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
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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))
66 let (context',ty,bo) =
67 collect_context ((Some (n,(C.Def (s,None))))::context) (howmany - 1) do_whd t
69 (context',ty,C.LetIn(n,s,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,t) -> C.LetIn (nn, aux n s, 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))
162 | Some (n,Cic.Def (s,None)) ->
163 Some (n,Cic.Def ((subst_in canonical_context' s),None))
165 | Some (n,Cic.Def (bo,Some ty)) ->
169 (subst_in canonical_context' bo,
170 Some (subst_in canonical_context' ty)))
172 entry'::canonical_context'
173 ) canonical_context []
176 ((i,canonical_context',ty')::old_uninst),new_uninst
178 old_uninst,((i,canonical_context',ty')::new_uninst)
181 (* Useful only inside apply_tac *)
183 generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
185 let module C = Cic in
187 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
188 CicUtil.params_of_obj o
190 let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
191 let next_fresh_meta = ref newmeta in
192 let newmetasenvfragment = ref [] in
193 let exp_named_subst_diff = ref [] in
199 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
201 C.Variable (_,_,ty,_,_) ->
202 CicSubstitution.subst_vars !exp_named_subst_diff ty
203 | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
205 (* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
207 C.Sort (C.Type _) as s -> (* TASSI: ?? *)
208 let fresh_meta = !next_fresh_meta in
209 let fresh_meta' = fresh_meta + 1 in
210 next_fresh_meta := !next_fresh_meta + 2 ;
211 let subst_item = uri,C.Meta (fresh_meta',[]) in
212 newmetasenvfragment :=
213 (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
215 (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
216 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
217 subst_item::(aux (tl,[]))
221 CicMkImplicit.identity_relocation_list_for_metavariable context
223 let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
224 newmetasenvfragment :=
225 (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
226 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
227 incr next_fresh_meta ;
228 subst_item::(aux (tl,[]))(*)*)
229 | uri::tl1,((uri',_) as s)::tl2 ->
230 assert (UriManager.eq uri uri') ;
232 | [],_ -> assert false
234 let exp_named_subst' = aux (params,exp_named_subst) in
235 !exp_named_subst_diff,!next_fresh_meta,
236 List.rev !newmetasenvfragment, exp_named_subst'
238 new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
241 let new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty termty goal_arity =
242 let (consthead,newmetasenv,arguments,_) =
243 TermUtil.saturate_term newmeta' metasenv' context termty
245 let subst,newmetasenv',_ =
246 CicUnification.fo_unif_subst
247 subst context newmetasenv consthead ty CicUniv.empty_ugraph
250 if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
254 let rec count_prods context ty =
255 match CicReduction.whd context ty with
256 Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
259 let apply_with_subst ~term ~subst ~maxmeta (proof, goal) =
260 (* Assumption: The term "term" must be closed in the current context *)
261 let module T = CicTypeChecker in
262 let module R = CicReduction in
263 let module C = Cic in
264 let (_,metasenv,_subst,_,_, _) = proof in
265 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
266 let newmeta = max (CicMkImplicit.new_meta metasenv subst) maxmeta in
267 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
269 C.Var (uri,exp_named_subst) ->
270 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
271 generalize_exp_named_subst_with_fresh_metas context newmeta uri
274 exp_named_subst_diff,newmeta',newmetasenvfragment,
275 C.Var (uri,exp_named_subst')
276 | C.Const (uri,exp_named_subst) ->
277 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
278 generalize_exp_named_subst_with_fresh_metas context newmeta uri
281 exp_named_subst_diff,newmeta',newmetasenvfragment,
282 C.Const (uri,exp_named_subst')
283 | C.MutInd (uri,tyno,exp_named_subst) ->
284 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
285 generalize_exp_named_subst_with_fresh_metas context newmeta uri
288 exp_named_subst_diff,newmeta',newmetasenvfragment,
289 C.MutInd (uri,tyno,exp_named_subst')
290 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
291 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
292 generalize_exp_named_subst_with_fresh_metas context newmeta uri
295 exp_named_subst_diff,newmeta',newmetasenvfragment,
296 C.MutConstruct (uri,tyno,consno,exp_named_subst')
297 | _ -> [],newmeta,[],term
299 let metasenv' = metasenv@newmetasenvfragment in
301 CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph
304 CicSubstitution.subst_vars exp_named_subst_diff termty in
305 let goal_arity = count_prods context ty in
306 let subst,newmetasenv',t =
307 let rec add_one_argument n =
309 new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty
311 with CicUnification.UnificationFailure _ when n > 0 ->
312 add_one_argument (n - 1)
314 add_one_argument goal_arity
316 let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
317 let apply_subst = CicMetaSubst.apply_subst subst in
318 let old_uninstantiatedmetas,new_uninstantiatedmetas =
319 (* subst_in doesn't need the context. Hence the underscore. *)
320 let subst_in _ = CicMetaSubst.apply_subst subst in
321 classify_metas newmeta in_subst_domain subst_in newmetasenv'
323 let bo' = apply_subst t in
324 let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
326 (* if we just apply the subtitution, the type is irrelevant:
327 we may use Implicit, since it will be dropped *)
328 ((metano,(context,bo',Cic.Implicit None))::subst)
330 let (newproof, newmetasenv''') =
331 ProofEngineHelpers.subst_meta_and_metasenv_in_proof proof metano subst_in
334 let subst = ((metano,(context,bo',ty))::subst) in
336 (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas),
337 max maxmeta (CicMkImplicit.new_meta newmetasenv''' subst)
341 let apply_with_subst ~term ?(subst=[]) ?(maxmeta=0) status =
343 (* apply_tac_verbose ~term status *)
344 apply_with_subst ~term ~subst ~maxmeta status
345 (* TODO cacciare anche altre eccezioni? *)
347 | CicUnification.UnificationFailure msg
348 | CicTypeChecker.TypeCheckerFailure msg -> raise (PET.Fail msg)
351 let apply_tac_verbose ~term status =
352 let subst, status, _ = apply_with_subst ~term status in
353 (CicMetaSubst.apply_subst subst), status
355 let apply_tac ~term status = snd (apply_tac_verbose ~term status)
357 (* TODO per implementare i tatticali e' necessario che tutte le tattiche
358 sollevino _solamente_ Fail *)
359 let apply_tac ~term =
360 let apply_tac ~term status =
362 apply_tac ~term status
363 (* TODO cacciare anche altre eccezioni? *)
365 | CicUnification.UnificationFailure msg
366 | CicTypeChecker.TypeCheckerFailure msg ->
369 PET.mk_tactic (apply_tac ~term)
371 let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
372 let intros_tac (proof, goal)
374 let module C = Cic in
375 let module R = CicReduction in
376 let (_,metasenv,_subst,_,_, _) = proof in
377 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
378 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
379 let (context',ty',bo') =
380 lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
383 ProofEngineHelpers.subst_meta_in_proof proof metano bo'
384 [newmeta,context',ty']
386 (newproof, [newmeta])
388 PET.mk_tactic intros_tac
390 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
392 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
395 let module C = Cic in
396 let curi,metasenv,_subst,pbo,pty, attrs = proof in
397 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
398 let newmeta1 = ProofEngineHelpers.new_meta_of_proof ~proof in
399 let newmeta2 = newmeta1 + 1 in
401 mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
402 let context_for_newmeta1 =
403 (Some (fresh_name,C.Decl term))::context in
405 CicMkImplicit.identity_relocation_list_for_metavariable
409 CicMkImplicit.identity_relocation_list_for_metavariable context
411 let newmeta1ty = CicSubstitution.lift 1 ty in
412 (* This is the pre-letin implementation
415 [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
416 C.Meta (newmeta2,irl2)]
420 Cic.LetIn (fresh_name, C.Meta (newmeta2,irl2), C.Meta (newmeta1,irl1))
423 ProofEngineHelpers.subst_meta_in_proof proof metano bo'
424 [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
426 (newproof, [newmeta1 ; newmeta2])
428 PET.mk_tactic (cut_tac ~mk_fresh_name_callback term)
430 let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
432 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
435 let module C = Cic in
436 let curi,metasenv,_subst,pbo,pty, attrs = proof in
439 let m = CicUtil.metas_of_term t in
440 List.exists (fun (j,_) -> i=j) m
442 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
443 if occur metano term then
445 (ProofEngineTypes.Fail (lazy
446 "You can't letin a term containing the current goal"));
448 CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
449 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
451 mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
452 let context_for_newmeta =
453 (Some (fresh_name,C.Def (term,None)))::context in
455 CicMkImplicit.identity_relocation_list_for_metavariable
458 let newmetaty = CicSubstitution.lift 1 ty in
459 let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
461 ProofEngineHelpers.subst_meta_in_proof
462 proof metano bo'[newmeta,context_for_newmeta,newmetaty]
464 (newproof, [newmeta])
466 PET.mk_tactic (letin_tac ~mk_fresh_name_callback term)
468 (** functional part of the "exact" tactic *)
469 let exact_tac ~term =
470 let exact_tac ~term (proof, goal) =
471 (* Assumption: the term bo must be closed in the current context *)
472 let (_,metasenv,_subst,_,_, _) = proof in
473 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
474 let module T = CicTypeChecker in
475 let module R = CicReduction in
476 let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
477 let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
480 let (newproof, metasenv') =
481 ProofEngineHelpers.subst_meta_in_proof proof metano term [] in
485 raise (PET.Fail (lazy "The type of the provided term is not the one expected."))
487 PET.mk_tactic (exact_tac ~term)
489 (* not really "primitive" tactics .... *)
491 module TC = CicTypeChecker
492 module UM = UriManager
493 module R = CicReduction
495 module PEH = ProofEngineHelpers
496 module PER = ProofEngineReduction
497 module MS = CicMetaSubst
498 module S = CicSubstitution
500 module RT = ReductionTactics
502 let rec args_init n f =
503 if n <= 0 then [] else f n :: args_init (pred n) f
505 let mk_predicate_for_elim
506 ~context ~metasenv ~ugraph ~goal ~arg ~using ~cpattern ~args_no =
507 let instantiated_eliminator =
508 let f n = if n = 1 then arg else C.Implicit None in
509 C.Appl (using :: args_init args_no f)
511 let _actual_arg, iety, _metasenv', _ugraph =
512 CicRefine.type_of_aux' metasenv context instantiated_eliminator ugraph
514 let _actual_meta, actual_args = match iety with
515 | C.Meta (i, _) -> i, []
516 | C.Appl (C.Meta (i, _) :: args) -> i, args
519 (* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
520 let rec mk_pred metasenv context' pred arg' cpattern' = function
521 | [] -> metasenv, pred, arg'
523 (* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
524 let argty, _ugraph = TC.type_of_aux' metasenv context arg ugraph in
525 let argty = CicReduction.whd context argty in
527 FreshNamesGenerator.mk_fresh_name
528 ~subst:[] metasenv context' C.Anonymous ~typ:argty
530 let hyp = Some (fresh_name, C.Decl argty) in
531 let lazy_term c m u =
532 let distance = List.length c - List.length context in
533 S.lift distance arg, m, u
535 let pattern = Some lazy_term, [], Some cpattern' in
536 let subst, metasenv, _ugraph, _conjecture, selected_terms =
537 ProofEngineHelpers.select
538 ~metasenv ~ugraph ~conjecture:(0, context, pred) ~pattern
540 let metasenv = MS.apply_subst_metasenv subst metasenv in
541 let map (_context_of_t, t) l = t :: l in
542 let what = List.fold_right map selected_terms [] in
543 let arg' = MS.apply_subst subst arg' in
544 let argty = MS.apply_subst subst argty in
545 let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
546 let pred = MS.apply_subst subst pred in
547 let pred = C.Lambda (fresh_name, argty, pred) in
548 let cpattern' = C.Lambda (C.Anonymous, C.Implicit None, cpattern') in
549 mk_pred metasenv (hyp :: context') pred arg' cpattern' tail
551 let metasenv, pred, arg =
552 mk_pred metasenv context goal arg cpattern (List.rev actual_args)
554 HLog.debug ("PREDICATE: " ^ CicPp.ppterm ~metasenv pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv) actual_args));
555 metasenv, pred, arg, actual_args
557 let beta_after_elim_tac upto predicate =
558 let beta_after_elim_tac status =
559 let proof, goal = status in
560 let _, metasenv, _subst, _, _, _ = proof in
561 let _, _, ty = CicUtil.lookup_meta goal metasenv in
562 let mk_pattern ~equality ~upto ~predicate ty =
563 (* code adapted from ProceduralConversion.generalize *)
564 let meta = C.Implicit None in
565 let hole = C.Implicit (Some `Hole) in
566 let anon = C.Anonymous in
569 | C.Implicit None when b -> b
572 List.fold_left map true
574 let rec gen_fix len k (name, i, ty, bo) =
575 name, i, gen_term k ty, gen_term (k + len) bo
576 and gen_cofix len k (name, ty, bo) =
577 name, gen_term k ty, gen_term (k + len) bo
578 and gen_term k = function
584 | C.MutConstruct (_, _, _, _)
587 | C.Appl (hd :: tl) when equality hd (S.lift k predicate) ->
588 assert (List.length tl = upto);
591 let ts = List.map (gen_term k) ts in
592 if is_meta ts then meta else C.Appl ts
594 let te, ty = gen_term k te, gen_term k ty in
595 if is_meta [te; ty] then meta else C.Cast (te, ty)
596 | C.MutCase (sp, i, outty, t, pl) ->
597 let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
598 if is_meta (outty :: t :: pl) then meta else hole (* C.MutCase (sp, i, outty, t, pl) *)
599 | C.Prod (_, s, t) ->
600 let s, t = gen_term k s, gen_term (succ k) t in
601 if is_meta [s; t] then meta else C.Prod (anon, s, t)
602 | C.Lambda (_, s, t) ->
603 let s, t = gen_term k s, gen_term (succ k) t in
604 if is_meta [s; t] then meta else C.Lambda (anon, s, t)
605 | C.LetIn (_, s, t) ->
606 let s, t = gen_term k s, gen_term (succ k) t in
607 if is_meta [s; t] then meta else C.LetIn (anon, s, t)
608 | C.Fix (i, fl) -> C.Fix (i, List.map (gen_fix (List.length fl) k) fl)
609 | C.CoFix (i, fl) -> C.CoFix (i, List.map (gen_cofix (List.length fl) k) fl)
611 None, [], Some (gen_term 0 ty)
613 let equality = CicUtil.alpha_equivalence in
614 let pattern = mk_pattern ~equality ~upto ~predicate ty in
615 let tactic = RT.head_beta_reduce_tac ~delta:false ~upto ~pattern in
616 PET.apply_tactic tactic status
618 PET.mk_tactic beta_after_elim_tac
620 let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
621 let elim_tac (proof, goal) =
622 let cpattern = match pattern with
623 | None, [], Some cpattern -> cpattern
624 | _ -> raise (PET.Fail (lazy "not implemented"))
626 let ugraph = CicUniv.empty_ugraph in
627 let curi, metasenv, _subst, proofbo, proofty, attrs = proof in
628 let conjecture = CicUtil.lookup_meta goal metasenv in
629 let metano, context, ty = conjecture in
630 let termty,_ugraph = TC.type_of_aux' metasenv context term ugraph in
631 let termty = CicReduction.whd context termty in
632 let termty, metasenv', arguments, _fresh_meta =
633 TermUtil.saturate_term
634 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
635 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
636 let uri, exp_named_subst, typeno, _args =
638 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
639 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
640 (uri,exp_named_subst,typeno,args)
641 | _ -> raise NotAnInductiveTypeToEliminate
644 let buri = UM.buri_of_uri uri in
646 let o,_ugraph = CicEnvironment.get_obj ugraph uri in
648 C.InductiveDefinition (tys,_,_,_) ->
649 let (name,_,_,_) = List.nth tys typeno in
653 let ty_ty,_ugraph = TC.type_of_aux' metasenv' context ty ugraph in
656 C.Sort C.Prop -> "_ind"
657 | C.Sort C.Set -> "_rec"
658 | C.Sort C.CProp -> "_rec"
659 | C.Sort (C.Type _)-> "_rect"
660 | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
663 UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
665 let eliminator_ref = match using with
666 | None -> C.Const (eliminator_uri, exp_named_subst)
670 TC.type_of_aux' metasenv' context eliminator_ref ugraph in
671 (* FG: ADDED PART ***********************************************************)
672 (* FG: we can not assume eliminator is the default eliminator ***************)
673 let splits, args_no = PEH.split_with_whd (context, ety) in
674 let pred_pos = match List.hd splits with
675 | _, C.Rel i when i > 1 && i <= args_no -> i
676 | _, C.Appl (C.Rel i :: _) when i > 1 && i <= args_no -> i
677 | _ -> raise NotAnEliminator
679 let metasenv', pred, term, actual_args = match pattern with
680 | None, [], Some (C.Implicit (Some `Hole)) ->
681 metasenv', C.Implicit None, term, []
683 mk_predicate_for_elim
684 ~args_no ~context ~ugraph ~cpattern
685 ~metasenv:metasenv' ~arg:term ~using:eliminator_ref ~goal:ty
687 (* FG: END OF ADDED PART ****************************************************)
690 if n = pred_pos then pred else
691 if n = 1 then term else C.Implicit None
693 C.Appl (eliminator_ref :: args_init args_no f)
695 let refined_term,_refined_termty,metasenv'',_ugraph =
696 CicRefine.type_of_aux' metasenv' context term_to_refine ugraph
699 ProofEngineHelpers.compare_metasenvs
700 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
702 let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
703 let proof'', new_goals' =
704 PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
706 (* The apply_tactic can have closed some of the new_goals *)
707 let patched_new_goals =
708 let (_,metasenv''',_subst,_,_, _) = proof'' in
710 (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
711 new_goals @ new_goals'
713 let res = proof'', patched_new_goals in
714 let upto = List.length actual_args in
715 if upto = 0 then res else
716 let continuation = beta_after_elim_tac upto pred in
717 let dummy_status = proof,goal in
719 (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
722 PET.mk_tactic elim_tac
725 let cases_intros_tac ?(howmany=(-1)) ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
726 let cases_tac ~term (proof, goal) =
727 let module TC = CicTypeChecker in
728 let module U = UriManager in
729 let module R = CicReduction in
730 let module C = Cic in
731 let (curi,metasenv,_subst, proofbo,proofty, attrs) = proof in
732 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
733 let termty,_ = TC.type_of_aux' metasenv context term CicUniv.empty_ugraph in
734 let termty = CicReduction.whd context termty in
735 let (termty,metasenv',arguments,fresh_meta) =
736 TermUtil.saturate_term
737 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
738 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
739 let uri,exp_named_subst,typeno,args =
741 | C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
742 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
743 (uri,exp_named_subst,typeno,args)
744 | _ -> raise NotAnInductiveTypeToEliminate
746 let paramsno,itty,patterns,right_args =
747 match CicEnvironment.get_obj CicUniv.empty_ugraph uri with
748 | C.InductiveDefinition (tys,_,paramsno,_),_ ->
749 let _,left_parameters,right_args =
751 (fun x (n,acc1,acc2) ->
752 if n > 0 then (n-1,acc1,x::acc2) else (n,x::acc1,acc2))
753 args (List.length args - paramsno, [],[])
755 let _,_,itty,cl = List.nth tys typeno in
756 let rec aux left_parameters context t =
757 match left_parameters,CicReduction.whd context t with
758 | [],C.Prod (name,source,target) ->
760 mk_fresh_name_callback metasenv' context name ~typ:source
762 C.Lambda (fresh_name,C.Implicit None,
763 aux [] (Some (fresh_name,C.Decl source)::context) target)
764 | hd::tl,C.Prod (name,source,target) ->
765 (* left parameters instantiation *)
766 aux tl context (CicSubstitution.subst hd target)
767 | [],_ -> C.Implicit None
771 List.map (function (_,cty) -> aux left_parameters context cty) cl,
776 let n_right_args = List.length right_args in
777 let n_lambdas = n_right_args + 1 in
778 let lifted_ty = CicSubstitution.lift n_lambdas ty in
781 List.map (CicSubstitution.lift n_lambdas) (right_args)
784 let rec mkargs = function
788 (if meta then Cic.Implicit None else Cic.Rel n)::(mkargs (n-1))
792 let replaced = ref false in
793 let replace = ProofEngineReduction.replace_lifting
794 ~equality:(fun _ a b -> let rc = CicUtil.alpha_equivalence a b in
795 if rc then replaced := true; rc)
799 replace ~what:[CicSubstitution.lift n_lambdas term]
800 ~with_what:[Cic.Rel 1] ~where:lifted_ty
802 if not !replaced then
803 (* this means the matched term is not there,
804 * but maybe right params are: we user rels (to right args lambdas) *)
805 replace ~what ~with_what:(with_what false) ~where:captured
807 (* since the matched is there, rights should be inferrable *)
808 replace ~what ~with_what:(with_what true) ~where:captured
810 let captured_term_ty =
811 let term_ty = CicSubstitution.lift n_right_args termty in
812 let rec mkrels = function 0 -> []|n -> (Cic.Rel n)::(mkrels (n-1)) in
813 let rec fstn acc l n =
814 if n = 0 then acc else fstn (acc@[List.hd l]) (List.tl l) (n-1)
817 | C.MutInd _ -> term_ty
818 | C.Appl ((C.MutInd (a,b,c))::args) ->
819 C.Appl ((C.MutInd (a,b,c))::
820 fstn [] args paramsno @ mkrels n_right_args)
821 | _ -> raise NotAnInductiveTypeToEliminate
823 let rec add_lambdas = function
826 C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas 0))
828 C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
829 C.Implicit None, (add_lambdas (n-1)))
831 add_lambdas n_lambdas
833 let term_to_refine = C.MutCase (uri,typeno,outtype,term,patterns) in
834 let refined_term,_,metasenv'',_ =
835 CicRefine.type_of_aux' metasenv' context term_to_refine
839 ProofEngineHelpers.compare_metasenvs
840 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
842 let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
843 let proof'', new_goals' =
844 PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
846 (* The apply_tactic can have closed some of the new_goals *)
847 let patched_new_goals =
848 let (_,metasenv''',_subst,_,_,_) = proof'' in
850 (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
851 new_goals @ new_goals'
853 proof'', patched_new_goals
855 PET.mk_tactic (cases_tac ~term)
859 let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
860 ?depth ?using ?pattern what =
861 Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
862 ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
865 (* The simplification is performed only on the conclusion *)
866 let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
867 ?depth ?using ?pattern what =
868 Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
871 ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
873 [ReductionTactics.simpl_tac
874 ~pattern:(ProofEngineTypes.conclusion_pattern None)])
877 (* FG: insetrts a "hole" in the context (derived from letin_tac) *)
880 let mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[] in
881 let term = C.Sort C.Set in
882 let letout_tac (proof, goal) =
883 let curi, metasenv, _subst, pbo, pty, attrs = proof in
884 let metano, context, ty = CicUtil.lookup_meta goal metasenv in
885 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
886 let fresh_name = mk_fresh_name_callback metasenv context (Cic.Name "hole") ~typ:term in
887 let context_for_newmeta = None :: context in
888 let irl = CicMkImplicit.identity_relocation_list_for_metavariable context_for_newmeta in
889 let newmetaty = CicSubstitution.lift 1 ty in
890 let bo' = C.LetIn (fresh_name, term, C.Meta (newmeta,irl)) in
891 let newproof, _ = ProofEngineHelpers.subst_meta_in_proof proof metano bo'[newmeta,context_for_newmeta,newmetaty] in
894 PET.mk_tactic letout_tac