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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23 * http://cs.unibo.it/helm/.
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
44 if debug then (fun x -> prerr_endline (Lazy.force x)) else (fun _ -> ())
46 (* funzione generale di rilocazione dei riferimenti locali *)
48 let relocate_term map t =
49 let rec map_xnss k xnss =
50 let imap (uri, t) = uri, map_term k t in
55 | Some t -> Some (map_term k t)
59 let imap (name, i, ty, bo) = name, i, map_term k ty, map_term (k + len) bo in
61 and map_cfs len k cfs =
62 let imap (name, ty, bo) = name, map_term k ty, map_term (k + len) bo in
64 and map_term k = function
65 | C.Rel m -> if m < k then C.Rel m else C.Rel (map (m - k))
67 | C.Implicit _ as t -> t
68 | C.Var (uri, xnss) -> C.Var (uri, map_xnss k xnss)
69 | C.Const (uri, xnss) -> C.Const (uri, map_xnss k xnss)
70 | C.MutInd (uri, tyno, xnss) -> C.MutInd (uri, tyno, map_xnss k xnss)
71 | C.MutConstruct (uri, tyno, consno, xnss) ->
72 C.MutConstruct (uri, tyno, consno, map_xnss k xnss)
73 | C.Meta (i, mss) -> C.Meta(i, map_mss k mss)
74 | C.Cast (te, ty) -> C.Cast (map_term k te, map_term k ty)
75 | C.Appl ts -> C.Appl (List.map (map_term k) ts)
76 | C.MutCase (sp, i, outty, t, pl) ->
77 C.MutCase (sp, i, map_term k outty, map_term k t, List.map (map_term k) pl)
78 | C.Prod (n, s, t) -> C.Prod (n, map_term k s, map_term (succ k) t)
79 | C.Lambda (n, s, t) -> C.Lambda (n, map_term k s, map_term (succ k) t)
80 | C.LetIn (n, s, t) -> C.LetIn (n, map_term k s, map_term (succ k) t)
81 | C.Fix (i, fs) -> C.Fix (i, map_fs (List.length fs) k fs)
82 | C.CoFix (i, cfs) -> C.CoFix (i, map_cfs (List.length cfs) k cfs)
88 let after continuation aftermap beforemap =
89 continuation ~map:(fun n -> aftermap (beforemap n))
91 let after2 continuation aftermap beforemap ~map =
92 continuation ~map:(fun n -> map (aftermap (beforemap n)))
94 (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
97 let discriminate_tac ~term =
99 match LibraryObjects.true_URI () with
101 | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
103 match LibraryObjects.false_URI () with
105 | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
106 let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
107 let find_discriminating_consno t1 t2 =
110 | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
111 | C.Appl ((C.MutConstruct _ as constr1) :: args1),
112 C.Appl ((C.MutConstruct _ as constr2) :: args2)
113 when constr1 = constr2 ->
114 let rec aux_list l1 l2 =
117 | hd1 :: tl1, hd2 :: tl2 ->
118 (match aux hd1 hd2 with
119 | None -> aux_list tl1 tl2
120 | Some _ as res -> res)
121 | _ -> (* same constructor applied to a different number of args *)
125 | ((C.MutConstruct (_,_,consno1,subst1)),
126 (C.MutConstruct (_,_,consno2,subst2)))
127 | ((C.MutConstruct (_,_,consno1,subst1)),
128 (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
129 | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
130 (C.MutConstruct (_,_,consno2,subst2)))
131 | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
132 (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
133 when (consno1 <> consno2) || (subst1 <> subst2) ->
135 | _ -> fail "not a discriminable equality"
139 let mk_branches_and_outtype turi typeno consno context args =
140 (* a list of "True" except for the element in position consno which
142 match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
143 | C.InductiveDefinition (ind_type_list,_,paramsno,_) ->
144 let _,_,rty,constructor_list = List.nth ind_type_list typeno in
145 let false_constr_id,_ = List.nth constructor_list (consno - 1) in
149 (* dubbio: e' corretto ridurre in questo context ??? *)
150 let red_ty = CR.whd context cty in
153 | C.Prod (_,_,target) when (k <= paramsno) ->
154 S.subst (List.nth args (k-1))
156 | C.Prod (binder,source,target) when (k > paramsno) ->
157 C.Lambda (binder, source, (aux target (k+1)))
159 if (id = false_constr_id)
160 then (C.MutInd(false_URI,0,[]))
161 else (C.MutInd(true_URI,0,[]))
163 (S.lift 1 (aux red_ty 1)))
167 let rec mk_lambdas rev_left_args =
169 0, args, C.Prod (_,so,ta) ->
171 (C.Name (incr seed; "x" ^ string_of_int !seed),
173 mk_lambdas rev_left_args (0,args,ta))
174 | 0, args, C.Sort _ ->
178 | n -> C.Rel n :: mk_rels (n - 1) in
179 let argsno = List.length args in
182 (if argsno + List.length rev_left_args > 0 then
184 (C.MutInd (turi, typeno, []) ::
186 (S.lift (argsno + 1))
187 (List.rev rev_left_args)) @
190 C.MutInd (turi,typeno,[])),
192 | 0, _, _ -> assert false (* seriously screwed up *)
193 | n, he::tl, C.Prod (_,_,ta) ->
194 mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
196 assert false (* we should probably reduce in some context *)
198 mk_lambdas [] (paramsno, args, rty)
203 let discriminate'_tac ~term status =
204 let (proof, goal) = status in
205 let _,metasenv,_subst,_,_, _ = proof in
206 let _,context,_ = CicUtil.lookup_meta goal metasenv in
208 CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
211 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
212 when LibraryObjects.is_eq_URI equri ->
213 let turi,typeno,exp_named_subst,args =
215 | (C.MutInd (turi,typeno,exp_named_subst)) ->
216 turi,typeno,exp_named_subst,[]
217 | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) ->
218 turi,typeno,exp_named_subst,args
219 | _ -> fail "not a discriminable equality"
222 match find_discriminating_consno t1 t2 with
223 | Some consno -> consno
224 | None -> fail "discriminating terms are structurally equal"
226 let branches,outtype =
227 mk_branches_and_outtype turi typeno consno context args
231 ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
236 ~pattern:(PET.conclusion_pattern None)
239 C.Lambda ( C.Name "x", tty,
240 C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
246 (ET.rewrite_simpl_tac
247 ~direction:`RightToLeft
248 ~pattern:(PET.conclusion_pattern None)
251 (IntroductionTactics.constructor_tac ~n:1)))) status
252 | _ -> fail "not an equality"
254 PET.mk_tactic (discriminate'_tac ~term)
257 PET.Fail (lazy "Injection: not a projectable equality")
259 PET.Fail (lazy "Injection: not an equality")
260 let exn_nothingtodo =
261 PET.Fail (lazy "Nothing to do")
262 let exn_discrnonind =
263 PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
264 let exn_injwronggoal =
265 PET.Fail (lazy "Injection: goal after cut is not correct")
267 PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
270 let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
273 let clear_term first_time context term =
274 let g () = if first_time then raise exn_nothingtodo else T.id_tac in
277 begin match List.nth context (pred n) with
278 | Some (C.Name id, _) -> PST.clear ~hyps:[id]
283 let simpl_in_term context = function
285 let name = match List.nth context (pred i) with
286 | Some (Cic.Name s, Cic.Def _) -> s
287 | Some (Cic.Name s, Cic.Decl _) -> s
290 RT.simpl_tac ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None)
291 | _ -> raise exn_nonproj
293 (* ~term vive nel contesto della tattica una volta ~mappato
294 * ~continuation riceve la mappa assoluta
296 let rec injection_tac ~map ~term ~i ~continuation =
297 let give_name seed = function
298 | C.Name _ as name -> name
299 | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
301 let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
302 let injection_tac status =
303 let (proof, goal) = status in
304 (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma
305 * differiscono (o potrebbero differire?) nell'i-esimo parametro
307 let _,metasenv,_subst,_,_, _ = proof in
308 let _,context,_ = CicUtil.lookup_meta goal metasenv in
309 let term = relocate_term map term in
311 CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
313 debug_print (lazy ("\ninjection su : " ^ pp context termty));
314 match termty with (* an equality *)
315 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
316 when LibraryObjects.is_eq_URI equri ->
317 let turi,typeno,ens,params =
318 match tty with (* some inductive type *)
319 | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[]
320 | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params
321 | _ -> raise exn_noneqind
323 let t1',t2',consno = (* sono i due sottotermini che differiscono *)
325 | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
326 C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
327 when (uri1 = uri2) && (typeno1 = typeno2) &&
328 (consno1 = consno2) && (ens1 = ens2) ->
329 (* controllo ridondante *)
330 List.nth applist1 (pred i),List.nth applist2 (pred i),consno2
333 let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in
334 let patterns,outtype =
335 match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
336 | C.InductiveDefinition (ind_type_list,_,paramsno,_)->
337 let left_params, right_params = HExtlib.split_nth paramsno params in
338 let _,_,_,constructor_list = List.nth ind_type_list typeno in
339 let i_constr_id,_ = List.nth constructor_list (consno - 1) in
343 (function (id,cty) ->
344 let reduced_cty = CR.whd context cty in
345 let rec aux k = function
346 | C.Prod (_,_,tgt) when k <= paramsno ->
347 let left = List.nth left_params (k-1) in
348 aux (k+1) (S.subst left tgt)
349 | C.Prod (binder,source,target) when k > paramsno ->
350 let binder' = give_name seed binder in
351 C.Lambda (binder',source,(aux (k+1) target))
353 let nr_param_constr = k - paramsno - 1 in
354 if id = i_constr_id then C.Rel (k - i)
355 else S.lift nr_param_constr t1'
356 (* + 1 per liftare anche il lambda aggiunto
357 * esternamente al case *)
358 in S.lift 1 (aux 1 reduced_cty))
361 (* this code should be taken from cases_tac *)
364 let rec to_lambdas te head =
365 match CR.whd context te with
366 | C.Prod (binder,so,ta) ->
367 let binder' = give_name seed binder in
368 C.Lambda (binder',so,to_lambdas ta head)
371 let rec skip_prods params te =
372 match params, CR.whd context te with
374 | left::tl, C.Prod (_,_,ta) ->
375 skip_prods tl (S.subst left ta)
376 | _, _ -> assert false
380 List.fold_left (fun x y -> S.subst y x) tty left_params
382 (* non lift, ma subst coi left! *)
383 match S.lift 1 tty with
384 | C.MutInd _ as tty' -> tty'
386 let keep,abstract = HExtlib.split_nth (paramsno +1) l in
387 let keep = List.map (S.lift paramsno) keep in
388 C.Appl (keep@mk_rels (List.length abstract))
391 match ind_type_list with
394 (* this is in general wrong, do as in cases_tac *)
395 to_lambdas (skip_prods left_params ty)
397 (C.Name "cased", abstracted_tty,
398 (* here we should capture right parameters *)
399 (* 1 for his Lambda, one for the Lambda outside the match
400 * and then one for each to_lambda *)
401 S.lift (2+List.length right_params) tty'))
404 | _ -> raise exn_discrnonind
406 let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in
408 C.Appl [ C.Lambda (C.Name "x", tty,
409 C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1]
411 (* check if cutted and changed are well typed and if t1' ~ changed *)
414 let _,g = CTC.type_of_aux' metasenv context cutted
417 let _,g = CTC.type_of_aux' metasenv context changed g in
418 fst (CR.are_convertible ~metasenv context t1' changed g)
420 | CTC.TypeCheckerFailure _ -> false
423 PET.apply_tactic (continuation ~map) status
427 debug_print (lazy "riempio il cut");
428 let (proof, goal) = status in
429 let _,metasenv,_subst,_,_, _ = proof in
430 let _,context,gty = CicUtil.lookup_meta goal metasenv in
431 let gty = Unshare.unshare gty in
432 let new_t1' = match gty with
433 | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t
434 | _ -> raise exn_injwronggoal
436 debug_print (lazy ("metto: " ^ pp context changed));
437 debug_print (lazy ("al posto di: " ^ pp context new_t1'));
438 debug_print (lazy ("nel goal: " ^ pp context gty));
439 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
440 debug_print (lazy ("e poi rewrite con: "^pp context term));
441 let tac = T.seq ~tactics:[
443 ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1']))
444 (fun _ m u -> changed,m,u);
446 ~direction:`LeftToRight
447 ~pattern:(PET.conclusion_pattern None)
451 PET.apply_tactic tac status
455 debug_print (lazy ("CUT: " ^ pp context cutted));
457 (T.thens ~start: (P.cut_tac cutted)
459 (destruct ~first_time:false ~term:(C.Rel 1) ~map:id
460 ~continuation:(after2 continuation succ map)
464 | _ -> raise exn_noneq
466 PET.mk_tactic injection_tac
468 (* ~term vive nel contesto della tattica una volta ~mappato
469 * ~continuation riceve la mappa assoluta
471 and subst_tac ~map ~term ~direction ~where ~continuation =
472 let fail_tactic = continuation ~map in
473 let subst_tac status =
474 let term = relocate_term map term in
475 let tactic = match where with
477 let pattern = PET.conclusion_pattern None in
478 let tactic = ET.rewrite_tac ~direction ~pattern term [] in
479 T.then_ ~start:(T.try_tactic ~tactic)
480 ~continuation:fail_tactic
482 let pattern = None, [name, PET.hole], None in
483 let start = ET.rewrite_tac ~direction ~pattern term [] in
485 destruct ~first_time:false ~term:(C.Rel 1) ~map:id
486 ~continuation:(after2 continuation succ map)
488 T.if_ ~start ~continuation ~fail:fail_tactic
490 PET.apply_tactic tactic status
492 PET.mk_tactic subst_tac
494 (* ~term vive nel contesto della tattica una volta ~mappato
495 * ~continuation riceve la mappa assoluta
497 and destruct ~first_time ~map ~term ~continuation =
498 let are_convertible hd1 hd2 metasenv context =
499 fst (CR.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph)
501 let destruct status =
502 let (proof, goal) = status in
503 let _,metasenv,_subst, _,_, _ = proof in
504 let _,context,_ = CicUtil.lookup_meta goal metasenv in
505 let term = relocate_term map term in
506 debug_print (lazy ("\nqnify di: " ^ pp context term));
507 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
509 CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
511 debug_print (lazy ("\nqnify su: " ^ pp context termty));
512 let tac = match termty with
513 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
514 when LibraryObjects.is_eq_URI equri -> begin
515 match (CR.whd ~delta:true context tty) with
517 | C.Appl (C.MutInd _ :: _) ->
518 begin match t1,t2 with
522 T.then_ ~start:(clear_term first_time context term)
523 ~continuation:(continuation ~map)
524 | C.Appl (C.MutConstruct _ as mc1 :: applist1),
525 C.Appl (C.MutConstruct _ as mc2 :: applist2)
527 let rec traverse_list first_time i l1 l2 =
531 T.then_ ~start:(clear_term first_time context term)
532 ~continuation:(after continuation aftermap map)
533 | hd1 :: tl1, hd2 :: tl2 ->
534 if are_convertible hd1 hd2 metasenv context then
535 traverse_list first_time (succ i) tl1 tl2
537 injection_tac ~i ~term ~continuation:
538 (traverse_list false (succ i) tl1 tl2)
540 (* i 2 termini hanno in testa lo stesso costruttore,
541 * ma applicato a un numero diverso di termini *)
543 traverse_list first_time 1 applist1 applist2 ~map:id
544 | C.MutConstruct (_,_,consno1,ens1),
545 C.MutConstruct (_,_,consno2,ens2)
546 | C.MutConstruct (_,_,consno1,ens1),
547 C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
548 | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
549 C.MutConstruct (_,_,consno2,ens2)
550 | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
551 C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
552 when (consno1 <> consno2) || (ens1 <> ens2) ->
553 discriminate_tac ~term
554 | _ when not first_time -> continuation ~map
555 | _ (* when first_time *) ->
556 T.then_ ~start:(simpl_in_term context term)
557 ~continuation:(destruct ~first_time:false ~term ~map ~continuation)
559 | _ when not first_time -> continuation ~map
560 | _ (* when first_time *) -> raise exn_nonproj
562 | _ -> raise exn_nonproj
564 PET.apply_tactic tac status
566 PET.mk_tactic destruct
568 (* destruct performs either injection or discriminate *)
569 (* equivalent to Coq's "analyze equality" *)
572 ~first_time:true ~map:id ~continuation:(fun ~map -> T.id_tac)