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
43 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 comp f g n = f (g n)
90 (* term ha tipo t1=t2; funziona solo se t1 e t2 hanno in testa costruttori
93 let discriminate_tac ~term =
95 match LibraryObjects.true_URI () with
97 | None -> raise (PET.Fail (lazy "You need to register the default \"true\" definition first. Please use the \"default\" command")) in
99 match LibraryObjects.false_URI () with
101 | None -> raise (PET.Fail (lazy "You need to register the default \"false\" definition first. Please use the \"default\" command")) in
102 let fail msg = raise (PET.Fail (lazy ("Discriminate: " ^ msg))) in
103 let find_discriminating_consno t1 t2 =
106 | C.MutConstruct _, C.MutConstruct _ when t1 = t2 -> None
107 | C.Appl ((C.MutConstruct _ as constr1) :: args1),
108 C.Appl ((C.MutConstruct _ as constr2) :: args2)
109 when constr1 = constr2 ->
110 let rec aux_list l1 l2 =
113 | hd1 :: tl1, hd2 :: tl2 ->
114 (match aux hd1 hd2 with
115 | None -> aux_list tl1 tl2
116 | Some _ as res -> res)
117 | _ -> (* same constructor applied to a different number of args *)
121 | ((C.MutConstruct (_,_,consno1,subst1)),
122 (C.MutConstruct (_,_,consno2,subst2)))
123 | ((C.MutConstruct (_,_,consno1,subst1)),
124 (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
125 | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
126 (C.MutConstruct (_,_,consno2,subst2)))
127 | ((C.Appl ((C.MutConstruct (_,_,consno1,subst1)) :: _)),
128 (C.Appl ((C.MutConstruct (_,_,consno2,subst2)) :: _)))
129 when (consno1 <> consno2) || (subst1 <> subst2) ->
131 | _ -> fail "not a discriminable equality"
135 let mk_branches_and_outtype turi typeno consno context args =
136 (* a list of "True" except for the element in position consno which
138 match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
139 | C.InductiveDefinition (ind_type_list,_,paramsno,_) ->
140 let _,_,rty,constructor_list = List.nth ind_type_list typeno in
141 let false_constr_id,_ = List.nth constructor_list (consno - 1) in
145 (* dubbio: e' corretto ridurre in questo context ??? *)
146 let red_ty = CR.whd context cty in
149 | C.Prod (_,_,target) when (k <= paramsno) ->
150 S.subst (List.nth args (k-1))
152 | C.Prod (binder,source,target) when (k > paramsno) ->
153 C.Lambda (binder, source, (aux target (k+1)))
155 if (id = false_constr_id)
156 then (C.MutInd(false_URI,0,[]))
157 else (C.MutInd(true_URI,0,[]))
159 (S.lift 1 (aux red_ty 1)))
163 let rec mk_lambdas rev_left_args =
165 0, args, C.Prod (_,so,ta) ->
167 (C.Name (incr seed; "x" ^ string_of_int !seed),
169 mk_lambdas rev_left_args (0,args,ta))
170 | 0, args, C.Sort _ ->
174 | n -> C.Rel n :: mk_rels (n - 1) in
175 let argsno = List.length args in
178 (if argsno + List.length rev_left_args > 0 then
180 (C.MutInd (turi, typeno, []) ::
182 (S.lift (argsno + 1))
183 (List.rev rev_left_args)) @
186 C.MutInd (turi,typeno,[])),
188 | 0, _, _ -> assert false (* seriously screwed up *)
189 | n, he::tl, C.Prod (_,_,ta) ->
190 mk_lambdas (he::rev_left_args)(n-1,tl,S.subst he ta)
192 assert false (* we should probably reduce in some context *)
194 mk_lambdas [] (paramsno, args, rty)
199 let discriminate'_tac ~term status =
200 let (proof, goal) = status in
201 let _,metasenv,_subst,_,_, _ = proof in
202 let _,context,_ = CicUtil.lookup_meta goal metasenv in
204 CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
207 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
208 when LibraryObjects.is_eq_URI equri ->
209 let turi,typeno,exp_named_subst,args =
211 | (C.MutInd (turi,typeno,exp_named_subst)) ->
212 turi,typeno,exp_named_subst,[]
213 | (C.Appl (C.MutInd (turi,typeno,exp_named_subst)::args)) ->
214 turi,typeno,exp_named_subst,args
215 | _ -> fail "not a discriminable equality"
218 match find_discriminating_consno t1 t2 with
219 | Some consno -> consno
220 | None -> fail "discriminating terms are structurally equal"
222 let branches,outtype =
223 mk_branches_and_outtype turi typeno consno context args
227 ~start:(EliminationTactics.elim_type_tac (C.MutInd (false_URI, 0, [])))
232 ~pattern:(PET.conclusion_pattern None)
235 C.Lambda ( C.Name "x", tty,
236 C.MutCase (turi, typeno, outtype, (C.Rel 1), branches));
242 (EqualityTactics.rewrite_simpl_tac
243 ~direction:`RightToLeft
244 ~pattern:(PET.conclusion_pattern None)
247 (IntroductionTactics.constructor_tac ~n:1)))) status
248 | _ -> fail "not an equality"
250 PET.mk_tactic (discriminate'_tac ~term)
253 PET.Fail (lazy "Injection: not a projectable equality")
255 PET.Fail (lazy "Injection: not an equality")
256 let exn_nothingtodo =
257 PET.Fail (lazy "Nothing to do")
258 let exn_discrnonind =
259 PET.Fail (lazy "Discriminate: object is not an Inductive Definition: it's imposible")
260 let exn_injwronggoal =
261 PET.Fail (lazy "Injection: goal after cut is not correct")
263 PET.Fail (lazy "Injection: not an equality over elements of an inductive type")
266 let names = List.map (function Some (n,_) -> Some n | None -> None) ctx in
269 let clear_term first_time context term =
270 let g () = if first_time then raise exn_nothingtodo else T.id_tac in
273 begin match List.nth context (pred n) with
274 | Some (C.Name id, _) -> PST.clear ~hyps:[id]
279 let simpl_in_term context = function
281 let name = match List.nth context (pred i) with
282 | Some (Cic.Name s, Cic.Def _) -> s
283 | Some (Cic.Name s, Cic.Decl _) -> s
286 RT.simpl_tac ~pattern:(None,[name,Cic.Implicit (Some `Hole)],None)
287 | _ -> raise exn_nonproj
289 (* ~term vive nel contesto della tattica
290 * ~continuation riceve la mappa relativa
292 let rec injection_tac ~term ~i ~continuation =
293 let give_name seed = function
294 | C.Name _ as name -> name
295 | C.Anonymous -> C.Name (incr seed; "y" ^ string_of_int !seed)
297 let rec mk_rels = function | 0 -> [] | n -> C.Rel n :: (mk_rels (n - 1)) in
298 let injection_tac status =
299 let (proof, goal) = status in
300 (* precondizione: t1 e t2 hanno in testa lo stesso costruttore ma
301 * differiscono (o potrebbero differire?) nell'i-esimo parametro
303 let _,metasenv,_subst,_,_, _ = proof in
304 let _,context,_ = CicUtil.lookup_meta goal metasenv in
306 CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
308 debug_print (lazy ("\ninjection su : " ^ pp context termty));
309 match termty with (* an equality *)
310 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
311 when LibraryObjects.is_eq_URI equri ->
312 let turi,typeno,ens,params =
313 match tty with (* some inductive type *)
314 | C.MutInd (turi,typeno,ens) -> turi,typeno,ens,[]
315 | C.Appl (C.MutInd (turi,typeno,ens)::params) -> turi,typeno,ens,params
316 | _ -> raise exn_noneqind
318 let t1',t2',consno = (* sono i due sottotermini che differiscono *)
320 | C.Appl ((C.MutConstruct (uri1,typeno1,consno1,ens1))::applist1),
321 C.Appl ((C.MutConstruct (uri2,typeno2,consno2,ens2))::applist2)
322 when (uri1 = uri2) && (typeno1 = typeno2) &&
323 (consno1 = consno2) && (ens1 = ens2) ->
324 (* controllo ridondante *)
325 List.nth applist1 (i-1),List.nth applist2 (i-1),consno2
328 let tty',_ = CTC.type_of_aux' metasenv context t1' CU.empty_ugraph in
329 let patterns,outtype =
330 match fst (CicEnvironment.get_obj CicUniv.empty_ugraph turi) with
331 | C.InductiveDefinition (ind_type_list,_,paramsno,_)->
332 let left_params, right_params = HExtlib.split_nth paramsno params in
333 let _,_,_,constructor_list = List.nth ind_type_list typeno in
334 let i_constr_id,_ = List.nth constructor_list (consno - 1) in
338 (function (id,cty) ->
339 let reduced_cty = CR.whd context cty in
340 let rec aux k = function
341 | C.Prod (_,_,tgt) when k <= paramsno ->
342 let left = List.nth left_params (k-1) in
343 aux (k+1) (S.subst left tgt)
344 | C.Prod (binder,source,target) when k > paramsno ->
345 let binder' = give_name seed binder in
346 C.Lambda (binder',source,(aux (k+1) target))
348 let nr_param_constr = k - paramsno - 1 in
349 if id = i_constr_id then C.Rel (k - i)
350 else S.lift nr_param_constr t1'
351 (* + 1 per liftare anche il lambda aggiunto
352 * esternamente al case *)
353 in S.lift 1 (aux 1 reduced_cty))
356 (* this code should be taken from cases_tac *)
359 let rec to_lambdas te head =
360 match CR.whd context te with
361 | C.Prod (binder,so,ta) ->
362 let binder' = give_name seed binder in
363 C.Lambda (binder',so,to_lambdas ta head)
366 let rec skip_prods params te =
367 match params, CR.whd context te with
369 | left::tl, C.Prod (_,_,ta) ->
370 skip_prods tl (S.subst left ta)
371 | _, _ -> assert false
375 List.fold_left (fun x y -> S.subst y x) tty left_params
377 (* non lift, ma subst coi left! *)
378 match S.lift 1 tty with
379 | C.MutInd _ as tty' -> tty'
381 let keep,abstract = HExtlib.split_nth (paramsno +1) l in
382 let keep = List.map (S.lift paramsno) keep in
383 C.Appl (keep@mk_rels (List.length abstract))
386 match ind_type_list with
389 (* this is in general wrong, do as in cases_tac *)
390 to_lambdas (skip_prods left_params ty)
392 (C.Name "cased", abstracted_tty,
393 (* here we should capture right parameters *)
394 (* 1 for his Lambda, one for the Lambda outside the match
395 * and then one for each to_lambda *)
396 S.lift (2+List.length right_params) tty'))
399 | _ -> raise exn_discrnonind
401 let cutted = C.Appl [C.MutInd (equri,0,[]) ; tty' ; t1' ; t2'] in
403 C.Appl [ C.Lambda (C.Name "x", tty,
404 C.MutCase (turi,typeno,outtype,C.Rel 1,patterns)) ; t1]
406 (* check if cutted and changed are well typed and if t1' ~ changed *)
409 let _,g = CTC.type_of_aux' metasenv context cutted
412 let _,g = CTC.type_of_aux' metasenv context changed g in
413 fst (CR.are_convertible ~metasenv context t1' changed g)
415 | CTC.TypeCheckerFailure _ -> false
418 PET.apply_tactic T.id_tac status (* FG: ??????? *)
422 debug_print (lazy "riempio il cut");
423 let (proof, goal) = status in
424 let _,metasenv,_subst,_,_, _ = proof in
425 let _,context,gty = CicUtil.lookup_meta goal metasenv in
426 let gty = Unshare.unshare gty in
427 let new_t1' = match gty with
428 | (C.Appl (C.MutInd (_,_,_)::_::t::_)) -> t
429 | _ -> raise exn_injwronggoal
431 debug_print (lazy ("metto: " ^ pp context changed));
432 debug_print (lazy ("al posto di: " ^ pp context new_t1'));
433 debug_print (lazy ("nel goal: " ^ pp context gty));
434 debug_print (lazy ("nel contesto:\n" ^ CicPp.ppcontext context));
435 debug_print (lazy ("e poi rewrite con: "^pp context term));
436 let tac = T.seq ~tactics:[
438 ~pattern:(None, [], Some (PEH.pattern_of ~term:gty [new_t1']))
439 (fun _ m u -> changed,m,u);
440 EqualityTactics.rewrite_simpl_tac
441 ~direction:`LeftToRight
442 ~pattern:(PET.conclusion_pattern None)
444 EqualityTactics.reflexivity_tac
446 PET.apply_tactic tac status
450 debug_print (lazy ("CUT: " ^ pp context cutted));
451 let continuation ~map = continuation ~map:(comp succ map) in
453 (T.thens ~start: (P.cut_tac cutted)
455 (qnify_tac ~first_time:false ~term:(C.Rel 1) ~map:id
459 | _ -> raise exn_noneq
461 PET.mk_tactic injection_tac
463 (* ~term vive nel contesto della tattica una volta ~mappato
464 * ~continuation riceve la mappa relativa
466 and qnify_tac ~first_time ~map ~term ~continuation =
467 let are_convertible hd1 hd2 metasenv context =
468 fst (CR.are_convertible ~metasenv context hd1 hd2 CicUniv.empty_ugraph)
470 let qnify_tac status =
471 let (proof, goal) = status in
472 let _,metasenv,_subst, _,_, _ = proof in
473 let _,context,_ = CicUtil.lookup_meta goal metasenv in
474 let term = relocate_term map term in
476 CTC.type_of_aux' metasenv context term CicUniv.empty_ugraph
478 debug_print (lazy ("\nqnify su: " ^ pp context termty));
479 let tac = match termty with
480 | C.Appl [(C.MutInd (equri, 0, [])) ; tty ; t1 ; t2]
481 when LibraryObjects.is_eq_URI equri -> begin
482 match (CR.whd ~delta:true context tty) with
484 | C.Appl (C.MutInd _ :: _) ->
485 begin match t1,t2 with
489 T.then_ ~start:(clear_term first_time context term)
490 ~continuation:(continuation ~map:id)
491 | C.Appl (C.MutConstruct _ as mc1 :: applist1),
492 C.Appl (C.MutConstruct _ as mc2 :: applist2)
494 let rec traverse_list i l1 l2 = match l1, l2 with
496 T.then_ ~start:(clear_term first_time context term)
497 ~continuation:(continuation ~map:id)
498 | hd1 :: tl1, hd2 :: tl2 ->
499 if are_convertible hd1 hd2 metasenv context then
500 traverse_list (succ i) tl1 tl2
502 injection_tac ~i ~term ~continuation:
503 (qnify_tac ~first_time:false ~term ~continuation)
505 (* i 2 termini hanno in testa lo stesso costruttore,
506 * ma applicato a un numero diverso di termini *)
508 traverse_list 1 applist1 applist2
509 | C.MutConstruct (_,_,consno1,ens1),
510 C.MutConstruct (_,_,consno2,ens2)
511 | C.MutConstruct (_,_,consno1,ens1),
512 C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
513 | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
514 C.MutConstruct (_,_,consno2,ens2)
515 | C.Appl ((C.MutConstruct (_,_,consno1,ens1))::_),
516 C.Appl ((C.MutConstruct (_,_,consno2,ens2))::_)
517 when (consno1 <> consno2) || (ens1 <> ens2) ->
518 discriminate_tac ~term
519 | _ when not first_time -> continuation ~map:id
520 | _ (* when first_time *) ->
521 T.then_ ~start:(simpl_in_term context term)
522 ~continuation:(qnify_tac ~first_time:false ~term ~map:id ~continuation)
524 | _ when not first_time -> continuation ~map:id
525 | _ (* when first_time *) -> raise exn_nonproj
527 | _ -> raise exn_nonproj
529 PET.apply_tactic tac status
531 PET.mk_tactic qnify_tac
533 (* destruct performs either injection or discriminate *)
534 (* equivalent to Coq's "analyze equality" *)
537 ~first_time:true ~map:id ~continuation:(fun ~map -> T.id_tac)