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.
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30 module P = PrimitiveTactics
32 module CR = CicReduction
33 module PST = ProofEngineStructuralRules
34 module PET = ProofEngineTypes
35 module CTC = CicTypeChecker
37 module S = CicSubstitution
38 module RT = ReductionTactics
39 module PEH = ProofEngineHelpers
40 module ET = EqualityTactics
41 module DTI = DoubleTypeInference
45 if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
47 (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
50 let discriminate_tac ~term =
52 match LibraryObjects.true_URI () with
54 | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
56 match LibraryObjects.false_URI () with
58 | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
59 let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
60 let find_discriminating_consno t1 t2 =
63 | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
64 | C.Appl ((C.MutConstruct _ as constr1) :: args1),
65 C.Appl ((C.MutConstruct _ as constr2) :: args2)
66 when constr1 = constr2 ->
67 let rec aux_list l1 l2 =
70 | hd1 :: tl1, hd2 :: tl2 ->
71 (match aux hd1 hd2 with
72 | None -> aux_list tl1 tl2
73 | Some _ as res -> res)
74 | _ -> (* same constructor applied to a different number of args *)
78 | ((C.MutConstruct (_,_,consno1,subst1)),
79 (C.MutConstruct (_,_,consno2,subst2)))
80 | ((C.MutConstruct (_,_,consno1,subst1)),
81 (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
82 | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
83 (C.MutConstruct (_,_,consno2,subst2)))
84 | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
85 (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
86 when (consno1 <> consno2) || (subst1 <> subst2) ->
88 | _ -> fail "not a discriminable equality"
92 let mk_branches_and_outtype turi typeno consno context args =
93 (* a list of "True" except for the element in position consno which
95 match fst (CicEnvironment.get_obj CU.empty_ugraph turi) with
96 | C.InductiveDefinition (ind_type_list,_,paramsno,_) ->
97 let _,_,rty,constructor_list = List.nth ind_type_list typeno in
98 let false_constr_id,_ = List.nth constructor_list (consno - 1) in
102 (* dubbio: e' corretto ridurre in questo context ??? *)
103 let red_ty = CR.whd context cty in
106 | C.Prod (_,_,target) when (k <= paramsno) ->
107 S.subst (List.nth args (k-1))
109 | C.Prod (binder,source,target) when (k > paramsno) ->
110 C.Lambda (binder, source, (aux target (k+1)))
112 if (id = false_constr_id)
113 then (C.MutInd(false_URI,0,[]))
114 else (C.MutInd(true_URI,0,[]))
116 (S.lift 1 (aux red_ty 1)))
120 let rec mk_lambdas rev_left_args =
122 0, args, C.Prod (_,so,ta) ->
124 (C.Name (incr seed; "x" ^ string_of_int !seed),
126 mk_lambdas rev_left_args (0,args,ta))
127 | 0, args, C.Sort _ ->
131 | n -> C.Rel n :: mk_rels (n - 1) in
132 let argsno = List.length args in
135 (if argsno + List.length rev_left_args > 0 then
137 (C.MutInd (turi, typeno, []) ::
139 (S.lift (argsno + 1))
140 (List.rev rev_left_args)) @
143 C.MutInd (turi,typeno,[])),
145 | 0, _, _ -> assert false (* seriously screwed up *)
146 | n, he::tl, C.Prod (_,_,ta) ->
147 mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
149 assert false (* we should probably reduce in some context *)
151 mk_lambdas [] (paramsno, args, rty)
156 let discriminate'_tac ~term status =
157 let (proof, goal) = status in
158 let _,metasenv,_subst,_,_, _ = proof in
159 let _,context,_ = CicUtil.lookup_meta goal metasenv in
161 CTC.type_of_aux' metasenv context term CU.empty_ugraph
164 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
165 when LibraryObjects.is_eq_URI equri ->
166 let turi,typeno,exp_named_subst,args =
168 | (C.MutInd (turi,typeno,exp_named_subst)) ->
169 turi,typeno,exp_named_subst,[]
170 | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) ->
171 turi,typeno,exp_named_subst,args
172 | _ -> fail "not a discriminable equality"
175 match find_discriminating_consno t1 t2 with
176 | Some consno -> consno
177 | None -> fail "discriminating terms are structurally equal"
179 let branches,outtype =
180 mk_branches_and_outtype turi typeno consno context args
184 ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
189 ~pattern:(PET.conclusion_pattern None)
192 C.Lambda ( C.Name "x", tty,
193 C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
199 (ET.rewrite_simpl_tac
200 ~direction:`RightToLeft
201 ~pattern:(PET.conclusion_pattern None)
204 (IntroductionTactics.constructor_tac ~n:1)))) status
205 | _ -> fail "not an equality"
207 PET.mk_tactic (discriminate'_tac ~term)
210 PET.Fail (lazy "Injection: not an equality")
211 let exn_nothingtodo =
212 PET.Fail (lazy "Nothing to do")
213 let exn_discrnonind =
214 PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
215 let exn_injwronggoal =
216 PET.Fail (lazy "Injection: goal after cut is not correct")
218 PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
221 let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
224 let clear_term first_time lterm =
225 let clear_term status =
226 let (proof, goal) = status in
227 let _,metasenv,_subst,_,_, _ = proof in
228 let _,context,_ = CicUtil.lookup_meta goal metasenv in
229 let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
230 debug_print (lazy ("\nclear di: " ^ pp context term));
231 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
232 let g () = if first_time then raise exn_nothingtodo else T.id_tac in
233 let tactic = match term with
235 begin match List.nth context (pred n) with
236 | Some (C.Name id, _) ->
237 T.if_ ~fail:(g ()) ~start:(PST.clear ~hyps:[id]) ~continuation:T.id_tac
242 PET.apply_tactic tactic status
244 PET.mk_tactic clear_term
246 let exists context = function
247 | C.Rel i -> List.nth context (pred i) <> None
250 let rec recur_on_child_tac ~before =
251 let recur_on_child status =
252 let (proof, goal) = status in
253 let _, metasenv, _subst, _, _, _ = proof in
254 let _, context, _ = CicUtil.lookup_meta goal metasenv in
255 debug_print (lazy ("\nrecur_on_child"));
256 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
257 let mk_lterm term c m ug =
258 let distance = List.length c - List.length context in
259 S.lift distance term, m, ug
261 let lterm = mk_lterm (Cic.Rel 1) in
262 let continuation = destruct ~first_time:false lterm in
263 let tactic = T.then_ ~start:before ~continuation in
264 PET.apply_tactic tactic status
266 PET.mk_tactic recur_on_child
268 and injection_tac ~lterm ~i ~continuation =
269 let give_name seed = function
270 | C.Name _ as name -> name
271 | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
273 let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
274 let injection_tac status =
275 let (proof, goal) = status in
276 (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma
277 * differiscono (o potrebbero differire?) nell'i-esimo parametro
279 let _,metasenv,_subst,_,_, _ = proof in
280 let _,context,_ = CicUtil.lookup_meta goal metasenv in
281 let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
283 CTC.type_of_aux' metasenv context term CU.empty_ugraph
285 debug_print (lazy ("\ninjection su : " ^ pp context termty));
286 match termty with (* an equality *)
287 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
288 when LibraryObjects.is_eq_URI equri ->
289 let turi,typeno,ens,params =
290 match tty with (* some inductive type *)
291 | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[]
292 | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params
293 | _ -> raise exn_noneqind
295 let t1',t2',consno = (* sono i due sottotermini che differiscono *)
297 | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
298 C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
299 when (uri1 = uri2) && (typeno1 = typeno2) &&
300 (consno1 = consno2) && (ens1 = ens2) ->
301 (* controllo ridondante *)
302 List.nth applist1 (pred i),List.nth applist2 (pred i),consno2
305 let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in
306 let patterns,outtype =
307 match fst (CicEnvironment.get_obj CU.empty_ugraph turi) with
308 | C.InductiveDefinition (ind_type_list,_,paramsno,_)->
309 let left_params, right_params = HExtlib.split_nth paramsno params in
310 let _,_,_,constructor_list = List.nth ind_type_list typeno in
311 let i_constr_id,_ = List.nth constructor_list (consno - 1) in
315 (function (id,cty) ->
316 let reduced_cty = CR.whd context cty in
317 let rec aux k = function
318 | C.Prod (_,_,tgt) when k <= paramsno ->
319 let left = List.nth left_params (k-1) in
320 aux (k+1) (S.subst left tgt)
321 | C.Prod (binder,source,target) when k > paramsno ->
322 let binder' = give_name seed binder in
323 C.Lambda (binder',source,(aux (k+1) target))
325 let nr_param_constr = k - paramsno - 1 in
326 if id = i_constr_id then C.Rel (k - i)
327 else S.lift nr_param_constr t1'
328 (* + 1 per liftare anche il lambda aggiunto
329 * esternamente al case *)
330 in S.lift 1 (aux 1 reduced_cty))
333 (* this code should be taken from cases_tac *)
336 let rec to_lambdas te head =
337 match CR.whd context te with
338 | C.Prod (binder,so,ta) ->
339 let binder' = give_name seed binder in
340 C.Lambda (binder',so,to_lambdas ta head)
343 let rec skip_prods params te =
344 match params, CR.whd context te with
346 | left::tl, C.Prod (_,_,ta) ->
347 skip_prods tl (S.subst left ta)
348 | _, _ -> assert false
352 List.fold_left (fun x y -> S.subst y x) tty left_params
354 (* non lift, ma subst coi left! *)
355 match S.lift 1 tty with
356 | C.MutInd _ as tty' -> tty'
358 let keep,abstract = HExtlib.split_nth (paramsno +1) l in
359 let keep = List.map (S.lift paramsno) keep in
360 C.Appl (keep@mk_rels (List.length abstract))
363 match ind_type_list with
366 (* this is in general wrong, do as in cases_tac *)
367 to_lambdas (skip_prods left_params ty)
369 (C.Name "cased", abstracted_tty,
370 (* here we should capture right parameters *)
371 (* 1 for his Lambda, one for the Lambda outside the match
372 * and then one for each to_lambda *)
373 S.lift (2+List.length right_params) tty'))
376 | _ -> raise exn_discrnonind
378 let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in
380 C.Appl [ C.Lambda (C.Name "x", tty,
381 C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1]
383 (* check if cutted and changed are well typed and if t1' ~ changed *)
386 let _,g = CTC.type_of_aux' metasenv context cutted
389 let _,g = CTC.type_of_aux' metasenv context changed g in
390 fst (CR.are_convertible ~metasenv context t1' changed g)
392 | CTC.TypeCheckerFailure _ -> false
394 if not go_on then begin
395 HLog.warn "destruct: injection failed";
396 PET.apply_tactic continuation status
398 let fill_cut_tac term =
399 let fill_cut status =
400 debug_print (lazy "riempio il cut");
401 let (proof, goal) = status in
402 let _,metasenv,_subst,_,_, _ = proof in
403 let _,context,gty = CicUtil.lookup_meta goal metasenv in
404 let gty = Unshare.unshare gty in
405 let new_t1' = match gty with
406 | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t
407 | _ -> raise exn_injwronggoal
409 debug_print (lazy ("metto: " ^ pp context changed));
410 debug_print (lazy ("al posto di: " ^ pp context new_t1'));
411 debug_print (lazy ("nel goal: " ^ pp context gty));
412 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
413 debug_print (lazy ("e poi rewrite con: "^pp context term));
414 let tac = T.seq ~tactics:[
416 ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1']))
417 (fun _ m u -> changed,m,u);
419 ~direction:`LeftToRight
420 ~pattern:(PET.conclusion_pattern None)
424 PET.apply_tactic tac status
426 PET.mk_tactic fill_cut
428 debug_print (lazy ("CUT: " ^ pp context cutted));
430 T.thens ~start: (P.cut_tac cutted)
432 recur_on_child_tac continuation;
436 PET.apply_tactic tactic status
437 | _ -> raise exn_noneq
439 PET.mk_tactic injection_tac
441 and subst_tac ~lterm ~direction ~where ~continuation =
442 let subst_tac status =
443 let (proof, goal) = status in
444 let _,metasenv,_subst,_,_, _ = proof in
445 let _,context,_ = CicUtil.lookup_meta goal metasenv in
446 let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
447 debug_print (lazy ("\nsubst " ^ (match direction with `LeftToRight -> "->" | `RightToLeft -> "<-") ^ " di: " ^ pp context term));
448 let tactic = match where with
450 debug_print (lazy ("nella conclusione"));
451 let pattern = PET.conclusion_pattern None in
452 let tactic = ET.rewrite_tac ~direction ~pattern term [] in
453 T.then_ ~start:(T.try_tactic ~tactic) ~continuation
455 debug_print (lazy ("nella premessa: " ^ name));
456 let pattern = None, [name, PET.hole], None in
457 let start = ET.rewrite_tac ~direction ~pattern term [] in
458 let ok_tactic = recur_on_child_tac continuation in
459 T.if_ ~start ~continuation:ok_tactic ~fail:continuation
461 PET.apply_tactic tactic status
463 PET.mk_tactic subst_tac
465 and destruct ~first_time lterm =
466 let are_convertible hd1 hd2 metasenv context =
467 fst (CR.are_convertible ~metasenv context hd1 hd2 CU.empty_ugraph)
469 let destruct status =
470 let (proof, goal) = status in
471 let _,metasenv,_subst, _,_, _ = proof in
472 let _,context,_ = CicUtil.lookup_meta goal metasenv in
473 let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
474 let tactic = if not (first_time || exists context term) then T.id_tac else begin
475 debug_print (lazy ("\ndestruct di: " ^ pp context term));
476 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
477 let termty,_ = CTC.type_of_aux' metasenv context term CU.empty_ugraph in
478 debug_print (lazy ("\ndestruct su: " ^ pp context termty));
479 let mk_lterm term c m ug =
480 let distance = List.length c - List.length context in
481 S.lift distance term, m, ug
483 let lterm = mk_lterm term in
484 let mk_subst_chain direction index with_what what =
485 let k = match term with C.Rel i -> i | _ -> -1 in
486 let rec traverse_context first_time j = function
490 clear_term first_time lterm;
491 clear_term false (mk_lterm what);
492 clear_term false (mk_lterm with_what)
495 subst_tac ~direction ~lterm ~where:None ~continuation
496 | Some (C.Name name, _) :: tl when j < index && j <> k ->
497 debug_print (lazy ("\nsubst programmata: cosa: " ^ string_of_int index ^ ", dove: " ^ string_of_int j));
498 subst_tac ~direction ~lterm ~where:(Some name)
499 ~continuation:(traverse_context false (succ j) tl)
500 | _ :: tl -> traverse_context first_time (succ j) tl
502 traverse_context first_time 1 context
505 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
506 when LibraryObjects.is_eq_URI equri ->
507 begin match t1,t2 with
511 when t1 = t2 -> clear_term first_time lterm
512 | C.Appl (C.MutConstruct _ as mc1 :: applist1),
513 C.Appl (C.MutConstruct _ as mc2 :: applist2)
515 let rec traverse_list first_time i l1 l2 =
517 | [], [] -> clear_term first_time lterm
518 | hd1 :: tl1, hd2 :: tl2 ->
519 if are_convertible hd1 hd2 metasenv context then
520 traverse_list first_time (succ i) tl1 tl2
522 injection_tac ~i ~lterm ~continuation:
523 (traverse_list false (succ i) tl1 tl2)
525 (* i 2 termini hanno in testa lo stesso costruttore,
526 * ma applicato a un numero diverso di termini *)
528 traverse_list first_time 1 applist1 applist2
529 (* discriminate part *)
530 | C.MutConstruct (_,_,consno1,ens1),
531 C.MutConstruct (_,_,consno2,ens2)
532 | C.MutConstruct (_,_,consno1,ens1),
533 C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
534 | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
535 C.MutConstruct (_,_,consno2,ens2)
536 | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
537 C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
538 when (consno1 <> consno2) || (ens1 <> ens2) ->
539 discriminate_tac ~term
541 | C.Rel _, C.Rel _ when t1 = t2 ->
543 clear_term first_time lterm;
544 clear_term false (mk_lterm t1)
546 | C.Rel i1, C.Rel i2 when i1 < i2 ->
547 mk_subst_chain `LeftToRight i1 t2 t1
548 | C.Rel i1, C.Rel i2 when i1 > i2 ->
549 mk_subst_chain `RightToLeft i2 t1 t2
550 | C.Rel i1, _ when DTI.does_not_occur i1 t2 ->
551 mk_subst_chain `LeftToRight i1 t2 t1
552 | _, C.Rel i2 when DTI.does_not_occur i2 t1 ->
553 mk_subst_chain `RightToLeft i2 t1 t2
555 | _ when first_time -> raise exn_nothingtodo
556 | _ (* when not first time *) -> T.id_tac
558 | _ when first_time -> raise exn_nothingtodo
559 | _ (* when not first time *) -> T.id_tac
561 PET.apply_tactic tactic status
563 PET.mk_tactic destruct
565 (* destruct performs either injection or discriminate or subst *)
566 let destruct_tac xterm =
567 let destruct status =
568 let (proof, goal) = status in
569 let _,metasenv,_subst,_,_, _ = proof in
570 let _,context,_ = CicUtil.lookup_meta goal metasenv in
571 let mk_lterm term c m ug =
572 let distance = List.length c - List.length context in
573 S.lift distance term, m, ug
575 let tactics = match xterm with
576 | Some term -> [destruct ~first_time:true (mk_lterm term)]
578 let rec mk_tactics first_time i tacs = function
579 | [] -> List.rev tacs
581 let lterm = mk_lterm (C.Rel i) in
582 let tacs = destruct ~first_time lterm :: tacs in
583 mk_tactics false (succ i) tacs tl
584 | _ :: tl -> mk_tactics first_time (succ i) tacs tl
586 mk_tactics false 1 [] context
588 PET.apply_tactic (T.seq ~tactics) status
590 PET.mk_tactic destruct