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 "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 (_,Cic.Def (_,Some _)) -> assert false
157 entry'::canonical_context'
158 ) canonical_context []
161 ((i,canonical_context',ty')::old_uninst),new_uninst
163 old_uninst,((i,canonical_context',ty')::new_uninst)
166 (* Useful only inside apply_tac *)
168 generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
170 let module C = Cic in
172 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
173 CicUtil.params_of_obj o
175 let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
176 let next_fresh_meta = ref newmeta in
177 let newmetasenvfragment = ref [] in
178 let exp_named_subst_diff = ref [] in
184 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
186 C.Variable (_,_,ty,_,_) ->
187 CicSubstitution.subst_vars !exp_named_subst_diff ty
188 | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
190 (* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
192 C.Sort (C.Type _) as s -> (* TASSI: ?? *)
193 let fresh_meta = !next_fresh_meta in
194 let fresh_meta' = fresh_meta + 1 in
195 next_fresh_meta := !next_fresh_meta + 2 ;
196 let subst_item = uri,C.Meta (fresh_meta',[]) in
197 newmetasenvfragment :=
198 (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
200 (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
201 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
202 subst_item::(aux (tl,[]))
206 CicMkImplicit.identity_relocation_list_for_metavariable context
208 let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
209 newmetasenvfragment :=
210 (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
211 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
212 incr next_fresh_meta ;
213 subst_item::(aux (tl,[]))(*)*)
214 | uri::tl1,((uri',_) as s)::tl2 ->
215 assert (UriManager.eq uri uri') ;
217 | [],_ -> assert false
219 let exp_named_subst' = aux (params,exp_named_subst) in
220 !exp_named_subst_diff,!next_fresh_meta,
221 List.rev !newmetasenvfragment, exp_named_subst'
223 new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
226 let new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty termty goal_arity =
227 let (consthead,newmetasenv,arguments,_) =
228 saturate_term newmeta' metasenv' context termty goal_arity in
229 let subst,newmetasenv',_ =
230 CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
233 if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
237 let rec count_prods context ty =
238 match CicReduction.whd context ty with
239 Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
242 let apply_tac_verbose ~term (proof, goal) =
243 (* Assumption: The term "term" must be closed in the current context *)
244 let module T = CicTypeChecker in
245 let module R = CicReduction in
246 let module C = Cic in
247 let (_,metasenv,_,_) = proof in
248 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
249 let newmeta = new_meta_of_proof ~proof in
250 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
252 C.Var (uri,exp_named_subst) ->
253 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
254 generalize_exp_named_subst_with_fresh_metas context newmeta uri
257 exp_named_subst_diff,newmeta',newmetasenvfragment,
258 C.Var (uri,exp_named_subst')
259 | C.Const (uri,exp_named_subst) ->
260 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
261 generalize_exp_named_subst_with_fresh_metas context newmeta uri
264 exp_named_subst_diff,newmeta',newmetasenvfragment,
265 C.Const (uri,exp_named_subst')
266 | C.MutInd (uri,tyno,exp_named_subst) ->
267 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
268 generalize_exp_named_subst_with_fresh_metas context newmeta uri
271 exp_named_subst_diff,newmeta',newmetasenvfragment,
272 C.MutInd (uri,tyno,exp_named_subst')
273 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
274 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
275 generalize_exp_named_subst_with_fresh_metas context newmeta uri
278 exp_named_subst_diff,newmeta',newmetasenvfragment,
279 C.MutConstruct (uri,tyno,consno,exp_named_subst')
280 | _ -> [],newmeta,[],term
282 let metasenv' = metasenv@newmetasenvfragment in
284 CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph
287 CicSubstitution.subst_vars exp_named_subst_diff termty in
288 let goal_arity = count_prods context ty in
289 let subst,newmetasenv',t =
290 let rec add_one_argument n =
292 new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty
294 with CicUnification.UnificationFailure _ when n > 0 ->
295 add_one_argument (n - 1)
297 add_one_argument goal_arity
299 let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
300 let apply_subst = CicMetaSubst.apply_subst subst in
301 let old_uninstantiatedmetas,new_uninstantiatedmetas =
302 (* subst_in doesn't need the context. Hence the underscore. *)
303 let subst_in _ = CicMetaSubst.apply_subst subst in
304 classify_metas newmeta in_subst_domain subst_in newmetasenv'
306 let bo' = apply_subst t in
307 let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
309 (* if we just apply the subtitution, the type is irrelevant:
310 we may use Implicit, since it will be dropped *)
311 CicMetaSubst.apply_subst ((metano,(context,bo',Cic.Implicit None))::subst)
313 let (newproof, newmetasenv''') =
314 subst_meta_and_metasenv_in_proof proof metano subst_in newmetasenv''
318 List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
320 let apply_tac ~term status = snd (apply_tac_verbose ~term status)
322 let apply_tac_verbose ~term status =
324 apply_tac_verbose ~term status
325 (* TODO cacciare anche altre eccezioni? *)
327 | CicUnification.UnificationFailure _ as e ->
328 raise (Fail (Printexc.to_string e))
329 | CicTypeChecker.TypeCheckerFailure _ as e ->
330 raise (Fail (Printexc.to_string e))
332 (* TODO per implementare i tatticali e' necessario che tutte le tattiche
333 sollevino _solamente_ Fail *)
334 let apply_tac ~term =
335 let apply_tac ~term status =
337 apply_tac ~term status
338 (* TODO cacciare anche altre eccezioni? *)
340 | CicUnification.UnificationFailure _ as e ->
341 raise (Fail (Printexc.to_string e))
342 | CicTypeChecker.TypeCheckerFailure _ as e ->
343 raise (Fail (Printexc.to_string e))
345 mk_tactic (apply_tac ~term)
347 let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
349 ?(mk_fresh_name_callback = (FreshNamesGenerator.mk_fresh_name ~subst:[])) ()
352 let module C = Cic in
353 let module R = CicReduction in
354 let (_,metasenv,_,_) = proof in
355 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
356 let newmeta = new_meta_of_proof ~proof in
357 let (context',ty',bo') =
358 lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
361 subst_meta_in_proof proof metano bo' [newmeta,context',ty']
363 (newproof, [newmeta])
365 mk_tactic (intros_tac ~mk_fresh_name_callback ())
367 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
369 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
372 let module C = Cic in
373 let curi,metasenv,pbo,pty = proof in
374 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
375 let newmeta1 = new_meta_of_proof ~proof in
376 let newmeta2 = newmeta1 + 1 in
378 mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
379 let context_for_newmeta1 =
380 (Some (fresh_name,C.Decl term))::context in
382 CicMkImplicit.identity_relocation_list_for_metavariable
386 CicMkImplicit.identity_relocation_list_for_metavariable context
388 let newmeta1ty = CicSubstitution.lift 1 ty in
391 [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
392 C.Meta (newmeta2,irl2)]
395 subst_meta_in_proof proof metano bo'
396 [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
398 (newproof, [newmeta1 ; newmeta2])
400 mk_tactic (cut_tac ~mk_fresh_name_callback term)
402 let letin_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,pbo,pty = proof in
409 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
410 let _,_ = (* TASSI: FIXME *)
411 CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
412 let newmeta = new_meta_of_proof ~proof in
414 mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
415 let context_for_newmeta =
416 (Some (fresh_name,C.Def (term,None)))::context in
418 CicMkImplicit.identity_relocation_list_for_metavariable
421 let newmetaty = CicSubstitution.lift 1 ty in
422 let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
425 proof metano bo'[newmeta,context_for_newmeta,newmetaty]
427 (newproof, [newmeta])
429 mk_tactic (letin_tac ~mk_fresh_name_callback term)
431 (** functional part of the "exact" tactic *)
432 let exact_tac ~term =
433 let exact_tac ~term (proof, goal) =
434 (* Assumption: the term bo must be closed in the current context *)
435 let (_,metasenv,_,_) = proof in
436 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
437 let module T = CicTypeChecker in
438 let module R = CicReduction in
439 let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
440 let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
443 let (newproof, metasenv') =
444 subst_meta_in_proof proof metano term [] in
448 raise (Fail "The type of the provided term is not the one expected.")
450 mk_tactic (exact_tac ~term)
452 (* not really "primitive" tactics .... *)
454 let elim_tac ~term (proof, goal) =
455 let module T = CicTypeChecker in
456 let module U = UriManager in
457 let module R = CicReduction in
458 let module C = Cic in
459 let (curi,metasenv,proofbo,proofty) = proof in
460 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
461 let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
462 let (termty,metasenv',arguments,fresh_meta) =
463 ProofEngineHelpers.saturate_term
464 (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
465 let term = if arguments = [] then term else Cic.Appl (term::arguments) in
466 let uri,exp_named_subst,typeno,args =
468 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
469 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
470 (uri,exp_named_subst,typeno,args)
471 | _ -> raise NotAnInductiveTypeToEliminate
474 let buri = U.buri_of_uri uri in
476 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
478 C.InductiveDefinition (tys,_,_,_) ->
479 let (name,_,_,_) = List.nth tys typeno in
483 let ty_ty,_ = T.type_of_aux' metasenv' context ty CicUniv.empty_ugraph in
486 C.Sort C.Prop -> "_ind"
487 | C.Sort C.Set -> "_rec"
488 | C.Sort C.CProp -> "_rec"
489 | C.Sort (C.Type _)-> "_rect"
490 | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
493 U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
495 let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) in
497 T.type_of_aux' metasenv' context eliminator_ref CicUniv.empty_ugraph in
498 let rec find_args_no =
500 C.Prod (_,_,t) -> 1 + find_args_no t
501 | C.Cast (s,_) -> find_args_no s
502 | C.LetIn (_,_,t) -> 0 + find_args_no t
505 let args_no = find_args_no ety in
507 let rec make_tl base_case =
510 | n -> (C.Implicit None)::(make_tl base_case (n - 1))
512 C.Appl (eliminator_ref :: make_tl term (args_no - 1))
514 let metasenv', term_to_refine' =
515 CicMkImplicit.expand_implicits metasenv' [] context term_to_refine in
516 let refined_term,_,metasenv'',_ =
517 CicRefine.type_of_aux' metasenv' context term_to_refine'
521 ProofEngineHelpers.compare_metasenvs
522 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
524 let proof' = curi,metasenv'',proofbo,proofty in
525 let proof'', new_goals' =
526 apply_tactic (apply_tac ~term:refined_term) (proof',goal)
528 (* The apply_tactic can have closed some of the new_goals *)
529 let patched_new_goals =
530 let (_,metasenv''',_,_) = proof'' in
532 (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
533 ) new_goals @ new_goals'
535 proof'', patched_new_goals
537 mk_tactic (elim_tac ~term)
540 let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
542 Tacticals.then_ ~start:(elim_tac ~term:what)
543 ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
546 (* The simplification is performed only on the conclusion *)
547 let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
549 Tacticals.then_ ~start:(elim_tac ~term:what)
552 ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
554 [ReductionTactics.simpl_tac
555 ~pattern:(ProofEngineTypes.conclusion_pattern None)])