1 (* Copyright (C) 2002, HELM Team.
3 * This file is part of HELM, an Hypertextual, Electronic
4 * Library of Mathematics, developed at the Computer Science
5 * Department, University of Bologna, Italy.
7 * HELM is free software; you can redistribute it and/or
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9 * as published by the Free Software Foundation; either version 2
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13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
17 * You should have received a copy of the GNU General Public License
18 * along with HELM; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
22 * For details, see the HELM World-Wide-Web page,
23 * http://cs.unibo.it/helm/.
26 open ProofEngineHelpers
29 exception NotAnInductiveTypeToEliminate
30 exception NotTheRightEliminatorShape
31 exception NoHypothesesFound
32 exception WrongUriToVariable of string
34 (* lambda_abstract newmeta ty *)
35 (* returns a triple [bo],[context],[ty'] where *)
36 (* [ty] = Pi/LetIn [context].[ty'] ([context] is a vector!) *)
37 (* and [bo] = Lambda/LetIn [context].(Meta [newmeta]) *)
38 (* So, lambda_abstract is the core of the implementation of *)
39 (* the Intros tactic. *)
40 let lambda_abstract metasenv context newmeta ty mk_fresh_name =
42 let rec collect_context context =
44 C.Cast (te,_) -> collect_context context te
46 let n' = mk_fresh_name metasenv context n ~typ:s in
47 let (context',ty,bo) =
48 collect_context ((Some (n',(C.Decl s)))::context) t
50 (context',ty,C.Lambda(n',s,bo))
52 let (context',ty,bo) =
53 collect_context ((Some (n,(C.Def (s,None))))::context) t
55 (context',ty,C.LetIn(n,s,bo))
58 CicMkImplicit.identity_relocation_list_for_metavariable context
60 context, t, (C.Meta (newmeta,irl))
62 collect_context context ty
64 let eta_expand metasenv context t arg =
65 let module T = CicTypeChecker in
66 let module S = CicSubstitution in
70 t' when t' = S.lift n arg -> C.Rel (1 + n)
71 | C.Rel m -> if m <= n then C.Rel m else C.Rel (m+1)
72 | C.Var (uri,exp_named_subst) ->
73 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
74 C.Var (uri,exp_named_subst')
77 List.map (function None -> None | Some t -> Some (aux n t)) l
81 | C.Implicit _ as t -> t
82 | C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
83 | C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
84 | C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
85 | C.LetIn (nn,s,t) -> C.LetIn (nn, aux n s, aux (n+1) t)
86 | C.Appl l -> C.Appl (List.map (aux n) l)
87 | C.Const (uri,exp_named_subst) ->
88 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
89 C.Const (uri,exp_named_subst')
90 | C.MutInd (uri,i,exp_named_subst) ->
91 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
92 C.MutInd (uri,i,exp_named_subst')
93 | C.MutConstruct (uri,i,j,exp_named_subst) ->
94 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
95 C.MutConstruct (uri,i,j,exp_named_subst')
96 | C.MutCase (sp,i,outt,t,pl) ->
97 C.MutCase (sp,i,aux n outt, aux n t,
100 let tylen = List.length fl in
103 (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
106 C.Fix (i, substitutedfl)
108 let tylen = List.length fl in
111 (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
114 C.CoFix (i, substitutedfl)
115 and aux_exp_named_subst n =
116 List.map (function uri,t -> uri,aux n t)
119 T.type_of_aux' metasenv context arg
122 FreshNamesGenerator.mk_fresh_name
123 metasenv context (Cic.Name "Heta") ~typ:argty
125 (C.Appl [C.Lambda (fresh_name,argty,aux 0 t) ; arg])
127 (*CSC: ma serve solamente la prima delle new_uninst e l'unione delle due!!! *)
128 let classify_metas newmeta in_subst_domain subst_in metasenv =
130 (fun (i,canonical_context,ty) (old_uninst,new_uninst) ->
131 if in_subst_domain i then
132 old_uninst,new_uninst
134 let ty' = subst_in canonical_context ty in
135 let canonical_context' =
137 (fun entry canonical_context' ->
140 Some (n,Cic.Decl s) ->
141 Some (n,Cic.Decl (subst_in canonical_context' s))
142 | Some (n,Cic.Def (s,None)) ->
143 Some (n,Cic.Def ((subst_in canonical_context' s),None))
145 | Some (_,Cic.Def (_,Some _)) -> assert false
147 entry'::canonical_context'
148 ) canonical_context []
151 ((i,canonical_context',ty')::old_uninst),new_uninst
153 old_uninst,((i,canonical_context',ty')::new_uninst)
156 (* Auxiliary function for apply: given a type (a backbone), it returns its *)
157 (* head, a META environment in which there is new a META for each hypothesis,*)
158 (* a list of arguments for the new applications and the indexes of the first *)
159 (* and last new METAs introduced. The nth argument in the list of arguments *)
160 (* is just the nth new META. *)
161 let new_metasenv_for_apply newmeta proof context ty =
162 let module C = Cic in
163 let module S = CicSubstitution in
164 let rec aux newmeta =
166 C.Cast (he,_) -> aux newmeta he
167 (* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
168 (* If the expected type is a Type, then also Set is OK ==>
169 * we accept any term of type Type *)
170 (*CSC: BUG HERE: in this way it is possible for the term of
171 * type Type to be different from a Sort!!! *)
172 | C.Prod (name,(C.Sort (C.Type _) as s),t) ->
173 (* TASSI: ask CSC if BUG HERE refers to the C.Cast or C.Propd case *)
175 CicMkImplicit.identity_relocation_list_for_metavariable context
177 let newargument = C.Meta (newmeta+1,irl) in
178 let (res,newmetasenv,arguments,lastmeta) =
179 aux (newmeta + 2) (S.subst newargument t)
182 (newmeta,[],s)::(newmeta+1,context,C.Meta (newmeta,[]))::newmetasenv,
183 newargument::arguments,lastmeta
185 | C.Prod (name,s,t) ->
187 CicMkImplicit.identity_relocation_list_for_metavariable context
189 let newargument = C.Meta (newmeta,irl) in
190 let (res,newmetasenv,arguments,lastmeta) =
191 aux (newmeta + 1) (S.subst newargument t)
193 res,(newmeta,context,s)::newmetasenv,newargument::arguments,lastmeta
194 | t -> t,[],[],newmeta
196 (* WARNING: here we are using the invariant that above the most *)
197 (* recente new_meta() there are no used metas. *)
198 let (res,newmetasenv,arguments,lastmeta) = aux newmeta ty in
199 res,newmetasenv,arguments,lastmeta
201 (* Useful only inside apply_tac *)
203 generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
205 let module C = Cic in
207 match CicEnvironment.get_obj uri with
208 C.Constant (_,_,_,params)
209 | C.CurrentProof (_,_,_,_,params)
210 | C.Variable (_,_,_,params)
211 | C.InductiveDefinition (_,params,_) -> params
213 let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
214 let next_fresh_meta = ref newmeta in
215 let newmetasenvfragment = ref [] in
216 let exp_named_subst_diff = ref [] in
222 match CicEnvironment.get_obj uri with
223 C.Variable (_,_,ty,_) ->
224 CicSubstitution.subst_vars !exp_named_subst_diff ty
225 | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
227 (* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
229 C.Sort (C.Type _) as s -> (* TASSI: ?? *)
230 let fresh_meta = !next_fresh_meta in
231 let fresh_meta' = fresh_meta + 1 in
232 next_fresh_meta := !next_fresh_meta + 2 ;
233 let subst_item = uri,C.Meta (fresh_meta',[]) in
234 newmetasenvfragment :=
235 (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
237 (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
238 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
239 subst_item::(aux (tl,[]))
243 CicMkImplicit.identity_relocation_list_for_metavariable context
245 let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
246 newmetasenvfragment :=
247 (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
248 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
249 incr next_fresh_meta ;
250 subst_item::(aux (tl,[]))(*)*)
251 | uri::tl1,((uri',_) as s)::tl2 ->
252 assert (UriManager.eq uri uri') ;
254 | [],_ -> assert false
256 let exp_named_subst' = aux (params,exp_named_subst) in
257 !exp_named_subst_diff,!next_fresh_meta,
258 List.rev !newmetasenvfragment, exp_named_subst'
260 new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
263 let apply_tac ~term (proof, goal) =
264 (* Assumption: The term "term" must be closed in the current context *)
265 let module T = CicTypeChecker in
266 let module R = CicReduction in
267 let module C = Cic in
268 let (_,metasenv,_,_) = proof in
269 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
270 let newmeta = new_meta_of_proof ~proof in
271 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
273 C.Var (uri,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.Var (uri,exp_named_subst')
280 | C.Const (uri,exp_named_subst) ->
281 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
282 generalize_exp_named_subst_with_fresh_metas context newmeta uri
285 exp_named_subst_diff,newmeta',newmetasenvfragment,
286 C.Const (uri,exp_named_subst')
287 | C.MutInd (uri,tyno,exp_named_subst) ->
288 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
289 generalize_exp_named_subst_with_fresh_metas context newmeta uri
292 exp_named_subst_diff,newmeta',newmetasenvfragment,
293 C.MutInd (uri,tyno,exp_named_subst')
294 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
295 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
296 generalize_exp_named_subst_with_fresh_metas context newmeta uri
299 exp_named_subst_diff,newmeta',newmetasenvfragment,
300 C.MutConstruct (uri,tyno,consno,exp_named_subst')
301 | _ -> [],newmeta,[],term
303 let metasenv' = metasenv@newmetasenvfragment in
305 CicSubstitution.subst_vars exp_named_subst_diff
306 (CicTypeChecker.type_of_aux' metasenv' context term)
308 (* newmeta is the lowest index of the new metas introduced *)
309 let (consthead,newmetas,arguments,_) =
310 new_metasenv_for_apply newmeta' proof context termty
312 let newmetasenv = metasenv'@newmetas in
313 let subst,newmetasenv' =
314 CicUnification.fo_unif newmetasenv context consthead ty
316 let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
317 let apply_subst = CicMetaSubst.apply_subst subst in
318 let old_uninstantiatedmetas,new_uninstantiatedmetas =
319 (* subst_in doesn't need the context. Hence the underscore. *)
320 let subst_in _ = CicMetaSubst.apply_subst subst in
321 classify_metas newmeta in_subst_domain subst_in newmetasenv'
325 (if List.length newmetas = 0 then
328 Cic.Appl (term'::arguments)
331 let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
332 let (newproof, newmetasenv''') =
334 CicMetaSubst.apply_subst ((metano,(context, bo'))::subst)
336 subst_meta_and_metasenv_in_proof
337 proof metano subst_in newmetasenv''
339 (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas)
341 (* TODO per implementare i tatticali e' necessario che tutte le tattiche
342 sollevino _solamente_ Fail *)
343 let apply_tac ~term =
344 let apply_tac ~term status =
346 apply_tac ~term status
347 (* TODO cacciare anche altre eccezioni? *)
348 with CicUnification.UnificationFailure _ as e ->
349 raise (Fail (Printexc.to_string e))
351 mk_tactic (apply_tac ~term)
353 let intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name) ()=
355 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name) ()
358 let module C = Cic in
359 let module R = CicReduction in
360 let (_,metasenv,_,_) = proof in
361 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
362 let newmeta = new_meta_of_proof ~proof in
363 let (context',ty',bo') =
364 lambda_abstract metasenv context newmeta ty mk_fresh_name_callback
367 subst_meta_in_proof proof metano bo' [newmeta,context',ty']
369 (newproof, [newmeta])
371 mk_tactic (intros_tac ~mk_fresh_name_callback ())
373 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name) term=
375 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name)
378 let module C = Cic in
379 let curi,metasenv,pbo,pty = proof in
380 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
381 let newmeta1 = new_meta_of_proof ~proof in
382 let newmeta2 = newmeta1 + 1 in
384 mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
385 let context_for_newmeta1 =
386 (Some (fresh_name,C.Decl term))::context in
388 CicMkImplicit.identity_relocation_list_for_metavariable
392 CicMkImplicit.identity_relocation_list_for_metavariable context
394 let newmeta1ty = CicSubstitution.lift 1 ty in
397 [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
398 C.Meta (newmeta2,irl2)]
401 subst_meta_in_proof proof metano bo'
402 [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
404 (newproof, [newmeta1 ; newmeta2])
406 mk_tactic (cut_tac ~mk_fresh_name_callback term)
408 let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name) term=
410 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name)
413 let module C = Cic in
414 let curi,metasenv,pbo,pty = proof in
415 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
416 let _ = CicTypeChecker.type_of_aux' metasenv context term in
417 let newmeta = new_meta_of_proof ~proof in
419 mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
420 let context_for_newmeta =
421 (Some (fresh_name,C.Def (term,None)))::context in
423 CicMkImplicit.identity_relocation_list_for_metavariable
426 let newmetaty = CicSubstitution.lift 1 ty in
427 let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
430 proof metano bo'[newmeta,context_for_newmeta,newmetaty]
432 (newproof, [newmeta])
434 mk_tactic (letin_tac ~mk_fresh_name_callback term)
436 (** functional part of the "exact" tactic *)
437 let exact_tac ~term =
438 let exact_tac ~term (proof, goal) =
439 (* Assumption: the term bo must be closed in the current context *)
440 let (_,metasenv,_,_) = proof in
441 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
442 let module T = CicTypeChecker in
443 let module R = CicReduction in
444 if R.are_convertible context (T.type_of_aux' metasenv context term) ty then
446 let (newproof, metasenv') =
447 subst_meta_in_proof proof metano term [] in
451 raise (Fail "The type of the provided term is not the one expected.")
453 mk_tactic (exact_tac ~term)
455 (* not really "primitive" tactics .... *)
457 let elim_tac ~term (proof, goal) =
458 let module T = CicTypeChecker in
459 let module U = UriManager in
460 let module R = CicReduction in
461 let module C = Cic in
462 let (curi,metasenv,proofbo,proofty) = proof in
463 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
464 let termty = T.type_of_aux' metasenv context term in
465 let uri,exp_named_subst,typeno,args =
467 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
468 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
469 (uri,exp_named_subst,typeno,args)
470 | _ -> raise NotAnInductiveTypeToEliminate
473 let buri = U.buri_of_uri uri in
475 match CicEnvironment.get_obj uri with
476 C.InductiveDefinition (tys,_,_) ->
477 let (name,_,_,_) = List.nth tys typeno in
482 match T.type_of_aux' metasenv context ty with
483 C.Sort C.Prop -> "_ind"
484 | C.Sort C.Set -> "_rec"
485 | C.Sort C.CProp -> "_rec"
486 | C.Sort (C.Type _)-> "_rect" (* TASSI *)
489 U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
491 let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) in
492 let ety = T.type_of_aux' metasenv context eliminator_ref in
493 let rec find_args_no =
495 C.Prod (_,_,t) -> 1 + find_args_no t
496 | C.Cast (s,_) -> find_args_no s
497 | C.LetIn (_,_,t) -> 0 + find_args_no t
500 let args_no = find_args_no ety in
502 let rec make_tl base_case =
505 | n -> (C.Implicit None)::(make_tl base_case (n - 1))
507 C.Appl (eliminator_ref :: make_tl term (args_no - 1))
509 let metasenv', term_to_refine' =
510 CicMkImplicit.expand_implicits metasenv [] context term_to_refine in
511 let refined_term,_,metasenv'' =
512 CicRefine.type_of_aux' metasenv' context term_to_refine'
515 ProofEngineHelpers.compare_metasenvs
516 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
518 let proof' = curi,metasenv'',proofbo,proofty in
519 let proof'', new_goals' =
520 apply_tactic (apply_tac ~term:refined_term) (proof',goal)
522 (* The apply_tactic can have closed some of the new_goals *)
523 let patched_new_goals =
524 let (_,metasenv''',_,_) = proof'' in
526 (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
527 ) new_goals @ new_goals'
529 proof'', patched_new_goals
531 mk_tactic (elim_tac ~term)
534 (* The simplification is performed only on the conclusion *)
535 let elim_intros_simpl_tac ~term =
536 Tacticals.then_ ~start:(elim_tac ~term)
539 ~start:(intros_tac ())
541 [ReductionTactics.simpl_tac ~also_in_hypotheses:false ~terms:None])
544 exception NotConvertible
546 (*CSC: Bug (or feature?). [with_what] is parsed in the context of the goal, *)
547 (*CSC: while [what] can have a richer context (because of binders) *)
548 (*CSC: So it is _NOT_ possible to use those binders in the [with_what] term. *)
549 (*CSC: Is that evident? Is that right? Or should it be changed? *)
550 let change_tac ~what ~with_what =
551 let change_tac ~what ~with_what (proof, goal) =
552 let curi,metasenv,pbo,pty = proof in
553 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
554 (* are_convertible works only on well-typed terms *)
555 ignore (CicTypeChecker.type_of_aux' metasenv context with_what) ;
556 if CicReduction.are_convertible context what with_what then
559 ProofEngineReduction.replace
560 ~equality:(==) ~what:[what] ~with_what:[with_what]
562 let ty' = replace ty in
566 Some (name,Cic.Def (t,None))->Some (name,Cic.Def ((replace t),None))
567 | Some (name,Cic.Decl t) -> Some (name,Cic.Decl (replace t))
569 | Some (_,Cic.Def (_,Some _)) -> assert false
575 (n,_,_) when n = metano -> (metano,context',ty')
579 (curi,metasenv',pbo,pty), [metano]
582 raise (ProofEngineTypes.Fail "Not convertible")
584 mk_tactic (change_tac ~what ~with_what)