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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15 * GNU General Public License for more details.
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22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
26 open ProofEngineHelpers
29 exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
30 exception NotAnInductiveTypeToEliminate
31 exception WrongUriToVariable of string
33 (* lambda_abstract newmeta ty *)
34 (* returns a triple [bo],[context],[ty'] where *)
35 (* [ty] = Pi/LetIn [context].[ty'] ([context] is a vector!) *)
36 (* and [bo] = Lambda/LetIn [context].(Meta [newmeta]) *)
37 (* So, lambda_abstract is the core of the implementation of *)
38 (* the Intros tactic. *)
39 (* howmany = -1 means Intros, howmany > 0 means Intros n *)
40 let lambda_abstract ?(howmany=(-1)) metasenv context newmeta ty mk_fresh_name =
42 let rec collect_context context howmany ty =
46 CicMkImplicit.identity_relocation_list_for_metavariable context
48 context, ty, (C.Meta (newmeta,irl))
51 C.Cast (te,_) -> collect_context context howmany te
53 let n' = mk_fresh_name metasenv context n ~typ:s in
54 let (context',ty,bo) =
55 collect_context ((Some (n',(C.Decl s)))::context) (howmany - 1) t
57 (context',ty,C.Lambda(n',s,bo))
59 let (context',ty,bo) =
60 collect_context ((Some (n,(C.Def (s,None))))::context) (howmany - 1) t
62 (context',ty,C.LetIn(n,s,bo))
66 CicMkImplicit.identity_relocation_list_for_metavariable context
68 context, t, (C.Meta (newmeta,irl))
70 raise (Fail (lazy "intro(s): not enough products or let-ins"))
72 collect_context context howmany ty
74 let eta_expand metasenv context t arg =
75 let module T = CicTypeChecker in
76 let module S = CicSubstitution in
80 t' when t' = S.lift n arg -> C.Rel (1 + n)
81 | C.Rel m -> if m <= n then C.Rel m else C.Rel (m+1)
82 | C.Var (uri,exp_named_subst) ->
83 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
84 C.Var (uri,exp_named_subst')
87 List.map (function None -> None | Some t -> Some (aux n t)) l
91 | C.Implicit _ as t -> t
92 | C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
93 | C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
94 | C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
95 | C.LetIn (nn,s,t) -> C.LetIn (nn, aux n s, aux (n+1) t)
96 | C.Appl l -> C.Appl (List.map (aux n) l)
97 | C.Const (uri,exp_named_subst) ->
98 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
99 C.Const (uri,exp_named_subst')
100 | C.MutInd (uri,i,exp_named_subst) ->
101 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
102 C.MutInd (uri,i,exp_named_subst')
103 | C.MutConstruct (uri,i,j,exp_named_subst) ->
104 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
105 C.MutConstruct (uri,i,j,exp_named_subst')
106 | C.MutCase (sp,i,outt,t,pl) ->
107 C.MutCase (sp,i,aux n outt, aux n t,
110 let tylen = List.length fl in
113 (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
116 C.Fix (i, substitutedfl)
118 let tylen = List.length fl in
121 (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
124 C.CoFix (i, substitutedfl)
125 and aux_exp_named_subst n =
126 List.map (function uri,t -> uri,aux n t)
129 T.type_of_aux' metasenv context arg CicUniv.empty_ugraph (* TASSI: FIXME *)
132 FreshNamesGenerator.mk_fresh_name ~subst:[]
133 metasenv context (Cic.Name "Heta") ~typ:argty
135 (C.Appl [C.Lambda (fresh_name,argty,aux 0 t) ; arg])
137 (*CSC: ma serve solamente la prima delle new_uninst e l'unione delle due!!! *)
138 let classify_metas newmeta in_subst_domain subst_in metasenv =
140 (fun (i,canonical_context,ty) (old_uninst,new_uninst) ->
141 if in_subst_domain i then
142 old_uninst,new_uninst
144 let ty' = subst_in canonical_context ty in
145 let canonical_context' =
147 (fun entry canonical_context' ->
150 Some (n,Cic.Decl s) ->
151 Some (n,Cic.Decl (subst_in canonical_context' s))
152 | Some (n,Cic.Def (s,None)) ->
153 Some (n,Cic.Def ((subst_in canonical_context' s),None))
155 | Some (n,Cic.Def (bo,Some ty)) ->
159 (subst_in canonical_context' bo,
160 Some (subst_in canonical_context' ty)))
162 entry'::canonical_context'
163 ) canonical_context []
166 ((i,canonical_context',ty')::old_uninst),new_uninst
168 old_uninst,((i,canonical_context',ty')::new_uninst)
171 (* Useful only inside apply_tac *)
173 generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
175 let module C = Cic in
177 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
178 CicUtil.params_of_obj o
180 let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
181 let next_fresh_meta = ref newmeta in
182 let newmetasenvfragment = ref [] in
183 let exp_named_subst_diff = ref [] in
189 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
191 C.Variable (_,_,ty,_,_) ->
192 CicSubstitution.subst_vars !exp_named_subst_diff ty
193 | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
195 (* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
197 C.Sort (C.Type _) as s -> (* TASSI: ?? *)
198 let fresh_meta = !next_fresh_meta in
199 let fresh_meta' = fresh_meta + 1 in
200 next_fresh_meta := !next_fresh_meta + 2 ;
201 let subst_item = uri,C.Meta (fresh_meta',[]) in
202 newmetasenvfragment :=
203 (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
205 (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
206 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
207 subst_item::(aux (tl,[]))
211 CicMkImplicit.identity_relocation_list_for_metavariable context
213 let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
214 newmetasenvfragment :=
215 (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
216 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
217 incr next_fresh_meta ;
218 subst_item::(aux (tl,[]))(*)*)
219 | uri::tl1,((uri',_) as s)::tl2 ->
220 assert (UriManager.eq uri uri') ;
222 | [],_ -> assert false
224 let exp_named_subst' = aux (params,exp_named_subst) in
225 !exp_named_subst_diff,!next_fresh_meta,
226 List.rev !newmetasenvfragment, exp_named_subst'
228 new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
231 let new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty termty goal_arity =
232 let (consthead,newmetasenv,arguments,_) =
233 saturate_term newmeta' metasenv' context termty goal_arity in
234 let subst,newmetasenv',_ =
235 CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
238 if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
242 let rec count_prods context ty =
243 match CicReduction.whd context ty with
244 Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
247 let apply_tac_verbose_with_subst ~term (proof, goal) =
248 (* Assumption: The term "term" must be closed in the current context *)
249 let module T = CicTypeChecker in
250 let module R = CicReduction in
251 let module C = Cic in
252 let (_,metasenv,_,_) = proof in
253 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
254 let newmeta = new_meta_of_proof ~proof in
255 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
257 C.Var (uri,exp_named_subst) ->
258 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
259 generalize_exp_named_subst_with_fresh_metas context newmeta uri
262 exp_named_subst_diff,newmeta',newmetasenvfragment,
263 C.Var (uri,exp_named_subst')
264 | C.Const (uri,exp_named_subst) ->
265 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
266 generalize_exp_named_subst_with_fresh_metas context newmeta uri
269 exp_named_subst_diff,newmeta',newmetasenvfragment,
270 C.Const (uri,exp_named_subst')
271 | C.MutInd (uri,tyno,exp_named_subst) ->
272 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
273 generalize_exp_named_subst_with_fresh_metas context newmeta uri
276 exp_named_subst_diff,newmeta',newmetasenvfragment,
277 C.MutInd (uri,tyno,exp_named_subst')
278 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
279 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
280 generalize_exp_named_subst_with_fresh_metas context newmeta uri
283 exp_named_subst_diff,newmeta',newmetasenvfragment,
284 C.MutConstruct (uri,tyno,consno,exp_named_subst')
285 | _ -> [],newmeta,[],term
287 let metasenv' = metasenv@newmetasenvfragment in
289 CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph
292 CicSubstitution.subst_vars exp_named_subst_diff termty in
293 let goal_arity = count_prods context ty in
294 let subst,newmetasenv',t =
295 let rec add_one_argument n =
297 new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty
299 with CicUnification.UnificationFailure _ when n > 0 ->
300 add_one_argument (n - 1)
302 add_one_argument goal_arity
304 let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
305 let apply_subst = CicMetaSubst.apply_subst subst in
306 let old_uninstantiatedmetas,new_uninstantiatedmetas =
307 (* subst_in doesn't need the context. Hence the underscore. *)
308 let subst_in _ = CicMetaSubst.apply_subst subst in
309 classify_metas newmeta in_subst_domain subst_in newmetasenv'
311 let bo' = apply_subst t in
312 let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
314 (* if we just apply the subtitution, the type is irrelevant:
315 we may use Implicit, since it will be dropped *)
316 CicMetaSubst.apply_subst ((metano,(context,bo',Cic.Implicit None))::subst)
318 let (newproof, newmetasenv''') =
319 subst_meta_and_metasenv_in_proof proof metano subst_in newmetasenv''
321 (((metano,(context,bo',Cic.Implicit None))::subst)(* subst_in *), (* ALB *)
323 List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
327 let apply_tac_verbose_with_subst ~term status =
329 (* apply_tac_verbose ~term status *)
330 apply_tac_verbose_with_subst ~term status
331 (* TODO cacciare anche altre eccezioni? *)
333 | CicUnification.UnificationFailure msg
334 | CicTypeChecker.TypeCheckerFailure msg ->
338 let apply_tac_verbose ~term status =
339 let subst, status = apply_tac_verbose_with_subst ~term status in
340 (CicMetaSubst.apply_subst subst), status
342 let apply_tac ~term status = snd (apply_tac_verbose ~term status)
344 (* TODO per implementare i tatticali e' necessario che tutte le tattiche
345 sollevino _solamente_ Fail *)
346 let apply_tac ~term =
347 let apply_tac ~term status =
349 apply_tac ~term status
350 (* TODO cacciare anche altre eccezioni? *)
352 | CicUnification.UnificationFailure msg
353 | CicTypeChecker.TypeCheckerFailure msg ->
356 mk_tactic (apply_tac ~term)
358 let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
360 ?(mk_fresh_name_callback = (FreshNamesGenerator.mk_fresh_name ~subst:[])) ()
363 let module C = Cic in
364 let module R = CicReduction in
365 let (_,metasenv,_,_) = proof in
366 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
367 let newmeta = new_meta_of_proof ~proof in
368 let (context',ty',bo') =
369 lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
372 subst_meta_in_proof proof metano bo' [newmeta,context',ty']
374 (newproof, [newmeta])
376 mk_tactic (intros_tac ~mk_fresh_name_callback ())
378 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
380 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
383 let module C = Cic in
384 let curi,metasenv,pbo,pty = proof in
385 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
386 let newmeta1 = new_meta_of_proof ~proof in
387 let newmeta2 = newmeta1 + 1 in
389 mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
390 let context_for_newmeta1 =
391 (Some (fresh_name,C.Decl term))::context in
393 CicMkImplicit.identity_relocation_list_for_metavariable
397 CicMkImplicit.identity_relocation_list_for_metavariable context
399 let newmeta1ty = CicSubstitution.lift 1 ty in
402 [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
403 C.Meta (newmeta2,irl2)]
406 subst_meta_in_proof proof metano bo'
407 [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
409 (newproof, [newmeta1 ; newmeta2])
411 mk_tactic (cut_tac ~mk_fresh_name_callback term)
413 let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
415 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
418 let module C = Cic in
419 let curi,metasenv,pbo,pty = proof in
420 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
421 let _,_ = (* TASSI: FIXME *)
422 CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
423 let newmeta = new_meta_of_proof ~proof in
425 mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
426 let context_for_newmeta =
427 (Some (fresh_name,C.Def (term,None)))::context in
429 CicMkImplicit.identity_relocation_list_for_metavariable
432 let newmetaty = CicSubstitution.lift 1 ty in
433 let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
436 proof metano bo'[newmeta,context_for_newmeta,newmetaty]
438 (newproof, [newmeta])
440 mk_tactic (letin_tac ~mk_fresh_name_callback term)
442 (** functional part of the "exact" tactic *)
443 let exact_tac ~term =
444 let exact_tac ~term (proof, goal) =
445 (* Assumption: the term bo must be closed in the current context *)
446 let (_,metasenv,_,_) = proof in
447 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
448 let module T = CicTypeChecker in
449 let module R = CicReduction in
450 let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
451 let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
454 let (newproof, metasenv') =
455 subst_meta_in_proof proof metano term [] in
459 raise (Fail (lazy "The type of the provided term is not the one expected."))
461 mk_tactic (exact_tac ~term)
463 (* not really "primitive" tactics .... *)
465 let elim_tac ~term (proof, goal) =
466 let module T = CicTypeChecker in
467 let module U = UriManager in
468 let module R = CicReduction in
469 let module C = Cic in
470 let (curi,metasenv,proofbo,proofty) = proof in
471 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
472 let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
473 let (termty,metasenv',arguments,fresh_meta) =
474 ProofEngineHelpers.saturate_term
475 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
476 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
477 let uri,exp_named_subst,typeno,args =
479 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
480 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
481 (uri,exp_named_subst,typeno,args)
482 | _ -> raise NotAnInductiveTypeToEliminate
485 let buri = U.buri_of_uri uri in
487 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
489 C.InductiveDefinition (tys,_,_,_) ->
490 let (name,_,_,_) = List.nth tys typeno in
494 let ty_ty,_ = T.type_of_aux' metasenv' context ty CicUniv.empty_ugraph in
497 C.Sort C.Prop -> "_ind"
498 | C.Sort C.Set -> "_rec"
499 | C.Sort C.CProp -> "_rec"
500 | C.Sort (C.Type _)-> "_rect"
501 | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
504 U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
506 let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) in
508 T.type_of_aux' metasenv' context eliminator_ref CicUniv.empty_ugraph in
509 let rec find_args_no =
511 C.Prod (_,_,t) -> 1 + find_args_no t
512 | C.Cast (s,_) -> find_args_no s
513 | C.LetIn (_,_,t) -> 0 + find_args_no t
516 let args_no = find_args_no ety in
518 let rec make_tl base_case =
521 | n -> (C.Implicit None)::(make_tl base_case (n - 1))
523 C.Appl (eliminator_ref :: make_tl term (args_no - 1))
525 let refined_term,_,metasenv'',_ =
526 CicRefine.type_of_aux' metasenv' context term_to_refine
530 ProofEngineHelpers.compare_metasenvs
531 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
533 let proof' = curi,metasenv'',proofbo,proofty in
534 let proof'', new_goals' =
535 apply_tactic (apply_tac ~term:refined_term) (proof',goal)
537 (* The apply_tactic can have closed some of the new_goals *)
538 let patched_new_goals =
539 let (_,metasenv''',_,_) = proof'' in
541 (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
542 ) new_goals @ new_goals'
544 proof'', patched_new_goals
546 mk_tactic (elim_tac ~term)
549 let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
551 Tacticals.then_ ~start:(elim_tac ~term:what)
552 ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
555 (* The simplification is performed only on the conclusion *)
556 let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
558 Tacticals.then_ ~start:(elim_tac ~term:what)
561 ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
563 [ReductionTactics.simpl_tac
564 ~pattern:(ProofEngineTypes.conclusion_pattern None)])