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
42 module FNG = FreshNamesGenerator
46 if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
48 (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
51 let discriminate_tac ~term =
53 match LibraryObjects.true_URI () with
55 | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
57 match LibraryObjects.false_URI () with
59 | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
60 let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
61 let find_discriminating_consno t1 t2 =
64 | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
65 | C.Appl ((C.MutConstruct _ as constr1) :: args1),
66 C.Appl ((C.MutConstruct _ as constr2) :: args2)
67 when constr1 = constr2 ->
68 let rec aux_list l1 l2 =
71 | hd1 :: tl1, hd2 :: tl2 ->
72 (match aux hd1 hd2 with
73 | None -> aux_list tl1 tl2
74 | Some _ as res -> res)
75 | _ -> (* same constructor applied to a different number of args *)
79 | ((C.MutConstruct (_,_,consno1,subst1)),
80 (C.MutConstruct (_,_,consno2,subst2)))
81 | ((C.MutConstruct (_,_,consno1,subst1)),
82 (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
83 | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
84 (C.MutConstruct (_,_,consno2,subst2)))
85 | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
86 (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
87 when (consno1 <> consno2) || (subst1 <> subst2) ->
89 | _ -> fail "not a discriminable equality"
93 let mk_branches_and_outtype turi typeno consno context args =
94 (* a list of "True" except for the element in position consno which
96 match fst (CicEnvironment.get_obj CU.empty_ugraph turi) with
97 | C.InductiveDefinition (ind_type_list,_,paramsno,_) ->
98 let _,_,rty,constructor_list = List.nth ind_type_list typeno in
99 let false_constr_id,_ = List.nth constructor_list (consno - 1) in
103 (* dubbio: e' corretto ridurre in questo context ??? *)
104 let red_ty = CR.whd context cty in
107 | C.Prod (_,_,target) when (k <= paramsno) ->
108 S.subst (List.nth args (k-1))
110 | C.Prod (binder,source,target) when (k > paramsno) ->
111 C.Lambda (binder, source, (aux target (k+1)))
113 if (id = false_constr_id)
114 then (C.MutInd(false_URI,0,[]))
115 else (C.MutInd(true_URI,0,[]))
117 (S.lift 1 (aux red_ty 1)))
121 let rec mk_lambdas rev_left_args =
123 0, args, C.Prod (_,so,ta) ->
125 (C.Name (incr seed; "x" ^ string_of_int !seed),
127 mk_lambdas rev_left_args (0,args,ta))
128 | 0, args, C.Sort _ ->
132 | n -> C.Rel n :: mk_rels (n - 1) in
133 let argsno = List.length args in
136 (if argsno + List.length rev_left_args > 0 then
138 (C.MutInd (turi, typeno, []) ::
140 (S.lift (argsno + 1))
141 (List.rev rev_left_args)) @
144 C.MutInd (turi,typeno,[])),
146 | 0, _, _ -> assert false (* seriously screwed up *)
147 | n, he::tl, C.Prod (_,_,ta) ->
148 mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
150 assert false (* we should probably reduce in some context *)
152 mk_lambdas [] (paramsno, args, rty)
157 let discriminate'_tac ~term status =
158 let (proof, goal) = status in
159 let _,metasenv,_subst,_,_, _ = proof in
160 let _,context,_ = CicUtil.lookup_meta goal metasenv in
162 CTC.type_of_aux' metasenv context term CU.empty_ugraph
165 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
166 when LibraryObjects.is_eq_URI equri ->
167 let turi,typeno,exp_named_subst,args =
169 | (C.MutInd (turi,typeno,exp_named_subst)) ->
170 turi,typeno,exp_named_subst,[]
171 | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) ->
172 turi,typeno,exp_named_subst,args
173 | _ -> fail "not a discriminable equality"
176 match find_discriminating_consno t1 t2 with
177 | Some consno -> consno
178 | None -> fail "discriminating terms are structurally equal"
180 let branches,outtype =
181 mk_branches_and_outtype turi typeno consno context args
185 ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
190 ~pattern:(PET.conclusion_pattern None)
193 C.Lambda ( C.Name "x", tty,
194 C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
200 (ET.rewrite_simpl_tac
201 ~direction:`RightToLeft
202 ~pattern:(PET.conclusion_pattern None)
205 (IntroductionTactics.constructor_tac ~n:1)))) status
206 | _ -> fail "not an equality"
208 PET.mk_tactic (discriminate'_tac ~term)
211 PET.Fail (lazy "Injection: not an equality")
212 let exn_nothingtodo =
213 PET.Fail (lazy "Nothing to do")
214 let exn_discrnonind =
215 PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
216 let exn_injwronggoal =
217 PET.Fail (lazy "Injection: goal after cut is not correct")
219 PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
222 let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
225 let clear_term first_time lterm =
226 let clear_term status =
227 let (proof, goal) = status in
228 let _,metasenv,_subst,_,_, _ = proof in
229 let _,context,_ = CicUtil.lookup_meta goal metasenv in
230 let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
231 debug_print (lazy ("\nclear di: " ^ pp context term));
232 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
233 let g () = if first_time then raise exn_nothingtodo else T.id_tac in
234 let tactic = match term with
236 begin match List.nth context (pred n) with
237 | Some (C.Name id, _) ->
238 T.if_ ~fail:(g ()) ~start:(PST.clear ~hyps:[id]) ~continuation:T.id_tac
243 PET.apply_tactic tactic status
245 PET.mk_tactic clear_term
247 let simpl_in_term context = function
249 let name = match List.nth context (pred i) with
250 | Some (Cic.Name s, Cic.Def _) -> s
251 | Some (Cic.Name s, Cic.Decl _) -> s
254 RT.simpl_tac ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None)
257 let mk_fresh_name metasenv context name typ =
258 let name = C.Name name in
259 match FNG.mk_fresh_name ~subst:[] metasenv context name ~typ with
261 | C.Anonymous -> assert false
263 let exists context = function
264 | C.Rel i -> List.nth context (pred i) <> None
267 let rec recur_on_child_tac name =
268 let recur_on_child status =
269 let (proof, goal) = status in
270 let _, metasenv, _subst, _, _, _ = proof in
271 let _, context, _ = CicUtil.lookup_meta goal metasenv in
272 debug_print (lazy ("\nrecur_on_child su: " ^ name));
273 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
274 let rec search_name i = function
276 | Some (Cic.Name n, _) :: _ when n = name ->
277 destruct ~first_time:false (Cic.Rel i)
278 | _ :: tl -> search_name (succ i) tl
280 PET.apply_tactic (search_name 1 context) status
282 PET.mk_tactic recur_on_child
284 and injection_tac ~lterm ~i ~continuation =
285 let give_name seed = function
286 | C.Name _ as name -> name
287 | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
289 let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
290 let injection_tac status =
291 let (proof, goal) = status in
292 (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma
293 * differiscono (o potrebbero differire?) nell'i-esimo parametro
295 let _,metasenv,_subst,_,_, _ = proof in
296 let _,context,_ = CicUtil.lookup_meta goal metasenv in
297 let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
299 CTC.type_of_aux' metasenv context term CU.empty_ugraph
301 debug_print (lazy ("\ninjection su : " ^ pp context termty));
302 match termty with (* an equality *)
303 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
304 when LibraryObjects.is_eq_URI equri ->
305 let turi,typeno,ens,params =
306 match tty with (* some inductive type *)
307 | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[]
308 | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params
309 | _ -> raise exn_noneqind
311 let t1',t2',consno = (* sono i due sottotermini che differiscono *)
313 | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
314 C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
315 when (uri1 = uri2) && (typeno1 = typeno2) &&
316 (consno1 = consno2) && (ens1 = ens2) ->
317 (* controllo ridondante *)
318 List.nth applist1 (pred i),List.nth applist2 (pred i),consno2
321 let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in
322 let patterns,outtype =
323 match fst (CicEnvironment.get_obj CU.empty_ugraph turi) with
324 | C.InductiveDefinition (ind_type_list,_,paramsno,_)->
325 let left_params, right_params = HExtlib.split_nth paramsno params in
326 let _,_,_,constructor_list = List.nth ind_type_list typeno in
327 let i_constr_id,_ = List.nth constructor_list (consno - 1) in
331 (function (id,cty) ->
332 let reduced_cty = CR.whd context cty in
333 let rec aux k = function
334 | C.Prod (_,_,tgt) when k <= paramsno ->
335 let left = List.nth left_params (k-1) in
336 aux (k+1) (S.subst left tgt)
337 | C.Prod (binder,source,target) when k > paramsno ->
338 let binder' = give_name seed binder in
339 C.Lambda (binder',source,(aux (k+1) target))
341 let nr_param_constr = k - paramsno - 1 in
342 if id = i_constr_id then C.Rel (k - i)
343 else S.lift nr_param_constr t1'
344 (* + 1 per liftare anche il lambda aggiunto
345 * esternamente al case *)
346 in S.lift 1 (aux 1 reduced_cty))
349 (* this code should be taken from cases_tac *)
352 let rec to_lambdas te head =
353 match CR.whd context te with
354 | C.Prod (binder,so,ta) ->
355 let binder' = give_name seed binder in
356 C.Lambda (binder',so,to_lambdas ta head)
359 let rec skip_prods params te =
360 match params, CR.whd context te with
362 | left::tl, C.Prod (_,_,ta) ->
363 skip_prods tl (S.subst left ta)
364 | _, _ -> assert false
368 List.fold_left (fun x y -> S.subst y x) tty left_params
370 (* non lift, ma subst coi left! *)
371 match S.lift 1 tty with
372 | C.MutInd _ as tty' -> tty'
374 let keep,abstract = HExtlib.split_nth (paramsno +1) l in
375 let keep = List.map (S.lift paramsno) keep in
376 C.Appl (keep@mk_rels (List.length abstract))
379 match ind_type_list with
382 (* this is in general wrong, do as in cases_tac *)
383 to_lambdas (skip_prods left_params ty)
385 (C.Name "cased", abstracted_tty,
386 (* here we should capture right parameters *)
387 (* 1 for his Lambda, one for the Lambda outside the match
388 * and then one for each to_lambda *)
389 S.lift (2+List.length right_params) tty'))
392 | _ -> raise exn_discrnonind
394 let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in
396 C.Appl [ C.Lambda (C.Name "x", tty,
397 C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1]
399 (* check if cutted and changed are well typed and if t1' ~ changed *)
402 let _,g = CTC.type_of_aux' metasenv context cutted
405 let _,g = CTC.type_of_aux' metasenv context changed g in
406 fst (CR.are_convertible ~metasenv context t1' changed g)
408 | CTC.TypeCheckerFailure _ -> false
410 if not go_on then begin
411 HLog.warn "destruct: injection failed";
412 PET.apply_tactic continuation status
414 let fill_cut_tac term =
415 let fill_cut status =
416 debug_print (lazy "riempio il cut");
417 let (proof, goal) = status in
418 let _,metasenv,_subst,_,_, _ = proof in
419 let _,context,gty = CicUtil.lookup_meta goal metasenv in
420 let gty = Unshare.unshare gty in
421 let new_t1' = match gty with
422 | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t
423 | _ -> raise exn_injwronggoal
425 debug_print (lazy ("metto: " ^ pp context changed));
426 debug_print (lazy ("al posto di: " ^ pp context new_t1'));
427 debug_print (lazy ("nel goal: " ^ pp context gty));
428 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
429 debug_print (lazy ("e poi rewrite con: "^pp context term));
430 let tac = T.seq ~tactics:[
432 ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1']))
433 (fun _ m u -> changed,m,u);
435 ~direction:`LeftToRight
436 ~pattern:(PET.conclusion_pattern None)
440 PET.apply_tactic tac status
442 PET.mk_tactic fill_cut
444 debug_print (lazy ("CUT: " ^ pp context cutted));
445 let name = mk_fresh_name metasenv context "Hcut" cutted in
446 let mk_fresh_name_callback = PEH.namer_of [Some name] in
447 debug_print (lazy ("figlio: " ^ name));
449 T.thens ~start: (P.cut_tac ~mk_fresh_name_callback cutted)
451 T.seq ~tactics:[continuation; recur_on_child_tac name];
455 PET.apply_tactic tactic status
456 | _ -> raise exn_noneq
458 PET.mk_tactic injection_tac
460 and subst_tac ~lterm ~direction ~where ~continuation =
461 let subst_tac status =
462 let (proof, goal) = status in
463 let _,metasenv,_subst,_,_, _ = proof in
464 let _,context,_ = CicUtil.lookup_meta goal metasenv in
465 let term, metasenv, _ugraph = lterm context metasenv CU.empty_ugraph in
466 debug_print (lazy ("\nsubst " ^ (match direction with `LeftToRight -> "->" | `RightToLeft -> "<-") ^ " di: " ^ pp context term));
467 let tactic = match where with
469 debug_print (lazy ("nella conclusione"));
470 let pattern = PET.conclusion_pattern None in
471 let tactic = ET.rewrite_tac ~direction ~pattern term [] in
472 T.then_ ~start:(T.try_tactic ~tactic) ~continuation
474 debug_print (lazy ("nella premessa: " ^ name));
475 let pattern = None, [name, PET.hole], None in
476 let start = ET.rewrite_tac ~direction ~pattern term [] in
478 T.seq ~tactics:[continuation; recur_on_child_tac name]
480 debug_print (lazy ("figlio: " ^ name));
481 T.if_ ~start ~continuation:ok_tactic ~fail:continuation
483 PET.apply_tactic tactic status
485 PET.mk_tactic subst_tac
487 and destruct ?(simplified = false) ~first_time term =
488 let are_convertible hd1 hd2 metasenv context =
489 fst (CR.are_convertible ~metasenv context hd1 hd2 CU.empty_ugraph)
491 let destruct status =
492 let (proof, goal) = status in
493 let _,metasenv,_subst, _,_, _ = proof in
494 let _,context,_ = CicUtil.lookup_meta goal metasenv in
495 debug_print (lazy ("\ndestruct di: " ^ pp context term));
496 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
498 CTC.type_of_aux' metasenv context term CU.empty_ugraph
500 debug_print (lazy ("\ndestruct su: " ^ pp context termty));
501 let mk_lterm term c m ug =
502 let distance = List.length c - List.length context in
503 S.lift distance term, m, ug
505 let lterm = mk_lterm term in
506 let mk_subst_chain direction index with_what what =
507 let k = match term with C.Rel i -> i | _ -> -1 in
508 let rec traverse_context first_time j = function
512 clear_term first_time lterm;
513 clear_term false (mk_lterm what);
514 clear_term false (mk_lterm with_what)
517 subst_tac ~direction ~lterm ~where:None ~continuation
518 | Some (C.Name name, _) :: tl when j < index && j <> k ->
519 debug_print (lazy ("\nsubst programmata: cosa: " ^ string_of_int index ^ ", dove: " ^ string_of_int j));
520 subst_tac ~direction ~lterm ~where:(Some name)
521 ~continuation:(traverse_context false (succ j) tl)
522 | _ :: tl -> traverse_context first_time (succ j) tl
524 traverse_context first_time 1 context
526 let tac = match termty with
527 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
528 when LibraryObjects.is_eq_URI equri ->
529 begin match t1,t2 with
533 when t1 = t2 -> clear_term first_time lterm
534 | C.Appl (C.MutConstruct _ as mc1 :: applist1),
535 C.Appl (C.MutConstruct _ as mc2 :: applist2)
537 let rec traverse_list first_time i l1 l2 =
539 | [], [] -> clear_term first_time lterm
540 | hd1 :: tl1, hd2 :: tl2 ->
541 if are_convertible hd1 hd2 metasenv context then
542 traverse_list first_time (succ i) tl1 tl2
544 injection_tac ~i ~lterm ~continuation:
545 (traverse_list false (succ i) tl1 tl2)
547 (* i 2 termini hanno in testa lo stesso costruttore,
548 * ma applicato a un numero diverso di termini *)
550 traverse_list first_time 1 applist1 applist2
551 (* discriminate part *)
552 | C.MutConstruct (_,_,consno1,ens1),
553 C.MutConstruct (_,_,consno2,ens2)
554 | C.MutConstruct (_,_,consno1,ens1),
555 C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
556 | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
557 C.MutConstruct (_,_,consno2,ens2)
558 | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
559 C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
560 when (consno1 <> consno2) || (ens1 <> ens2) ->
561 discriminate_tac ~term
563 | C.Rel _, C.Rel _ when t1 = t2 ->
565 clear_term first_time lterm;
566 clear_term false (mk_lterm t1)
568 | C.Rel i1, C.Rel i2 when i1 < i2 ->
569 mk_subst_chain `LeftToRight i1 t2 t1
570 | C.Rel i1, C.Rel i2 when i1 > i2 ->
571 mk_subst_chain `RightToLeft i2 t1 t2
572 | C.Rel i1, _ when DTI.does_not_occur i1 t2 ->
573 mk_subst_chain `LeftToRight i1 t2 t1
574 | _, C.Rel i2 when DTI.does_not_occur i2 t1 ->
575 mk_subst_chain `RightToLeft i2 t1 t2
577 | _ when first_time && simplified -> raise exn_nothingtodo
578 | _ when simplified (* && not first time *) -> T.id_tac
579 | _ (* when not simplified *) ->
580 T.then_ ~start:(simpl_in_term context term)
581 ~continuation:(destruct ~simplified:true ~first_time term)
583 | _ when first_time && simplified -> raise exn_nothingtodo
584 | _ when simplified (* && not first time *) -> T.id_tac
585 | _ (* when not simplified *) ->
586 T.then_ ~start:(simpl_in_term context term)
587 ~continuation:(destruct ~simplified:true ~first_time term)
589 PET.apply_tactic tac status
591 PET.mk_tactic destruct
593 let lazy_destruct_tac ~first_time ~lterm =
594 let lazy_destruct status =
595 let (proof, goal) = status in
596 let _,metasenv,_subst,_,_, _ = proof in
597 let _,context,_ = CicUtil.lookup_meta goal metasenv in
598 let term, _, _ = lterm context metasenv CU.empty_ugraph in
600 if exists context term then destruct ~first_time term else T.id_tac
602 PET.apply_tactic tactic status
604 PET.mk_tactic lazy_destruct
606 (* destruct performs either injection or discriminate *)
607 (* equivalent to Coq's "analyze equality" *)
608 let destruct_tac = function
609 | Some term -> destruct ~first_time:true term
611 let destruct_all status =
612 let (proof, goal) = status in
613 let _,metasenv,_subst,_,_, _ = proof in
614 let _,context,_ = CicUtil.lookup_meta goal metasenv in
615 let mk_lterm term c m ug =
616 let distance = List.length c - List.length context in
617 S.lift distance term, m, ug
619 let rec mk_tactics first_time i tacs = function
620 | [] -> List.rev tacs
622 let lterm = mk_lterm (C.Rel i) in
623 let tacs = lazy_destruct_tac ~first_time ~lterm :: tacs in
624 mk_tactics false (succ i) tacs tl
625 | _ :: tl -> mk_tactics first_time (succ i) tacs tl
627 let tactics = mk_tactics false 1 [] context in
628 PET.apply_tactic (T.seq ~tactics) status
630 PET.mk_tactic destruct_all