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 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.oblivion_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 applyP_tac ~term =
370 let applyP_tac status =
371 let res = PET.apply_tactic (apply_tac ~term) status in res
373 PET.mk_tactic applyP_tac
375 let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
376 let intros_tac (proof, goal)
378 let module C = Cic in
379 let module R = CicReduction in
380 let (_,metasenv,_subst,_,_, _) = proof in
381 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
382 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
383 let (context',ty',bo') =
384 lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
387 ProofEngineHelpers.subst_meta_in_proof proof metano bo'
388 [newmeta,context',ty']
390 (newproof, [newmeta])
392 PET.mk_tactic intros_tac
394 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
396 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
399 let module C = Cic in
400 let curi,metasenv,_subst,pbo,pty, attrs = proof in
401 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
402 let newmeta1 = ProofEngineHelpers.new_meta_of_proof ~proof in
403 let newmeta2 = newmeta1 + 1 in
405 mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
406 let context_for_newmeta1 =
407 (Some (fresh_name,C.Decl term))::context in
409 CicMkImplicit.identity_relocation_list_for_metavariable
413 CicMkImplicit.identity_relocation_list_for_metavariable context
415 let newmeta1ty = CicSubstitution.lift 1 ty in
417 Cic.LetIn (fresh_name, C.Meta (newmeta2,irl2), term, C.Meta (newmeta1,irl1))
420 ProofEngineHelpers.subst_meta_in_proof proof metano bo'
421 [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
423 (newproof, [newmeta1 ; newmeta2])
425 PET.mk_tactic (cut_tac ~mk_fresh_name_callback term)
427 let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
429 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
432 let module C = Cic in
433 let curi,metasenv,_subst,pbo,pty, attrs = proof in
436 let m = CicUtil.metas_of_term t in
437 List.exists (fun (j,_) -> i=j) m
439 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
440 if occur metano term then
442 (ProofEngineTypes.Fail (lazy
443 "You can't letin a term containing the current goal"));
445 CicTypeChecker.type_of_aux' metasenv context term CicUniv.oblivion_ugraph in
446 let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
448 mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
449 let context_for_newmeta =
450 (Some (fresh_name,C.Def (term,tty)))::context in
452 CicMkImplicit.identity_relocation_list_for_metavariable
455 let newmetaty = CicSubstitution.lift 1 ty in
456 let bo' = C.LetIn (fresh_name,term,tty,C.Meta (newmeta,irl)) in
458 ProofEngineHelpers.subst_meta_in_proof
459 proof metano bo'[newmeta,context_for_newmeta,newmetaty]
461 (newproof, [newmeta])
463 PET.mk_tactic (letin_tac ~mk_fresh_name_callback term)
465 (* FG: exact_tac := apply_tac as in NTactics *)
466 let exact_tac ~term = apply_tac ~term
468 (* not really "primitive" tactics .... *)
470 module TC = CicTypeChecker
471 module UM = UriManager
472 module R = CicReduction
474 module PEH = ProofEngineHelpers
475 module PER = ProofEngineReduction
476 module MS = CicMetaSubst
477 module S = CicSubstitution
479 module RT = ReductionTactics
481 let rec args_init n f =
482 if n <= 0 then [] else f n :: args_init (pred n) f
484 let mk_predicate_for_elim
485 ~context ~metasenv ~ugraph ~goal ~arg ~using ~cpattern ~args_no =
486 let instantiated_eliminator =
487 let f n = if n = 1 then arg else C.Implicit None in
488 C.Appl (using :: args_init args_no f)
490 let _actual_arg, iety, _metasenv', _ugraph =
491 CicRefine.type_of_aux' metasenv context instantiated_eliminator ugraph
493 let _actual_meta, actual_args = match iety with
494 | C.Meta (i, _) -> i, []
495 | C.Appl (C.Meta (i, _) :: args) -> i, args
498 (* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
499 let rec mk_pred metasenv context' pred arg' cpattern' = function
500 | [] -> metasenv, pred, arg'
502 (* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
503 let argty, _ugraph = TC.type_of_aux' metasenv context arg ugraph in
504 let argty = CicReduction.whd context argty in
506 FreshNamesGenerator.mk_fresh_name
507 ~subst:[] metasenv context' C.Anonymous ~typ:argty in
508 let hyp = Some (fresh_name, C.Decl argty) in
509 let lazy_term c m u =
510 let distance = List.length c - List.length context in
511 S.lift distance arg, m, u in
512 let pattern = Some lazy_term, [], Some cpattern' in
513 let subst, metasenv, _ugraph, _conjecture, selected_terms =
514 ProofEngineHelpers.select ~metasenv ~ugraph
515 ~conjecture:(0, context, pred) ~pattern in
516 let metasenv = MS.apply_subst_metasenv subst metasenv in
517 let map (_context_of_t, t) l = t :: l in
518 let what = List.fold_right map selected_terms [] in
519 let arg' = MS.apply_subst subst arg' in
520 let argty = MS.apply_subst subst argty in
521 let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
522 let pred = MS.apply_subst subst pred in
523 let pred = C.Lambda (fresh_name, argty, pred) in
524 let cpattern' = C.Lambda (C.Anonymous, C.Implicit None, cpattern') in
525 mk_pred metasenv (hyp :: context') pred arg' cpattern' tail
527 let metasenv, pred, arg =
528 mk_pred metasenv context goal arg cpattern (List.rev actual_args)
530 HLog.debug ("PREDICATE: " ^ CicPp.ppterm ~metasenv pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv) actual_args));
531 metasenv, pred, arg, actual_args
533 let beta_after_elim_tac upto predicate =
534 let beta_after_elim_tac status =
535 let proof, goal = status in
536 let _, metasenv, _subst, _, _, _ = proof in
537 let _, _, ty = CicUtil.lookup_meta goal metasenv in
538 let mk_pattern ~equality ~upto ~predicate ty =
539 (* code adapted from ProceduralConversion.generalize *)
540 let meta = C.Implicit None in
541 let hole = C.Implicit (Some `Hole) in
542 let anon = C.Anonymous in
545 | C.Implicit None when b -> b
548 List.fold_left map true
550 let rec gen_fix len k (name, i, ty, bo) =
551 name, i, gen_term k ty, gen_term (k + len) bo
552 and gen_cofix len k (name, ty, bo) =
553 name, gen_term k ty, gen_term (k + len) bo
554 and gen_term k = function
560 | C.MutConstruct (_, _, _, _)
563 | C.Appl (hd :: tl) when equality hd (S.lift k predicate) ->
564 assert (List.length tl = upto);
567 let ts = List.map (gen_term k) ts in
568 if is_meta ts then meta else C.Appl ts
570 let te, ty = gen_term k te, gen_term k ty in
571 if is_meta [te; ty] then meta else C.Cast (te, ty)
572 | C.MutCase (sp, i, outty, t, pl) ->
573 let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
574 if is_meta (outty :: t :: pl) then meta else hole (* C.MutCase (sp, i, outty, t, pl) *)
575 | C.Prod (_, s, t) ->
576 let s, t = gen_term k s, gen_term (succ k) t in
577 if is_meta [s; t] then meta else C.Prod (anon, s, t)
578 | C.Lambda (_, s, t) ->
579 let s, t = gen_term k s, gen_term (succ k) t in
580 if is_meta [s; t] then meta else C.Lambda (anon, s, t)
581 | C.LetIn (_, s, ty, t) ->
582 let s,ty,t = gen_term k s, gen_term k ty, gen_term (succ k) t in
583 if is_meta [s; t] then meta else C.LetIn (anon, s, ty, t)
584 | C.Fix (i, fl) -> C.Fix (i, List.map (gen_fix (List.length fl) k) fl)
585 | C.CoFix (i, fl) -> C.CoFix (i, List.map (gen_cofix (List.length fl) k) fl)
587 None, [], Some (gen_term 0 ty)
589 let equality = CicUtil.alpha_equivalence in
590 let pattern = mk_pattern ~equality ~upto ~predicate ty in
591 let tactic = RT.head_beta_reduce_tac ~delta:false ~upto ~pattern in
592 PET.apply_tactic tactic status
594 PET.mk_tactic beta_after_elim_tac
596 (* ANCORA DA DEBUGGARE *)
598 exception UnableToDetectTheTermThatMustBeGeneralizedYouMustGiveItExplicitly;;
599 exception TheSelectedTermsMustLiveInTheGoalContext
600 exception AllSelectedTermsMustBeConvertible;;
601 exception GeneralizationInHypothesesNotImplementedYet;;
604 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
607 let module PET = ProofEngineTypes in
608 let generalize_tac mk_fresh_name_callback
609 ~pattern:(term,hyps_pat,_) status
611 if hyps_pat <> [] then raise GeneralizationInHypothesesNotImplementedYet;
612 let (proof, goal) = status in
613 let module C = Cic in
614 let module T = Tacticals in
615 let uri,metasenv,_subst,pbo,pty, attrs = proof in
616 let (_,context,ty) as conjecture = CicUtil.lookup_meta goal metasenv in
617 let subst,metasenv,u,selected_hyps,terms_with_context =
618 ProofEngineHelpers.select ~metasenv ~ugraph:CicUniv.oblivion_ugraph
619 ~conjecture ~pattern in
620 let context = CicMetaSubst.apply_subst_context subst context in
621 let metasenv = CicMetaSubst.apply_subst_metasenv subst metasenv in
622 let pbo = lazy (CicMetaSubst.apply_subst subst (Lazy.force pbo)) in
623 let pty = CicMetaSubst.apply_subst subst pty in
628 Some (fun context metasenv ugraph ->
629 let term, metasenv, ugraph = term context metasenv ugraph in
630 CicMetaSubst.apply_subst subst term,
631 CicMetaSubst.apply_subst_metasenv subst metasenv,
634 let u,typ,term, metasenv' =
635 let context_of_t, (t, metasenv, u) =
636 match terms_with_context, term with
639 UnableToDetectTheTermThatMustBeGeneralizedYouMustGiveItExplicitly
640 | [], Some t -> context, t context metasenv u
641 | (context_of_t, _)::_, Some t ->
642 context_of_t, t context_of_t metasenv u
643 | (context_of_t, t)::_, None -> context_of_t, (t, metasenv, u)
645 let t,subst,metasenv' =
647 CicMetaSubst.delift_rels [] metasenv
648 (List.length context_of_t - List.length context) t
650 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
651 raise TheSelectedTermsMustLiveInTheGoalContext
653 (*CSC: I am not sure about the following two assertions;
654 maybe I need to propagate the new subst and metasenv *)
656 assert (metasenv' = metasenv);
657 let typ,u = CicTypeChecker.type_of_aux' ~subst metasenv context t u in
661 1. whether they live in the context of the goal;
662 if they do they are also well-typed since they are closed subterms
663 of a well-typed term in the well-typed context of the well-typed
665 2. whether they are convertible
669 (fun u (context_of_t,t) ->
671 let t,subst,metasenv'' =
673 CicMetaSubst.delift_rels [] metasenv'
674 (List.length context_of_t - List.length context) t
676 CicMetaSubst.DeliftingARelWouldCaptureAFreeVariable ->
677 raise TheSelectedTermsMustLiveInTheGoalContext in
678 (*CSC: I am not sure about the following two assertions;
679 maybe I need to propagate the new subst and metasenv *)
681 assert (metasenv'' = metasenv');
683 let b,u1 = CicReduction.are_convertible ~subst context term t u in
685 raise AllSelectedTermsMustBeConvertible
688 ) u terms_with_context) ;
689 let status = (uri,metasenv',_subst,pbo,pty, attrs),goal in
696 (mk_fresh_name_callback metasenv context C.Anonymous ~typ:typ),
698 (ProofEngineReduction.replace_lifting_csc 1
700 ~what:(List.map snd terms_with_context)
701 ~with_what:(List.map (function _ -> C.Rel 1) terms_with_context)
705 [(apply_tac ~term:(C.Appl [C.Rel 1; CicSubstitution.lift 1 term])) ;
709 let _,metasenv'',_subst,_,_, _ = proof in
710 (* CSC: the following is just a bad approximation since a meta
711 can be closed and then re-opened! *)
715 (fun j -> List.exists (fun (i,_,_) -> i = j) metasenv'')
716 (ProofEngineHelpers.compare_metasenvs ~oldmetasenv:metasenv
717 ~newmetasenv:metasenv')))
719 PET.mk_tactic (generalize_tac mk_fresh_name_callback ~pattern)
722 let generalize_pattern_tac pattern =
723 let generalize_pattern_tac (proof,goal) =
724 let _,metasenv,_,_,_,_ = proof in
725 let conjecture = CicUtil.lookup_meta goal metasenv in
726 let _,context,_ = conjecture in
727 let generalize_hyps =
728 let _,hpatterns,_ = ProofEngineHelpers.sort_pattern_hyps context pattern in
729 List.map fst hpatterns in
730 let ids_and_patterns =
733 let rel,_ = ProofEngineHelpers.find_hyp id context in
734 id,(Some (fun ctx m u -> CicSubstitution.lift (List.length ctx - List.length context) rel,m,u), [], Some (ProofEngineTypes.hole))
738 (function (id,pattern) ->
739 Tacticals.then_ ~start:(generalize_tac pattern)
740 ~continuation:(Tacticals.try_tactic
741 (ProofEngineStructuralRules.clear [id]))
744 PET.apply_tactic (Tacticals.seq tactics) (proof,goal)
746 PET.mk_tactic (generalize_pattern_tac)
749 let pattern_after_generalize_pattern_tac (tp, hpatterns, cpattern) =
752 None -> ProofEngineTypes.hole
757 (fun t (_,ty) -> Cic.Prod (Cic.Anonymous, ty, t)) cpattern hpatterns
759 tp, [], Some cpattern
762 let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
763 let elim_tac pattern (proof, goal) =
764 let ugraph = CicUniv.oblivion_ugraph in
765 let curi, metasenv, _subst, proofbo, proofty, attrs = proof in
766 let conjecture = CicUtil.lookup_meta goal metasenv in
767 let metano, context, ty = conjecture in
768 let pattern = pattern_after_generalize_pattern_tac pattern in
771 | None, [], Some cpattern -> cpattern
772 | _ -> raise (PET.Fail (lazy "not implemented")) in
773 let termty,_ugraph = TC.type_of_aux' metasenv context term ugraph in
774 let termty = CicReduction.whd context termty in
775 let termty, metasenv', arguments, _fresh_meta =
776 TermUtil.saturate_term
777 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
778 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
779 let uri, exp_named_subst, typeno, _args =
781 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
782 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
783 (uri,exp_named_subst,typeno,args)
784 | _ -> raise NotAnInductiveTypeToEliminate
787 let buri = UM.buri_of_uri uri in
789 let o,_ugraph = CicEnvironment.get_obj ugraph uri in
791 C.InductiveDefinition (tys,_,_,_) ->
792 let (name,_,_,_) = List.nth tys typeno in
796 let ty_ty,_ugraph = TC.type_of_aux' metasenv' context ty ugraph in
799 C.Sort C.Prop -> "_ind"
800 | C.Sort C.Set -> "_rec"
801 | C.Sort (C.CProp _) -> "_rect"
802 | C.Sort (C.Type _)-> "_rect"
803 | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
806 UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
808 let eliminator_ref = match using with
809 | None -> C.Const (eliminator_uri, exp_named_subst)
813 TC.type_of_aux' metasenv' context eliminator_ref ugraph in
814 (* FG: ADDED PART ***********************************************************)
815 (* FG: we can not assume eliminator is the default eliminator ***************)
816 let splits, args_no = PEH.split_with_whd (context, ety) in
817 let pred_pos = match List.hd splits with
818 | _, C.Rel i when i > 1 && i <= args_no -> i
819 | _, C.Appl (C.Rel i :: _) when i > 1 && i <= args_no -> i
820 | _ -> raise NotAnEliminator
822 let metasenv', pred, term, actual_args = match pattern with
823 | None, [], Some (C.Implicit (Some `Hole)) ->
824 metasenv', C.Implicit None, term, []
826 mk_predicate_for_elim
827 ~args_no ~context ~ugraph ~cpattern
828 ~metasenv:metasenv' ~arg:term ~using:eliminator_ref ~goal:ty
830 (* FG: END OF ADDED PART ****************************************************)
833 if n = pred_pos then pred else
834 if n = 1 then term else C.Implicit None
836 C.Appl (eliminator_ref :: args_init args_no f)
838 let refined_term,_refined_termty,metasenv'',_ugraph =
839 CicRefine.type_of_aux' metasenv' context term_to_refine ugraph
842 ProofEngineHelpers.compare_metasenvs
843 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
845 let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
846 let proof'', new_goals' =
847 PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
849 (* The apply_tactic can have closed some of the new_goals *)
850 let patched_new_goals =
851 let (_,metasenv''',_subst,_,_, _) = proof'' in
853 (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
854 new_goals @ new_goals'
856 let res = proof'', patched_new_goals in
857 let upto = List.length actual_args in
858 if upto = 0 then res else
859 let continuation = beta_after_elim_tac upto pred in
860 let dummy_status = proof,goal in
862 (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
865 let reorder_pattern ((proof, goal) as status) =
866 let _,metasenv,_,_,_,_ = proof in
867 let conjecture = CicUtil.lookup_meta goal metasenv in
868 let _,context,_ = conjecture in
869 let pattern = ProofEngineHelpers.sort_pattern_hyps context pattern in
871 (Tacticals.then_ ~start:(generalize_pattern_tac pattern)
872 ~continuation:(PET.mk_tactic (elim_tac pattern))) status
874 PET.mk_tactic reorder_pattern
877 let cases_intros_tac ?(howmany=(-1)) ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ?(pattern = PET.conclusion_pattern None) term =
878 let cases_tac pattern (proof, goal) =
879 let module TC = CicTypeChecker in
880 let module U = UriManager in
881 let module R = CicReduction in
882 let module C = Cic in
883 let (curi,metasenv,_subst, proofbo,proofty, attrs) = proof in
884 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
885 let pattern = pattern_after_generalize_pattern_tac pattern in
888 | None, [], Some cpattern ->
891 Cic.Implicit (Some `Hole) -> true
892 | Cic.Prod (Cic.Anonymous,so,tgt) -> is_hole so && is_hole tgt
895 if not (is_hole cpattern) then
896 raise (PET.Fail (lazy "not implemented"))
897 | _ -> raise (PET.Fail (lazy "not implemented")) in
898 let termty,_ = TC.type_of_aux' metasenv context term CicUniv.oblivion_ugraph in
899 let termty = CicReduction.whd context termty in
900 let (termty,metasenv',arguments,fresh_meta) =
901 TermUtil.saturate_term
902 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
903 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
904 let uri,exp_named_subst,typeno,args =
906 | C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
907 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
908 (uri,exp_named_subst,typeno,args)
909 | _ -> raise NotAnInductiveTypeToEliminate
911 let paramsno,itty,patterns,right_args =
912 match CicEnvironment.get_obj CicUniv.oblivion_ugraph uri with
913 | C.InductiveDefinition (tys,_,paramsno,_),_ ->
914 let _,left_parameters,right_args =
916 (fun x (n,acc1,acc2) ->
917 if n > 0 then (n-1,acc1,x::acc2) else (n,x::acc1,acc2))
918 args (List.length args - paramsno, [],[])
920 let _,_,itty,cl = List.nth tys typeno in
921 let rec aux left_parameters context t =
922 match left_parameters,CicReduction.whd context t with
923 | [],C.Prod (name,source,target) ->
925 mk_fresh_name_callback metasenv' context name ~typ:source
927 C.Lambda (fresh_name,C.Implicit None,
928 aux [] (Some (fresh_name,C.Decl source)::context) target)
929 | hd::tl,C.Prod (name,source,target) ->
930 (* left parameters instantiation *)
931 aux tl context (CicSubstitution.subst hd target)
932 | [],_ -> C.Implicit None
936 List.map (function (_,cty) -> aux left_parameters context cty) cl,
941 let n_right_args = List.length right_args in
942 let n_lambdas = n_right_args + 1 in
943 let lifted_ty = CicSubstitution.lift n_lambdas ty in
946 List.map (CicSubstitution.lift n_lambdas) (right_args)
949 let rec mkargs = function
953 (if meta then Cic.Implicit None else Cic.Rel n)::(mkargs (n-1))
957 let replaced = ref false in
958 let replace = ProofEngineReduction.replace_lifting
959 ~equality:(fun _ a b -> let rc = CicUtil.alpha_equivalence a b in
960 if rc then replaced := true; rc)
964 replace ~what:[CicSubstitution.lift n_lambdas term]
965 ~with_what:[Cic.Rel 1] ~where:lifted_ty
967 if not !replaced then
968 (* this means the matched term is not there,
969 * but maybe right params are: we user rels (to right args lambdas) *)
970 [replace ~what ~with_what:(with_what false) ~where:captured]
972 (* since the matched is there, rights should be inferrable *)
973 [replace ~what ~with_what:(with_what false) ~where:captured;
974 replace ~what ~with_what:(with_what true) ~where:captured]
976 let captured_term_ty =
977 let term_ty = CicSubstitution.lift n_right_args termty in
978 let rec mkrels = function 0 -> []|n -> (Cic.Rel n)::(mkrels (n-1)) in
979 let rec fstn acc l n =
980 if n = 0 then acc else fstn (acc@[List.hd l]) (List.tl l) (n-1)
983 | C.MutInd _ -> term_ty
984 | C.Appl ((C.MutInd (a,b,c))::args) ->
985 C.Appl ((C.MutInd (a,b,c))::
986 fstn [] args paramsno @ mkrels n_right_args)
987 | _ -> raise NotAnInductiveTypeToEliminate
989 let rec add_lambdas captured_ty = function
992 C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas captured_ty 0))
994 C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
995 C.Implicit None, (add_lambdas captured_ty (n-1)))
997 List.map (fun x -> add_lambdas x n_lambdas) captured_ty
999 let rec first = (* easier than using tacticals *)
1001 | [] -> raise (PET.Fail (lazy ("unable to generate a working outtype")))
1003 let term_to_refine = C.MutCase (uri,typeno,outtype,term,patterns) in
1005 let refined_term,_,metasenv'',_ =
1006 CicRefine.type_of_aux' metasenv' context term_to_refine
1007 CicUniv.oblivion_ugraph
1010 ProofEngineHelpers.compare_metasenvs
1011 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
1013 let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
1014 let proof'', new_goals' =
1015 PET.apply_tactic (apply_tac ~term:refined_term) (proof',goal)
1017 (* The apply_tactic can have closed some of the new_goals *)
1018 let patched_new_goals =
1019 let (_,metasenv''',_subst,_,_,_) = proof'' in
1021 (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
1022 new_goals @ new_goals'
1024 proof'', patched_new_goals
1025 with PET.Fail _ | CicRefine.RefineFailure _ | CicRefine.Uncertain _ -> first rest
1029 let reorder_pattern ((proof, goal) as status) =
1030 let _,metasenv,_,_,_,_ = proof in
1031 let conjecture = CicUtil.lookup_meta goal metasenv in
1032 let _,context,_ = conjecture in
1033 let pattern = ProofEngineHelpers.sort_pattern_hyps context pattern in
1035 (Tacticals.then_ ~start:(generalize_pattern_tac pattern)
1036 ~continuation:(PET.mk_tactic (cases_tac pattern))) status
1038 PET.mk_tactic reorder_pattern
1042 let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
1043 ?depth ?using ?pattern what =
1044 Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
1045 ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
1048 (* The simplification is performed only on the conclusion *)
1049 let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
1050 ?depth ?using ?pattern what =
1051 Tacticals.then_ ~start:(elim_tac ?using ?pattern what)
1054 ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
1056 [ReductionTactics.simpl_tac
1057 ~pattern:(ProofEngineTypes.conclusion_pattern None)])