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
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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.
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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/.
28 exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
29 exception NotAnInductiveTypeToEliminate
30 exception WrongUriToVariable of string
31 exception NotAnEliminator
33 module PET = ProofEngineTypes
35 (* lambda_abstract newmeta ty *)
36 (* returns a triple [bo],[context],[ty'] where *)
37 (* [ty] = Pi/LetIn [context].[ty'] ([context] is a vector!) *)
38 (* and [bo] = Lambda/LetIn [context].(Meta [newmeta]) *)
39 (* So, lambda_abstract is the core of the implementation of *)
40 (* the Intros tactic. *)
41 (* howmany = -1 means Intros, howmany > 0 means Intros n *)
42 let lambda_abstract ?(howmany=(-1)) metasenv context newmeta ty mk_fresh_name =
44 let rec collect_context context howmany do_whd ty =
48 CicMkImplicit.identity_relocation_list_for_metavariable context
50 context, ty, (C.Meta (newmeta,irl))
53 C.Cast (te,_) -> collect_context context howmany do_whd te
55 let n' = mk_fresh_name metasenv context n ~typ:s in
56 let (context',ty,bo) =
57 let entry = match n' with
58 | C.Name _ -> Some (n',(C.Decl s))
61 let ctx = entry :: context in
62 collect_context ctx (howmany - 1) do_whd t
64 (context',ty,C.Lambda(n',s,bo))
65 | C.LetIn (n,s,sty,t) ->
66 let (context',ty,bo) =
67 collect_context ((Some (n,(C.Def (s,sty))))::context) (howmany - 1) do_whd t
69 (context',ty,C.LetIn(n,s,sty,bo))
73 CicMkImplicit.identity_relocation_list_for_metavariable context
75 context, t, (C.Meta (newmeta,irl))
77 let t = CicReduction.whd ~delta:true context t in
78 collect_context context howmany false t
80 raise (PET.Fail (lazy "intro(s): not enough products or let-ins"))
82 collect_context context howmany true ty
84 let eta_expand metasenv context t arg =
85 let module T = CicTypeChecker in
86 let module S = CicSubstitution in
90 t' when t' = S.lift n arg -> C.Rel (1 + n)
91 | C.Rel m -> if m <= n then C.Rel m else C.Rel (m+1)
92 | C.Var (uri,exp_named_subst) ->
93 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
94 C.Var (uri,exp_named_subst')
97 List.map (function None -> None | Some t -> Some (aux n t)) l
101 | C.Implicit _ as t -> t
102 | C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
103 | C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
104 | C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
105 | C.LetIn (nn,s,ty,t) -> C.LetIn (nn, aux n s, aux n ty, aux (n+1) t)
106 | C.Appl l -> C.Appl (List.map (aux n) l)
107 | C.Const (uri,exp_named_subst) ->
108 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
109 C.Const (uri,exp_named_subst')
110 | C.MutInd (uri,i,exp_named_subst) ->
111 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
112 C.MutInd (uri,i,exp_named_subst')
113 | C.MutConstruct (uri,i,j,exp_named_subst) ->
114 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
115 C.MutConstruct (uri,i,j,exp_named_subst')
116 | C.MutCase (sp,i,outt,t,pl) ->
117 C.MutCase (sp,i,aux n outt, aux n t,
120 let tylen = List.length fl in
123 (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
126 C.Fix (i, substitutedfl)
128 let tylen = List.length fl in
131 (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
134 C.CoFix (i, substitutedfl)
135 and aux_exp_named_subst n =
136 List.map (function uri,t -> uri,aux n t)
139 T.type_of_aux' metasenv context arg CicUniv.empty_ugraph (* TASSI: FIXME *)
142 FreshNamesGenerator.mk_fresh_name ~subst:[]
143 metasenv context (Cic.Name "Heta") ~typ:argty
145 (C.Appl [C.Lambda (fresh_name,argty,aux 0 t) ; arg])
147 (*CSC: ma serve solamente la prima delle new_uninst e l'unione delle due!!! *)
148 let classify_metas newmeta in_subst_domain subst_in metasenv =
150 (fun (i,canonical_context,ty) (old_uninst,new_uninst) ->
151 if in_subst_domain i then
152 old_uninst,new_uninst
154 let ty' = subst_in canonical_context ty in
155 let canonical_context' =
157 (fun entry canonical_context' ->
160 Some (n,Cic.Decl s) ->
161 Some (n,Cic.Decl (subst_in canonical_context' s))
163 | Some (n,Cic.Def (bo,ty)) ->
167 (subst_in canonical_context' bo,
168 subst_in canonical_context' ty))
170 entry'::canonical_context'
171 ) canonical_context []
174 ((i,canonical_context',ty')::old_uninst),new_uninst
176 old_uninst,((i,canonical_context',ty')::new_uninst)
179 (* Useful only inside apply_tac *)
181 generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
183 let module C = Cic in
185 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
186 CicUtil.params_of_obj o
188 let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
189 let next_fresh_meta = ref newmeta in
190 let newmetasenvfragment = ref [] in
191 let exp_named_subst_diff = ref [] in
197 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
199 C.Variable (_,_,ty,_,_) ->
200 CicSubstitution.subst_vars !exp_named_subst_diff ty
201 | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
203 (* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
205 C.Sort (C.Type _) as s -> (* TASSI: ?? *)
206 let fresh_meta = !next_fresh_meta in
207 let fresh_meta' = fresh_meta + 1 in
208 next_fresh_meta := !next_fresh_meta + 2 ;
209 let subst_item = uri,C.Meta (fresh_meta',[]) in
210 newmetasenvfragment :=
211 (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
213 (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
214 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
215 subst_item::(aux (tl,[]))
219 CicMkImplicit.identity_relocation_list_for_metavariable context
221 let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
222 newmetasenvfragment :=
223 (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
224 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
225 incr next_fresh_meta ;
226 subst_item::(aux (tl,[]))(*)*)
227 | uri::tl1,((uri',_) as s)::tl2 ->
228 assert (UriManager.eq uri uri') ;
230 | [],_ -> assert false
232 let exp_named_subst' = aux (params,exp_named_subst) in
233 !exp_named_subst_diff,!next_fresh_meta,
234 List.rev !newmetasenvfragment, exp_named_subst'
236 new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
239 let new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty termty goal_arity =
240 let (consthead,newmetasenv,arguments,_) =
241 TermUtil.saturate_term newmeta' metasenv' context termty
243 let subst,newmetasenv',_ =
244 CicUnification.fo_unif_subst
245 subst context newmetasenv consthead ty CicUniv.empty_ugraph
248 if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
252 let rec count_prods context ty =
253 match CicReduction.whd context ty with
254 Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
257 let apply_with_subst ~term ~subst ~maxmeta (proof, goal) =
258 (* Assumption: The term "term" must be closed in the current context *)
259 let module T = CicTypeChecker in
260 let module R = CicReduction in
261 let module C = Cic in
262 let (_,metasenv,_subst,_,_, _) = proof in
263 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
264 let newmeta = max (CicMkImplicit.new_meta metasenv subst) maxmeta in
265 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
267 C.Var (uri,exp_named_subst) ->
268 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
269 generalize_exp_named_subst_with_fresh_metas context newmeta uri
272 exp_named_subst_diff,newmeta',newmetasenvfragment,
273 C.Var (uri,exp_named_subst')
274 | C.Const (uri,exp_named_subst) ->
275 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
276 generalize_exp_named_subst_with_fresh_metas context newmeta uri
279 exp_named_subst_diff,newmeta',newmetasenvfragment,
280 C.Const (uri,exp_named_subst')
281 | C.MutInd (uri,tyno,exp_named_subst) ->
282 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
283 generalize_exp_named_subst_with_fresh_metas context newmeta uri
286 exp_named_subst_diff,newmeta',newmetasenvfragment,
287 C.MutInd (uri,tyno,exp_named_subst')
288 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
289 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
290 generalize_exp_named_subst_with_fresh_metas context newmeta uri
293 exp_named_subst_diff,newmeta',newmetasenvfragment,
294 C.MutConstruct (uri,tyno,consno,exp_named_subst')
295 | _ -> [],newmeta,[],term
297 let metasenv' = metasenv@newmetasenvfragment in
299 CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph
302 CicSubstitution.subst_vars exp_named_subst_diff termty in
303 let goal_arity = count_prods context ty in
304 let subst,newmetasenv',t =
305 let rec add_one_argument n =
307 new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty
309 with CicUnification.UnificationFailure _ when n > 0 ->
310 add_one_argument (n - 1)
312 add_one_argument goal_arity
314 let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
315 let apply_subst = CicMetaSubst.apply_subst subst in
316 let old_uninstantiatedmetas,new_uninstantiatedmetas =
317 (* subst_in doesn't need the context. Hence the underscore. *)
318 let subst_in _ = CicMetaSubst.apply_subst subst in
319 classify_metas newmeta in_subst_domain subst_in newmetasenv'
321 let bo' = apply_subst t in
322 let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
324 (* if we just apply the subtitution, the type is irrelevant:
325 we may use Implicit, since it will be dropped *)
326 ((metano,(context,bo',Cic.Implicit None))::subst)
328 let (newproof, newmetasenv''') =
329 ProofEngineHelpers.subst_meta_and_metasenv_in_proof proof metano subst_in
332 let subst = ((metano,(context,bo',ty))::subst) in
334 (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas),
335 max maxmeta (CicMkImplicit.new_meta newmetasenv''' subst)
339 let apply_with_subst ~term ?(subst=[]) ?(maxmeta=0) status =
341 (* apply_tac_verbose ~term status *)
342 apply_with_subst ~term ~subst ~maxmeta status
343 (* TODO cacciare anche altre eccezioni? *)
345 | CicUnification.UnificationFailure msg
346 | CicTypeChecker.TypeCheckerFailure msg -> raise (PET.Fail msg)
349 let apply_tac_verbose ~term status =
350 let subst, status, _ = apply_with_subst ~term status in
351 (CicMetaSubst.apply_subst subst), status
353 let apply_tac ~term status = snd (apply_tac_verbose ~term status)
355 (* TODO per implementare i tatticali e' necessario che tutte le tattiche
356 sollevino _solamente_ Fail *)
357 let apply_tac ~term =
358 let apply_tac ~term status =
360 apply_tac ~term status
361 (* TODO cacciare anche altre eccezioni? *)
363 | CicUnification.UnificationFailure msg
364 | CicTypeChecker.TypeCheckerFailure msg ->
367 PET.mk_tactic (apply_tac ~term)
369 let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
370 let intros_tac (proof, goal)
372 let module C = Cic in
373 let module R = CicReduction in
374 let (_,metasenv,_subst,_,_, _) = proof in
375 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
376 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
377 let (context',ty',bo') =
378 lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
381 ProofEngineHelpers.subst_meta_in_proof proof metano bo'
382 [newmeta,context',ty']
384 (newproof, [newmeta])
386 PET.mk_tactic intros_tac
388 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
390 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
393 let module C = Cic in
394 let curi,metasenv,_subst,pbo,pty, attrs = proof in
395 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
396 let newmeta1 = ProofEngineHelpers.new_meta_of_proof ~proof in
397 let newmeta2 = newmeta1 + 1 in
399 mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
400 let context_for_newmeta1 =
401 (Some (fresh_name,C.Decl term))::context in
403 CicMkImplicit.identity_relocation_list_for_metavariable
407 CicMkImplicit.identity_relocation_list_for_metavariable context
409 let newmeta1ty = CicSubstitution.lift 1 ty in
411 Cic.LetIn (fresh_name, C.Meta (newmeta2,irl2), term, C.Meta (newmeta1,irl1))
414 ProofEngineHelpers.subst_meta_in_proof proof metano bo'
415 [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
417 (newproof, [newmeta1 ; newmeta2])
419 PET.mk_tactic (cut_tac ~mk_fresh_name_callback term)
421 let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
423 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
426 let module C = Cic in
427 let curi,metasenv,_subst,pbo,pty, attrs = proof in
430 let m = CicUtil.metas_of_term t in
431 List.exists (fun (j,_) -> i=j) m
433 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
434 if occur metano term then
436 (ProofEngineTypes.Fail (lazy
437 "You can't letin a term containing the current goal"));
439 CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
440 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
442 mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
443 let context_for_newmeta =
444 (Some (fresh_name,C.Def (term,tty)))::context in
446 CicMkImplicit.identity_relocation_list_for_metavariable
449 let newmetaty = CicSubstitution.lift 1 ty in
450 let bo' = C.LetIn (fresh_name,term,tty,C.Meta (newmeta,irl)) in
452 ProofEngineHelpers.subst_meta_in_proof
453 proof metano bo'[newmeta,context_for_newmeta,newmetaty]
455 (newproof, [newmeta])
457 PET.mk_tactic (letin_tac ~mk_fresh_name_callback term)
459 (** functional part of the "exact" tactic *)
460 let exact_tac ~term =
461 let exact_tac ~term (proof, goal) =
462 (* Assumption: the term bo must be closed in the current context *)
463 let (_,metasenv,_subst,_,_, _) = proof in
464 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
465 let module T = CicTypeChecker in
466 let module R = CicReduction in
467 let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
468 let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
471 let (newproof, metasenv') =
472 ProofEngineHelpers.subst_meta_in_proof proof metano term [] in
476 raise (PET.Fail (lazy "The type of the provided term is not the one expected."))
478 PET.mk_tactic (exact_tac ~term)
480 (* not really "primitive" tactics .... *)
482 module TC = CicTypeChecker
483 module UM = UriManager
484 module R = CicReduction
486 module PEH = ProofEngineHelpers
487 module PER = ProofEngineReduction
488 module MS = CicMetaSubst
489 module S = CicSubstitution
491 module RT = ReductionTactics
493 let rec args_init n f =
494 if n <= 0 then [] else f n :: args_init (pred n) f
496 let mk_predicate_for_elim
497 ~context ~metasenv ~ugraph ~goal ~arg ~using ~cpattern ~args_no =
498 let instantiated_eliminator =
499 let f n = if n = 1 then arg else C.Implicit None in
500 C.Appl (using :: args_init args_no f)
502 let _actual_arg, iety, _metasenv', _ugraph =
503 CicRefine.type_of_aux' metasenv context instantiated_eliminator ugraph
505 let _actual_meta, actual_args = match iety with
506 | C.Meta (i, _) -> i, []
507 | C.Appl (C.Meta (i, _) :: args) -> i, args
510 (* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
511 let rec mk_pred metasenv context' pred arg' cpattern' = function
512 | [] -> metasenv, pred, arg'
514 (* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
515 let argty, _ugraph = TC.type_of_aux' metasenv context arg ugraph in
516 let argty = CicReduction.whd context argty in
518 FreshNamesGenerator.mk_fresh_name
519 ~subst:[] metasenv context' C.Anonymous ~typ:argty
521 let hyp = Some (fresh_name, C.Decl argty) in
522 let lazy_term c m u =
523 let distance = List.length c - List.length context in
524 S.lift distance arg, m, u
526 let pattern = Some lazy_term, [], Some cpattern' in
527 let subst, metasenv, _ugraph, _conjecture, selected_terms =
528 ProofEngineHelpers.select
529 ~metasenv ~ugraph ~conjecture:(0, context, pred) ~pattern
531 let metasenv = MS.apply_subst_metasenv subst metasenv in
532 let map (_context_of_t, t) l = t :: l in
533 let what = List.fold_right map selected_terms [] in
534 let arg' = MS.apply_subst subst arg' in
535 let argty = MS.apply_subst subst argty in
536 let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
537 let pred = MS.apply_subst subst pred in
538 let pred = C.Lambda (fresh_name, argty, pred) in
539 let cpattern' = C.Lambda (C.Anonymous, C.Implicit None, cpattern') in
540 mk_pred metasenv (hyp :: context') pred arg' cpattern' tail
542 let metasenv, pred, arg =
543 mk_pred metasenv context goal arg cpattern (List.rev actual_args)
545 HLog.debug ("PREDICATE: " ^ CicPp.ppterm ~metasenv pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv) actual_args));
546 metasenv, pred, arg, actual_args
548 let beta_after_elim_tac upto predicate =
549 let beta_after_elim_tac status =
550 let proof, goal = status in
551 let _, metasenv, _subst, _, _, _ = proof in
552 let _, _, ty = CicUtil.lookup_meta goal metasenv in
553 let mk_pattern ~equality ~upto ~predicate ty =
554 (* code adapted from ProceduralConversion.generalize *)
555 let meta = C.Implicit None in
556 let hole = C.Implicit (Some `Hole) in
557 let anon = C.Anonymous in
560 | C.Implicit None when b -> b
563 List.fold_left map true
565 let rec gen_fix len k (name, i, ty, bo) =
566 name, i, gen_term k ty, gen_term (k + len) bo
567 and gen_cofix len k (name, ty, bo) =
568 name, gen_term k ty, gen_term (k + len) bo
569 and gen_term k = function
575 | C.MutConstruct (_, _, _, _)
578 | C.Appl (hd :: tl) when equality hd (S.lift k predicate) ->
579 assert (List.length tl = upto);
582 let ts = List.map (gen_term k) ts in
583 if is_meta ts then meta else C.Appl ts
585 let te, ty = gen_term k te, gen_term k ty in
586 if is_meta [te; ty] then meta else C.Cast (te, ty)
587 | C.MutCase (sp, i, outty, t, pl) ->
588 let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
589 if is_meta (outty :: t :: pl) then meta else hole (* C.MutCase (sp, i, outty, t, pl) *)
590 | C.Prod (_, s, t) ->
591 let s, t = gen_term k s, gen_term (succ k) t in
592 if is_meta [s; t] then meta else C.Prod (anon, s, t)
593 | C.Lambda (_, s, t) ->
594 let s, t = gen_term k s, gen_term (succ k) t in
595 if is_meta [s; t] then meta else C.Lambda (anon, s, t)
596 | C.LetIn (_, s, ty, t) ->
597 let s,ty,t = gen_term k s, gen_term k ty, gen_term (succ k) t in
598 if is_meta [s; t] then meta else C.LetIn (anon, s, ty, t)
599 | C.Fix (i, fl) -> C.Fix (i, List.map (gen_fix (List.length fl) k) fl)
600 | C.CoFix (i, fl) -> C.CoFix (i, List.map (gen_cofix (List.length fl) k) fl)
602 None, [], Some (gen_term 0 ty)
604 let equality = CicUtil.alpha_equivalence in
605 let pattern = mk_pattern ~equality ~upto ~predicate ty in
606 let tactic = RT.head_beta_reduce_tac ~delta:false ~upto ~pattern in
607 PET.apply_tactic tactic status
609 PET.mk_tactic beta_after_elim_tac
611 let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
612 let elim_tac (proof, goal) =
613 let cpattern = match pattern with
614 | None, [], Some cpattern -> cpattern
615 | _ -> raise (PET.Fail (lazy "not implemented"))
617 let ugraph = CicUniv.empty_ugraph in
618 let curi, metasenv, _subst, proofbo, proofty, attrs = proof in
619 let conjecture = CicUtil.lookup_meta goal metasenv in
620 let metano, context, ty = conjecture in
621 let termty,_ugraph = TC.type_of_aux' metasenv context term ugraph in
622 let termty = CicReduction.whd context termty in
623 let termty, metasenv', arguments, _fresh_meta =
624 TermUtil.saturate_term
625 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
626 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
627 let uri, exp_named_subst, typeno, _args =
629 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
630 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
631 (uri,exp_named_subst,typeno,args)
632 | _ -> raise NotAnInductiveTypeToEliminate
635 let buri = UM.buri_of_uri uri in
637 let o,_ugraph = CicEnvironment.get_obj ugraph uri in
639 C.InductiveDefinition (tys,_,_,_) ->
640 let (name,_,_,_) = List.nth tys typeno in
644 let ty_ty,_ugraph = TC.type_of_aux' metasenv' context ty ugraph in
647 C.Sort C.Prop -> "_ind"
648 | C.Sort C.Set -> "_rec"
649 | C.Sort C.CProp -> "_rec"
650 | C.Sort (C.Type _)-> "_rect"
651 | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
654 UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
656 let eliminator_ref = match using with
657 | None -> C.Const (eliminator_uri, exp_named_subst)
661 TC.type_of_aux' metasenv' context eliminator_ref ugraph in
662 (* FG: ADDED PART ***********************************************************)
663 (* FG: we can not assume eliminator is the default eliminator ***************)
664 let splits, args_no = PEH.split_with_whd (context, ety) in
665 let pred_pos = match List.hd splits with
666 | _, C.Rel i when i > 1 && i <= args_no -> i
667 | _, C.Appl (C.Rel i :: _) when i > 1 && i <= args_no -> i
668 | _ -> raise NotAnEliminator
670 let metasenv', pred, term, actual_args = match pattern with
671 | None, [], Some (C.Implicit (Some `Hole)) ->
672 metasenv', C.Implicit None, term, []
674 mk_predicate_for_elim
675 ~args_no ~context ~ugraph ~cpattern
676 ~metasenv:metasenv' ~arg:term ~using:eliminator_ref ~goal:ty
678 (* FG: END OF ADDED PART ****************************************************)
681 if n = pred_pos then pred else
682 if n = 1 then term else C.Implicit None
684 C.Appl (eliminator_ref :: args_init args_no f)
686 let refined_term,_refined_termty,metasenv'',_ugraph =
687 CicRefine.type_of_aux' metasenv' context term_to_refine ugraph
690 ProofEngineHelpers.compare_metasenvs
691 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
693 let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
694 let proof'', new_goals' =
695 PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
697 (* The apply_tactic can have closed some of the new_goals *)
698 let patched_new_goals =
699 let (_,metasenv''',_subst,_,_, _) = proof'' in
701 (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
702 new_goals @ new_goals'
704 let res = proof'', patched_new_goals in
705 let upto = List.length actual_args in
706 if upto = 0 then res else
707 let continuation = beta_after_elim_tac upto pred in
708 let dummy_status = proof,goal in
710 (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
713 PET.mk_tactic elim_tac
716 let cases_intros_tac ?(howmany=(-1)) ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
717 let cases_tac ~term (proof, goal) =
718 let module TC = CicTypeChecker in
719 let module U = UriManager in
720 let module R = CicReduction in
721 let module C = Cic in
722 let (curi,metasenv,_subst, proofbo,proofty, attrs) = proof in
723 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
724 let termty,_ = TC.type_of_aux' metasenv context term CicUniv.empty_ugraph in
725 let termty = CicReduction.whd context termty in
726 let (termty,metasenv',arguments,fresh_meta) =
727 TermUtil.saturate_term
728 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
729 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
730 let uri,exp_named_subst,typeno,args =
732 | C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
733 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
734 (uri,exp_named_subst,typeno,args)
735 | _ -> raise NotAnInductiveTypeToEliminate
737 let paramsno,itty,patterns,right_args =
738 match CicEnvironment.get_obj CicUniv.empty_ugraph uri with
739 | C.InductiveDefinition (tys,_,paramsno,_),_ ->
740 let _,left_parameters,right_args =
742 (fun x (n,acc1,acc2) ->
743 if n > 0 then (n-1,acc1,x::acc2) else (n,x::acc1,acc2))
744 args (List.length args - paramsno, [],[])
746 let _,_,itty,cl = List.nth tys typeno in
747 let rec aux left_parameters context t =
748 match left_parameters,CicReduction.whd context t with
749 | [],C.Prod (name,source,target) ->
751 mk_fresh_name_callback metasenv' context name ~typ:source
753 C.Lambda (fresh_name,C.Implicit None,
754 aux [] (Some (fresh_name,C.Decl source)::context) target)
755 | hd::tl,C.Prod (name,source,target) ->
756 (* left parameters instantiation *)
757 aux tl context (CicSubstitution.subst hd target)
758 | [],_ -> C.Implicit None
762 List.map (function (_,cty) -> aux left_parameters context cty) cl,
767 let n_right_args = List.length right_args in
768 let n_lambdas = n_right_args + 1 in
769 let lifted_ty = CicSubstitution.lift n_lambdas ty in
772 List.map (CicSubstitution.lift n_lambdas) (right_args)
775 let rec mkargs = function
779 (if meta then Cic.Implicit None else Cic.Rel n)::(mkargs (n-1))
783 let replaced = ref false in
784 let replace = ProofEngineReduction.replace_lifting
785 ~equality:(fun _ a b -> let rc = CicUtil.alpha_equivalence a b in
786 if rc then replaced := true; rc)
790 replace ~what:[CicSubstitution.lift n_lambdas term]
791 ~with_what:[Cic.Rel 1] ~where:lifted_ty
793 if not !replaced then
794 (* this means the matched term is not there,
795 * but maybe right params are: we user rels (to right args lambdas) *)
796 replace ~what ~with_what:(with_what false) ~where:captured
798 (* since the matched is there, rights should be inferrable *)
799 replace ~what ~with_what:(with_what true) ~where:captured
801 let captured_term_ty =
802 let term_ty = CicSubstitution.lift n_right_args termty in
803 let rec mkrels = function 0 -> []|n -> (Cic.Rel n)::(mkrels (n-1)) in
804 let rec fstn acc l n =
805 if n = 0 then acc else fstn (acc@[List.hd l]) (List.tl l) (n-1)
808 | C.MutInd _ -> term_ty
809 | C.Appl ((C.MutInd (a,b,c))::args) ->
810 C.Appl ((C.MutInd (a,b,c))::
811 fstn [] args paramsno @ mkrels n_right_args)
812 | _ -> raise NotAnInductiveTypeToEliminate
814 let rec add_lambdas = function
817 C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas 0))
819 C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
820 C.Implicit None, (add_lambdas (n-1)))
822 add_lambdas n_lambdas
824 let term_to_refine = C.MutCase (uri,typeno,outtype,term,patterns) in
825 let refined_term,_,metasenv'',_ =
826 CicRefine.type_of_aux' metasenv' context term_to_refine
830 ProofEngineHelpers.compare_metasenvs
831 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
833 let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
834 let proof'', new_goals' =
835 PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
837 (* The apply_tactic can have closed some of the new_goals *)
838 let patched_new_goals =
839 let (_,metasenv''',_subst,_,_,_) = proof'' in
841 (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
842 new_goals @ new_goals'
844 proof'', patched_new_goals
846 PET.mk_tactic (cases_tac ~term)
850 let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
851 ?depth ?using ?pattern what =
852 Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
853 ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
856 (* The simplification is performed only on the conclusion *)
857 let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
858 ?depth ?using ?pattern what =
859 Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
862 ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
864 [ReductionTactics.simpl_tac
865 ~pattern:(ProofEngineTypes.conclusion_pattern None)])