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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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.oblivion_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.oblivion_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.oblivion_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.oblivion_ugraph
248 if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
252 let rec count_prods subst context ty =
253 match CicReduction.whd ~subst context ty with
254 Cic.Prod (n,s,t) -> 1 + count_prods subst (Some (n,Cic.Decl s)::context) t
257 let apply_with_subst ~term ~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'
300 metasenv' ~subst context term' CicUniv.oblivion_ugraph
303 CicSubstitution.subst_vars exp_named_subst_diff termty in
304 let goal_arity = count_prods subst context ty in
305 let subst,newmetasenv',t =
306 let rec add_one_argument n =
308 new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty
310 with CicUnification.UnificationFailure _ when n > 0 ->
311 add_one_argument (n - 1)
313 add_one_argument goal_arity
315 let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
316 let apply_subst = CicMetaSubst.apply_subst subst in
317 let old_uninstantiatedmetas,new_uninstantiatedmetas =
318 (* subst_in doesn't need the context. Hence the underscore. *)
319 let subst_in _ = CicMetaSubst.apply_subst subst in
320 classify_metas newmeta in_subst_domain subst_in newmetasenv'
322 let bo' = apply_subst t in
323 let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
325 (* if we just apply the subtitution, the type is irrelevant:
326 we may use Implicit, since it will be dropped *)
327 ((metano,(context,bo',Cic.Implicit None))::subst)
329 let (newproof, newmetasenv''') =
330 ProofEngineHelpers.subst_meta_and_metasenv_in_proof proof metano subst_in
333 let subst = ((metano,(context,bo',ty))::subst) in
335 let u,m,_,p,t,l = newproof in
339 (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas),
340 max maxmeta (CicMkImplicit.new_meta newmetasenv''' subst)
344 let apply_with_subst ~term ?(subst=[]) ?(maxmeta=0) status =
348 let (u,m,_,p,t,l), g = status in (u,m,subst,p,t,l), g
351 apply_with_subst ~term ~maxmeta status
353 | CicUnification.UnificationFailure msg
354 | CicTypeChecker.TypeCheckerFailure msg -> raise (PET.Fail msg)
357 let apply_tac_verbose ~term status =
358 let subst, status, _ = apply_with_subst ~term status in
359 (CicMetaSubst.apply_subst subst), status
361 let apply_tac ~term status = snd (apply_tac_verbose ~term status)
363 (* TODO per implementare i tatticali e' necessario che tutte le tattiche
364 sollevino _solamente_ Fail *)
365 let apply_tac ~term =
366 let apply_tac ~term status =
368 apply_tac ~term status
369 (* TODO cacciare anche altre eccezioni? *)
371 | CicUnification.UnificationFailure msg
372 | CicTypeChecker.TypeCheckerFailure msg ->
375 PET.mk_tactic (apply_tac ~term)
377 let applyP_tac ~term =
378 let applyP_tac status =
379 let res = PET.apply_tactic (apply_tac ~term) status in res
381 PET.mk_tactic applyP_tac
383 let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
384 let intros_tac (proof, goal)
386 let module C = Cic in
387 let module R = CicReduction in
388 let (_,metasenv,_subst,_,_, _) = proof in
389 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
390 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
391 let (context',ty',bo') =
392 lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
395 ProofEngineHelpers.subst_meta_in_proof proof metano bo'
396 [newmeta,context',ty']
398 (newproof, [newmeta])
400 PET.mk_tactic intros_tac
402 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
404 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
407 let module C = Cic in
408 let curi,metasenv,_subst,pbo,pty, attrs = proof in
409 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
410 let newmeta1 = ProofEngineHelpers.new_meta_of_proof ~proof in
411 let newmeta2 = newmeta1 + 1 in
413 mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
414 let context_for_newmeta1 =
415 (Some (fresh_name,C.Decl term))::context in
417 CicMkImplicit.identity_relocation_list_for_metavariable
421 CicMkImplicit.identity_relocation_list_for_metavariable context
423 let newmeta1ty = CicSubstitution.lift 1 ty in
425 Cic.LetIn (fresh_name, C.Meta (newmeta2,irl2), term, C.Meta (newmeta1,irl1))
428 ProofEngineHelpers.subst_meta_in_proof proof metano bo'
429 [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
431 (newproof, [newmeta1 ; newmeta2])
433 PET.mk_tactic (cut_tac ~mk_fresh_name_callback term)
435 let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
437 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
440 let module C = Cic in
441 let curi,metasenv,_subst,pbo,pty, attrs = proof in
444 let m = CicUtil.metas_of_term t in
445 List.exists (fun (j,_) -> i=j) m
447 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
448 if occur metano term then
450 (ProofEngineTypes.Fail (lazy
451 "You can't letin a term containing the current goal"));
453 CicTypeChecker.type_of_aux' metasenv context term CicUniv.oblivion_ugraph in
454 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
456 mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
457 let context_for_newmeta =
458 (Some (fresh_name,C.Def (term,tty)))::context in
460 CicMkImplicit.identity_relocation_list_for_metavariable
463 let newmetaty = CicSubstitution.lift 1 ty in
464 let bo' = C.LetIn (fresh_name,term,tty,C.Meta (newmeta,irl)) in
466 ProofEngineHelpers.subst_meta_in_proof
467 proof metano bo'[newmeta,context_for_newmeta,newmetaty]
469 (newproof, [newmeta])
471 PET.mk_tactic (letin_tac ~mk_fresh_name_callback term)
473 (* FG: exact_tac := apply_tac as in NTactics *)
474 let exact_tac ~term = apply_tac ~term
476 (* not really "primitive" tactics .... *)
478 module TC = CicTypeChecker
479 module UM = UriManager
480 module R = CicReduction
482 module PEH = ProofEngineHelpers
483 module PER = ProofEngineReduction
484 module MS = CicMetaSubst
485 module S = CicSubstitution
487 module RT = ReductionTactics
489 let rec args_init n f =
490 if n <= 0 then [] else f n :: args_init (pred n) f
492 let mk_predicate_for_elim
493 ~context ~metasenv ~subst ~ugraph ~goal ~arg ~using ~cpattern ~args_no
495 let instantiated_eliminator =
496 let f n = if n = 1 then arg else C.Implicit None in
497 C.Appl (using :: args_init args_no f)
499 let _actual_arg, iety, _metasenv', _ugraph =
500 CicRefine.type_of_aux' metasenv context instantiated_eliminator ugraph
502 let _actual_meta, actual_args = match iety with
503 | C.Meta (i, _) -> i, []
504 | C.Appl (C.Meta (i, _) :: args) -> i, args
507 (* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
508 let rec mk_pred metasenv subst context' pred arg' cpattern' = function
509 | [] -> metasenv, subst, pred, arg'
511 (* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
512 let argty, _ = TC.type_of_aux' metasenv ~subst context arg ugraph in
513 let argty = CicReduction.whd ~subst context argty in
515 FreshNamesGenerator.mk_fresh_name
516 ~subst metasenv context' C.Anonymous ~typ:argty in
517 let hyp = Some (fresh_name, C.Decl argty) in
518 let lazy_term c m u =
519 let distance = List.length c - List.length context in
520 S.lift distance arg, m, u in
521 let pattern = Some lazy_term, [], Some cpattern' in
522 let subst, metasenv, _ugraph, _conjecture, selected_terms =
523 ProofEngineHelpers.select ~subst ~metasenv ~ugraph
524 ~conjecture:(0, context, pred) ~pattern in
525 let metasenv = MS.apply_subst_metasenv subst metasenv in
526 let map (_context_of_t, t) l = t :: l in
527 let what = List.fold_right map selected_terms [] in
528 let arg' = MS.apply_subst subst arg' in
529 let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
530 let pred = MS.apply_subst subst pred in
531 let pred = C.Lambda (fresh_name, C.Implicit None, pred) in
532 let cpattern' = C.Lambda (C.Anonymous, C.Implicit None, cpattern') in
533 mk_pred metasenv subst (hyp :: context') pred arg' cpattern' tail
535 let metasenv, subst, pred, arg =
536 mk_pred metasenv subst context goal arg cpattern (List.rev actual_args)
538 HLog.debug ("PREDICATE CONTEXT:\n" ^ CicPp.ppcontext ~metasenv context);
539 HLog.debug ("PREDICATE: " ^ CicPp.ppterm ~metasenv pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv) actual_args));
540 metasenv, subst, pred, arg, actual_args
542 let beta_after_elim_tac upto predicate =
543 let beta_after_elim_tac status =
544 let proof, goal = status in
545 let _, metasenv, _subst, _, _, _ = proof in
546 let _, _, ty = CicUtil.lookup_meta goal metasenv in
547 let mk_pattern ~equality ~upto ~predicate ty =
548 (* code adapted from ProceduralConversion.generalize *)
549 let meta = C.Implicit None in
550 let hole = C.Implicit (Some `Hole) in
551 let anon = C.Anonymous in
554 | C.Implicit None when b -> b
557 List.fold_left map true
559 let rec gen_fix len k (name, i, ty, bo) =
560 name, i, gen_term k ty, gen_term (k + len) bo
561 and gen_cofix len k (name, ty, bo) =
562 name, gen_term k ty, gen_term (k + len) bo
563 and gen_term k = function
569 | C.MutConstruct (_, _, _, _)
572 | C.Appl (hd :: tl) when equality hd (S.lift k predicate) ->
573 assert (List.length tl = upto);
576 let ts = List.map (gen_term k) ts in
577 if is_meta ts then meta else C.Appl ts
579 let te, ty = gen_term k te, gen_term k ty in
580 if is_meta [te; ty] then meta else C.Cast (te, ty)
581 | C.MutCase (sp, i, outty, t, pl) ->
582 let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
583 if is_meta (outty :: t :: pl) then meta else hole (* C.MutCase (sp, i, outty, t, pl) *)
584 | C.Prod (_, s, t) ->
585 let s, t = gen_term k s, gen_term (succ k) t in
586 if is_meta [s; t] then meta else C.Prod (anon, s, t)
587 | C.Lambda (_, s, t) ->
588 let s, t = gen_term k s, gen_term (succ k) t in
589 if is_meta [s; t] then meta else C.Lambda (anon, s, t)
590 | C.LetIn (_, s, ty, t) ->
591 let s,ty,t = gen_term k s, gen_term k ty, gen_term (succ k) t in
592 if is_meta [s; t] then meta else C.LetIn (anon, s, ty, t)
593 | C.Fix (i, fl) -> C.Fix (i, List.map (gen_fix (List.length fl) k) fl)
594 | C.CoFix (i, fl) -> C.CoFix (i, List.map (gen_cofix (List.length fl) k) fl)
596 None, [], Some (gen_term 0 ty)
598 let equality = CicUtil.alpha_equivalence in
599 let pattern = mk_pattern ~equality ~upto ~predicate ty in
600 let tactic = RT.head_beta_reduce_tac ~delta:false ~upto ~pattern in
601 PET.apply_tactic tactic status
603 PET.mk_tactic beta_after_elim_tac
605 (* ANCORA DA DEBUGGARE *)
607 exception UnableToDetectTheTermThatMustBeGeneralizedYouMustGiveItExplicitly;;
608 exception TheSelectedTermsMustLiveInTheGoalContext
609 exception AllSelectedTermsMustBeConvertible;;
610 exception GeneralizationInHypothesesNotImplementedYet;;
613 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
616 let module PET = ProofEngineTypes in
617 let generalize_tac mk_fresh_name_callback
618 ~pattern:(term,hyps_pat,_) status
620 if hyps_pat <> [] then raise GeneralizationInHypothesesNotImplementedYet;
621 let (proof, goal) = status in
622 let module C = Cic in
623 let module T = Tacticals in
624 let uri,metasenv,subst,pbo,pty, attrs = proof in
625 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
626 let subst,metasenv,u,selected_hyps,terms_with_context =
627 ProofEngineHelpers.select ~metasenv ~subst ~ugraph:CicUniv.oblivion_ugraph
628 ~conjecture ~pattern in
629 let context = CicMetaSubst.apply_subst_context subst context in
630 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
631 let pbo = lazy (CicMetaSubst.apply_subst subst (Lazy.force pbo)) in
632 let pty = CicMetaSubst.apply_subst subst pty in
637 Some (fun context metasenv ugraph ->
638 let term, metasenv, ugraph = term context metasenv ugraph in
639 CicMetaSubst.apply_subst subst term,
640 CicMetaSubst.apply_subst_metasenv subst metasenv,
643 let u,typ,term, metasenv' =
644 let context_of_t, (t, metasenv, u) =
645 match terms_with_context, term with
648 UnableToDetectTheTermThatMustBeGeneralizedYouMustGiveItExplicitly
649 | [], Some t -> context, t context metasenv u
650 | (context_of_t, _)::_, Some t ->
651 context_of_t, t context_of_t metasenv u
652 | (context_of_t, t)::_, None -> context_of_t, (t, metasenv, u)
654 let t,e_subst,metasenv' =
656 CicMetaSubst.delift_rels [] metasenv
657 (List.length context_of_t - List.length context) t
659 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
660 raise TheSelectedTermsMustLiveInTheGoalContext
662 (*CSC: I am not sure about the following two assertions;
663 maybe I need to propagate the new subst and metasenv *)
664 assert (e_subst = []);
665 assert (metasenv' = metasenv);
666 let typ,u = CicTypeChecker.type_of_aux' ~subst metasenv context t u in
670 1. whether they live in the context of the goal;
671 if they do they are also well-typed since they are closed subterms
672 of a well-typed term in the well-typed context of the well-typed
674 2. whether they are convertible
678 (fun u (context_of_t,t) ->
680 let t,subst,metasenv'' =
682 CicMetaSubst.delift_rels [] metasenv'
683 (List.length context_of_t - List.length context) t
685 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
686 raise TheSelectedTermsMustLiveInTheGoalContext in
687 (*CSC: I am not sure about the following two assertions;
688 maybe I need to propagate the new subst and metasenv *)
690 assert (metasenv'' = metasenv');
692 let b,u1 = CicReduction.are_convertible ~subst context term t u in
694 raise AllSelectedTermsMustBeConvertible
697 ) u terms_with_context) ;
698 let status = (uri,metasenv',subst,pbo,pty, attrs),goal in
705 (mk_fresh_name_callback metasenv context C.Anonymous ~typ:typ),
707 (ProofEngineReduction.replace_lifting_csc 1
709 ~what:(List.map snd terms_with_context)
710 ~with_what:(List.map (function _ -> C.Rel 1) terms_with_context)
714 [(apply_tac ~term:(C.Appl [C.Rel 1; CicSubstitution.lift 1 term])) ;
718 let _,metasenv'',_,_,_, _ = proof in
719 (* CSC: the following is just a bad approximation since a meta
720 can be closed and then re-opened! *)
724 (fun j -> List.exists (fun (i,_,_) -> i = j) metasenv'')
725 (ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
726 ~newmetasenv:metasenv')))
728 PET.mk_tactic (generalize_tac mk_fresh_name_callback ~pattern)
731 let generalize_pattern_tac pattern =
732 let generalize_pattern_tac (proof,goal) =
733 let _,metasenv,_,_,_,_ = proof in
734 let conjecture = CicUtil.lookup_meta goal metasenv in
735 let _,context,_ = conjecture in
736 let generalize_hyps =
737 let _,hpatterns,_ = ProofEngineHelpers.sort_pattern_hyps context pattern in
738 List.map fst hpatterns in
739 let ids_and_patterns =
742 let rel,_ = ProofEngineHelpers.find_hyp id context in
743 id,(Some (fun ctx m u -> CicSubstitution.lift (List.length ctx - List.length context) rel,m,u), [], Some (ProofEngineTypes.hole))
747 (function (id,pattern) ->
748 Tacticals.then_ ~start:(generalize_tac pattern)
749 ~continuation:(Tacticals.try_tactic
750 (ProofEngineStructuralRules.clear [id]))
753 PET.apply_tactic (Tacticals.seq tactics) (proof,goal)
755 PET.mk_tactic (generalize_pattern_tac)
758 let pattern_after_generalize_pattern_tac (tp, hpatterns, cpattern) =
761 None -> ProofEngineTypes.hole
766 (fun t (_,ty) -> Cic.Prod (Cic.Anonymous, ty, t)) cpattern hpatterns
768 tp, [], Some cpattern
771 let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
772 let elim_tac pattern (proof, goal) =
773 let ugraph = CicUniv.oblivion_ugraph in
774 let curi, metasenv, subst, proofbo, proofty, attrs = proof in
775 let conjecture = CicUtil.lookup_meta goal metasenv in
776 let metano, context, ty = conjecture in
777 let pattern = pattern_after_generalize_pattern_tac pattern in
780 | None, [], Some cpattern -> cpattern
781 | _ -> raise (PET.Fail (lazy "not implemented")) in
782 let termty,_ugraph = TC.type_of_aux' metasenv ~subst context term ugraph in
783 let termty = CicReduction.whd ~subst context termty in
784 let termty, metasenv', arguments, _fresh_meta =
785 TermUtil.saturate_term
786 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
787 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
788 let uri, exp_named_subst, typeno, _args =
790 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
791 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
792 (uri,exp_named_subst,typeno,args)
793 | _ -> raise NotAnInductiveTypeToEliminate
796 let buri = UM.buri_of_uri uri in
798 let o,_ugraph = CicEnvironment.get_obj ugraph uri in
800 C.InductiveDefinition (tys,_,_,_) ->
801 let (name,_,_,_) = List.nth tys typeno in
805 let ty_ty,_ugraph = TC.type_of_aux' metasenv' ~subst context ty ugraph in
808 C.Sort C.Prop -> "_ind"
809 | C.Sort C.Set -> "_rec"
810 | C.Sort (C.CProp _) -> "_rect"
811 | C.Sort (C.Type _)-> "_rect"
812 | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
815 UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
817 let eliminator_ref = match using with
818 | None -> C.Const (eliminator_uri, exp_named_subst)
822 TC.type_of_aux' metasenv' ~subst context eliminator_ref ugraph in
823 (* FG: ADDED PART ***********************************************************)
824 (* FG: we can not assume eliminator is the default eliminator ***************)
825 let splits, args_no = PEH.split_with_whd (context, ety) in
826 let pred_pos = match List.hd splits with
827 | _, C.Rel i when i > 1 && i <= args_no -> i
828 | _, C.Appl (C.Rel i :: _) when i > 1 && i <= args_no -> i
829 | _ -> raise NotAnEliminator
831 let metasenv', subst, pred, term, actual_args = match pattern with
832 | None, [], Some (C.Implicit (Some `Hole)) ->
833 metasenv', subst, C.Implicit None, term, []
835 mk_predicate_for_elim
836 ~args_no ~context ~ugraph ~cpattern
837 ~metasenv:metasenv' ~subst ~arg:term ~using:eliminator_ref ~goal:ty
839 (* FG: END OF ADDED PART ****************************************************)
842 if n = pred_pos then pred else
843 if n = 1 then term else C.Implicit None
845 C.Appl (eliminator_ref :: args_init args_no f)
847 let refined_term,_refined_termty,metasenv'',subst,_ugraph =
848 CicRefine.type_of metasenv' subst context term_to_refine ugraph
850 let ipred = match refined_term with
851 | C.Appl ts -> List.nth ts (List.length ts - pred_pos)
855 ProofEngineHelpers.compare_metasenvs
856 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
858 let proof' = curi,metasenv'',subst,proofbo,proofty, attrs in
859 let proof'', new_goals' =
860 PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
862 (* The apply_tactic can have closed some of the new_goals *)
863 let patched_new_goals =
864 let (_,metasenv''',_,_,_, _) = proof'' in
866 (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
867 new_goals @ new_goals'
869 let res = proof'', patched_new_goals in
870 let upto = List.length actual_args in
871 if upto = 0 then res else
872 (* FG: we use ipred (instantiated pred) instead of pred (not instantiated) *)
873 let continuation = beta_after_elim_tac upto ipred in
874 let dummy_status = proof,goal in
876 (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
879 let reorder_pattern ((proof, goal) as status) =
880 let _,metasenv,_,_,_,_ = proof in
881 let conjecture = CicUtil.lookup_meta goal metasenv in
882 let _,context,_ = conjecture in
883 let pattern = ProofEngineHelpers.sort_pattern_hyps context pattern in
885 (Tacticals.then_ ~start:(generalize_pattern_tac pattern)
886 ~continuation:(PET.mk_tactic (elim_tac pattern))) status
888 PET.mk_tactic reorder_pattern
891 let cases_intros_tac ?(howmany=(-1)) ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ?(pattern = PET.conclusion_pattern None) term =
892 let cases_tac pattern (proof, goal) =
893 let module TC = CicTypeChecker in
894 let module U = UriManager in
895 let module R = CicReduction in
896 let module C = Cic in
897 let (curi,metasenv,_subst, proofbo,proofty, attrs) = proof in
898 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
899 let pattern = pattern_after_generalize_pattern_tac pattern in
902 | None, [], Some cpattern ->
905 Cic.Implicit (Some `Hole) -> true
906 | Cic.Prod (Cic.Anonymous,so,tgt) -> is_hole so && is_hole tgt
909 if not (is_hole cpattern) then
910 raise (PET.Fail (lazy "not implemented"))
911 | _ -> raise (PET.Fail (lazy "not implemented")) in
912 let termty,_ = TC.type_of_aux' metasenv context term CicUniv.oblivion_ugraph in
913 let termty = CicReduction.whd context termty in
914 let (termty,metasenv',arguments,fresh_meta) =
915 TermUtil.saturate_term
916 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
917 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
918 let uri,exp_named_subst,typeno,args =
920 | C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
921 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
922 (uri,exp_named_subst,typeno,args)
923 | _ -> raise NotAnInductiveTypeToEliminate
925 let paramsno,itty,patterns,right_args =
926 match CicEnvironment.get_obj CicUniv.oblivion_ugraph uri with
927 | C.InductiveDefinition (tys,_,paramsno,_),_ ->
928 let _,left_parameters,right_args =
930 (fun x (n,acc1,acc2) ->
931 if n > 0 then (n-1,acc1,x::acc2) else (n,x::acc1,acc2))
932 args (List.length args - paramsno, [],[])
934 let _,_,itty,cl = List.nth tys typeno in
935 let rec aux left_parameters context t =
936 match left_parameters,CicReduction.whd context t with
937 | [],C.Prod (name,source,target) ->
939 mk_fresh_name_callback metasenv' context name ~typ:source
941 C.Lambda (fresh_name,C.Implicit None,
942 aux [] (Some (fresh_name,C.Decl source)::context) target)
943 | hd::tl,C.Prod (name,source,target) ->
944 (* left parameters instantiation *)
945 aux tl context (CicSubstitution.subst hd target)
946 | [],_ -> C.Implicit None
950 List.map (function (_,cty) -> aux left_parameters context cty) cl,
955 let n_right_args = List.length right_args in
956 let n_lambdas = n_right_args + 1 in
957 let lifted_ty = CicSubstitution.lift n_lambdas ty in
960 List.map (CicSubstitution.lift n_lambdas) (right_args)
963 let rec mkargs = function
967 (if meta then Cic.Implicit None else Cic.Rel n)::(mkargs (n-1))
971 let replaced = ref false in
972 let replace = ProofEngineReduction.replace_lifting
973 ~equality:(fun _ a b -> let rc = CicUtil.alpha_equivalence a b in
974 if rc then replaced := true; rc)
978 replace ~what:[CicSubstitution.lift n_lambdas term]
979 ~with_what:[Cic.Rel 1] ~where:lifted_ty
981 if not !replaced then
982 (* this means the matched term is not there,
983 * but maybe right params are: we user rels (to right args lambdas) *)
984 [replace ~what ~with_what:(with_what false) ~where:captured]
986 (* since the matched is there, rights should be inferrable *)
987 [replace ~what ~with_what:(with_what false) ~where:captured;
988 replace ~what ~with_what:(with_what true) ~where:captured]
990 let captured_term_ty =
991 let term_ty = CicSubstitution.lift n_right_args termty in
992 let rec mkrels = function 0 -> []|n -> (Cic.Rel n)::(mkrels (n-1)) in
993 let rec fstn acc l n =
994 if n = 0 then acc else fstn (acc@[List.hd l]) (List.tl l) (n-1)
997 | C.MutInd _ -> term_ty
998 | C.Appl ((C.MutInd (a,b,c))::args) ->
999 C.Appl ((C.MutInd (a,b,c))::
1000 fstn [] args paramsno @ mkrels n_right_args)
1001 | _ -> raise NotAnInductiveTypeToEliminate
1003 let rec add_lambdas captured_ty = function
1006 C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas captured_ty 0))
1008 C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
1009 C.Implicit None, (add_lambdas captured_ty (n-1)))
1011 List.map (fun x -> add_lambdas x n_lambdas) captured_ty
1013 let rec first = (* easier than using tacticals *)
1015 | [] -> raise (PET.Fail (lazy ("unable to generate a working outtype")))
1017 let term_to_refine = C.MutCase (uri,typeno,outtype,term,patterns) in
1019 let refined_term,_,metasenv'',_ =
1020 CicRefine.type_of_aux' metasenv' context term_to_refine
1021 CicUniv.oblivion_ugraph
1024 ProofEngineHelpers.compare_metasenvs
1025 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
1027 let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
1028 let proof'', new_goals' =
1029 PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
1031 (* The apply_tactic can have closed some of the new_goals *)
1032 let patched_new_goals =
1033 let (_,metasenv''',_subst,_,_,_) = proof'' in
1035 (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
1036 new_goals @ new_goals'
1038 proof'', patched_new_goals
1039 with PET.Fail _ | CicRefine.RefineFailure _ | CicRefine.Uncertain _ -> first rest
1043 let reorder_pattern ((proof, goal) as status) =
1044 let _,metasenv,_,_,_,_ = proof in
1045 let conjecture = CicUtil.lookup_meta goal metasenv in
1046 let _,context,_ = conjecture in
1047 let pattern = ProofEngineHelpers.sort_pattern_hyps context pattern in
1049 (Tacticals.then_ ~start:(generalize_pattern_tac pattern)
1050 ~continuation:(PET.mk_tactic (cases_tac pattern))) status
1052 PET.mk_tactic reorder_pattern
1056 let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
1057 ?depth ?using ?pattern what =
1058 Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
1059 ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
1062 (* The simplification is performed only on the conclusion *)
1063 let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
1064 ?depth ?using ?pattern what =
1065 Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
1068 ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
1070 [ReductionTactics.simpl_tac
1071 ~pattern:(ProofEngineTypes.conclusion_pattern None)])