))
933 (* ********************* TATTICA ******************************** *)
935 let rec fourier ~status:(s_proof,s_goal)=
936 let s_curi,s_metasenv,s_pbo,s_pty = s_proof in
937 let s_metano,s_context,s_ty = List.find (function (m,_,_) -> m=s_goal)
940 debug ("invoco fourier_tac sul goal "^string_of_int(s_goal)^" e contesto :\n");
941 debug_pcontext s_context;
943 let fhyp = String.copy "new_hyp_for_fourier" in
945 (* here we need to negate the thesis, but to do this we need to apply the right
946 theoreme,so let's parse our thesis *)
948 let th_to_appl = ref _Rfourier_not_le_gt in
950 Cic.Appl ( Cic.Const(u,boh)::args) ->
951 (match UriManager.string_of_uri u with
952 "cic:/Coq/Reals/Rdefinitions/Rlt.con" -> th_to_appl :=
954 |"cic:/Coq/Reals/Rdefinitions/Rle.con" -> th_to_appl :=
956 |"cic:/Coq/Reals/Rdefinitions/Rgt.con" -> th_to_appl :=
958 |"cic:/Coq/Reals/Rdefinitions/Rge.con" -> th_to_appl :=
960 |_-> failwith "fourier can't be applyed")
961 |_-> failwith "fourier can't be applyed");
962 (* fix maybe strip_outer_cast goes here?? *)
964 (* now let's change our thesis applying the th and put it with hp *)
966 let proof,gl = Tacticals.then_
967 ~start:(PrimitiveTactics.apply_tac ~term:!th_to_appl)
968 ~continuation:(PrimitiveTactics.intros_tac ~name:fhyp)
969 ~status:(s_proof,s_goal) in
970 let goal = if List.length gl = 1 then List.hd gl
971 else failwith "a new goal" in
973 debug ("port la tesi sopra e la nego. contesto :\n");
974 debug_pcontext s_context;
976 (* now we have all the right environment *)
978 let curi,metasenv,pbo,pty = proof in
979 let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
982 (* now we want to convert hp to inequations, but first we must lift
983 everyting to thesis level, so that a variable has the save Rel(n)
984 in each hp ( needed by ineq1_of_term ) *)
986 (* ? fix if None ?????*)
987 (* fix change superlift with a real name *)
989 let l_context = superlift context 1 in
990 let hyps = filter_real_hyp l_context l_context in
992 debug ("trasformo in diseq. "^ string_of_int (List.length hyps)^" ipotesi\n");
996 (* transform hyps into inequations *)
998 List.iter (fun h -> try (lineq:=(ineq1_of_term h)@(!lineq))
1003 debug ("applico fourier a "^ string_of_int (List.length !lineq)^
1006 let res=fourier_lineq (!lineq) in
1007 let tac=ref Tacticals.id_tac in
1009 (print_string "Tactic Fourier fails.\n";flush stdout;
1010 failwith "fourier_tac fails")
1013 match res with (*match res*)
1016 (* in lc we have the coefficient to "reduce" the system *)
1018 print_string "Fourier's method can prove the goal...\n";flush stdout;
1020 debug "I coeff di moltiplicazione rit sono: ";
1024 (fun (h,c) -> if c<>r0 then (lutil:=(h,c)::(!lutil);
1025 (* DBG *)Fourier.print_rational(c);print_string " "(* DBG *))
1027 (List.combine (!lineq) lc);
1029 print_string (" quindi lutil e' lunga "^
1030 string_of_int (List.length (!lutil))^"\n");
1032 (* on construit la combinaison linéaire des inéquation *)
1034 (match (!lutil) with (*match (!lutil) *)
1036 debug ("elem di lutil ");Fourier.print_rational c1;print_string "\n";
1038 let s=ref (h1.hstrict) in
1041 let t1 = ref (Cic.Appl [_Rmult;rational_to_real c1;h1.hleft] ) in
1042 let t2 = ref (Cic.Appl [_Rmult;rational_to_real c1;h1.hright]) in
1044 List.iter (fun (h,c) ->
1045 s:=(!s)||(h.hstrict);
1046 t1:=(Cic.Appl [_Rplus;!t1;Cic.Appl
1047 [_Rmult;rational_to_real c;h.hleft ] ]);
1048 t2:=(Cic.Appl [_Rplus;!t2;Cic.Appl
1049 [_Rmult;rational_to_real c;h.hright] ]))
1052 let ineq=Cic.Appl [(if (!s) then _Rlt else _Rle);!t1;!t2 ] in
1053 let tc=rational_to_real cres in
1056 (* ora ho i termini che descrivono i passi di fourier per risolvere il sistema *)
1058 debug "inizio a costruire tac1\n";
1059 Fourier.print_rational(c1);
1061 let tac1=ref ( fun ~status ->
1066 debug ("inizio t1 strict\n");
1067 let curi,metasenv,pbo,pty = proof in
1068 let metano,context,ty = List.find
1069 (function (m,_,_) -> m=goal) metasenv in
1070 debug ("th = "^ CicPp.ppterm _Rfourier_lt ^"\n");
1071 debug ("ty = "^ CicPp.ppterm ty^"\n");
1072 PrimitiveTactics.apply_tac ~term:_Rfourier_lt ~status)
1073 ~continuations:[tac_use h1;tac_zero_inf_pos
1074 (rational_to_fraction c1)]
1079 ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le)
1080 ~continuations:[tac_use h1;tac_zero_inf_pos
1081 (rational_to_fraction c1)] ~status
1087 List.iter (fun (h,c) ->
1091 tac1:=(Tacticals.thens
1092 ~start:(PrimitiveTactics.apply_tac
1093 ~term:_Rfourier_lt_lt)
1094 ~continuations:[!tac1;tac_use h;tac_zero_inf_pos
1095 (rational_to_fraction c)])
1099 Fourier.print_rational(c1);
1100 tac1:=(Tacticals.thens
1103 debug("INIZIO TAC 1 2\n");
1104 let curi,metasenv,pbo,pty = proof in
1105 let metano,context,ty = List.find (function (m,_,_) -> m=goal)
1107 debug ("th = "^ CicPp.ppterm _Rfourier_lt_le ^"\n");
1108 debug ("ty = "^ CicPp.ppterm ty^"\n");
1109 PrimitiveTactics.apply_tac ~term:_Rfourier_lt_le ~status)
1110 ~continuations:[!tac1;tac_use h;tac_zero_inf_pos
1111 (rational_to_fraction c)])
1117 tac1:=(Tacticals.thens
1118 ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_lt)
1119 ~continuations:[!tac1;tac_use h;tac_zero_inf_pos
1120 (rational_to_fraction c)])
1124 tac1:=(Tacticals.thens
1125 ~start:(PrimitiveTactics.apply_tac ~term:_Rfourier_le_le)
1126 ~continuations:[!tac1;tac_use h;tac_zero_inf_pos
1127 (rational_to_fraction c)])
1131 s:=(!s)||(h.hstrict)) lutil;(*end List.iter*)
1135 tac_zero_inf_false goal (rational_to_fraction cres)
1137 tac_zero_infeq_false goal (rational_to_fraction cres)
1139 tac:=(Tacticals.thens
1140 ~start:(my_cut ~term:ineq)
1141 ~continuations:[Tacticals.then_
1142 ~start:(fun ~status:(proof,goal as status) ->
1143 let curi,metasenv,pbo,pty = proof in
1144 let metano,context,ty = List.find (function (m,_,_) -> m=goal)
1146 PrimitiveTactics.change_tac ~what:ty
1147 ~with_what:(Cic.Appl [ _not; ineq]) ~status)
1148 ~continuation:(Tacticals.then_
1149 ~start:(PrimitiveTactics.apply_tac ~term:
1150 (if sres then _Rnot_lt_lt else _Rnot_le_le))
1151 ~continuation:(Tacticals.thens
1154 let r = equality_replace (Cic.Appl [_Rminus;!t2;!t1] ) tc
1157 (match r with (p,gl) ->
1158 debug("eq1 ritorna "^string_of_int(List.length gl)^"\n" ));
1160 ~continuations:[(Tacticals.thens
1163 let r = equality_replace (Cic.Appl[_Rinv;_R1]) _R1 ~status in
1164 (match r with (p,gl) ->
1165 debug("eq2 ritorna "^string_of_int(List.length gl)^"\n" ));
1168 [PrimitiveTactics.apply_tac ~term:_Rinv_R1
1169 (* CSC: Il nostro goal e' 1^-1 = 1 e non 1 = 1^-1. Quindi non c'e' bisogno
1170 di applicare sym_eqT. Perche' in Coq il goal e' al contrario? Forse i
1171 parametri della equality_replace vengono passati al contrario? Oppure la
1172 tattica usa i parametri al contrario?
1173 CODICE NEL COMMENTO NON PORTATO. ORA ESISTE ANCHE LA TATTICA symmetry_tac
1174 ~continuations:[Tacticals.then_
1176 fun ~status:(proof,goal as status) ->
1178 let curi,metasenv,pbo,pty = proof in
1179 let metano,context,ty = List.find (function (m,_,_) -> m=
1181 debug("ty = "^CicPp.ppterm ty^"\n");
1182 let r = PrimitiveTactics.apply_tac ~term:_sym_eqT
1184 debug("fine ECCOCI\n");
1186 ~continuation:(PrimitiveTactics.apply_tac ~term:_Rinv_R1)
1188 ;Tacticals.try_tactics
1189 ~tactics:[ "ring", (fun ~status ->
1190 debug("begin RING\n");
1191 let r = Ring.ring_tac ~status in
1192 debug ("end RING\n");
1194 ; "id", Tacticals.id_tac]
1199 fun ~status:(proof,goal as status) ->
1200 let curi,metasenv,pbo,pty = proof in
1201 let metano,context,ty = List.find (function (m,_,_) -> m=
1203 (* check if ty is of type *)
1205 debug("qui c'e' gia' l'or "^CicPp.ppterm ty^"\n");
1207 (* Fix: aspetta mail di Claudio per capire cosa comporta anonimous*)
1208 Cic.Prod (Cic.Anonymous,a,b) -> (Cic.Appl [_not;a])
1211 let r = PrimitiveTactics.change_tac ~what:ty ~with_what:w1 ~status in
1212 debug("fine MY_CHNGE\n");
1215 ~continuation:(*PORTINGTacticals.id_tac*)tac2]))
1216 ;(*Tacticals.id_tac*)!tac1]);(*end tac:=*)
1217 tac:=(Tacticals.thens
1218 ~start:(PrimitiveTactics.cut_tac ~term:_False)
1219 ~continuations:[Tacticals.then_
1220 ~start:(PrimitiveTactics.intros_tac ~name:"??")
1221 ~continuation:contradiction_tac
1225 |_-> assert false)(*match (!lutil) *)
1226 |_-> assert false); (*match res*)
1227 debug ("finalmente applico tac\n");
1228 (!tac ~status:(proof,goal))
1231 let fourier_tac ~status:(proof,goal) = fourier ~status:(proof,goal);;