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
8 * modify it under the terms of the GNU General Public License
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.
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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 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))
65 CicMkImplicit.identity_relocation_list_for_metavariable context
67 context, t, (C.Meta (newmeta,irl))
69 collect_context context howmany ty
71 let eta_expand metasenv context t arg =
72 let module T = CicTypeChecker in
73 let module S = CicSubstitution in
77 t' when t' = S.lift n arg -> C.Rel (1 + n)
78 | C.Rel m -> if m <= n then C.Rel m else C.Rel (m+1)
79 | C.Var (uri,exp_named_subst) ->
80 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
81 C.Var (uri,exp_named_subst')
84 List.map (function None -> None | Some t -> Some (aux n t)) l
88 | C.Implicit _ as t -> t
89 | C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
90 | C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
91 | C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
92 | C.LetIn (nn,s,t) -> C.LetIn (nn, aux n s, aux (n+1) t)
93 | C.Appl l -> C.Appl (List.map (aux n) l)
94 | C.Const (uri,exp_named_subst) ->
95 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
96 C.Const (uri,exp_named_subst')
97 | C.MutInd (uri,i,exp_named_subst) ->
98 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
99 C.MutInd (uri,i,exp_named_subst')
100 | C.MutConstruct (uri,i,j,exp_named_subst) ->
101 let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
102 C.MutConstruct (uri,i,j,exp_named_subst')
103 | C.MutCase (sp,i,outt,t,pl) ->
104 C.MutCase (sp,i,aux n outt, aux n t,
107 let tylen = List.length fl in
110 (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
113 C.Fix (i, substitutedfl)
115 let tylen = List.length fl in
118 (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
121 C.CoFix (i, substitutedfl)
122 and aux_exp_named_subst n =
123 List.map (function uri,t -> uri,aux n t)
126 T.type_of_aux' metasenv context arg CicUniv.empty_ugraph (* TASSI: FIXME *)
129 FreshNamesGenerator.mk_fresh_name ~subst:[]
130 metasenv context (Cic.Name "Heta") ~typ:argty
132 (C.Appl [C.Lambda (fresh_name,argty,aux 0 t) ; arg])
134 (*CSC: ma serve solamente la prima delle new_uninst e l'unione delle due!!! *)
135 let classify_metas newmeta in_subst_domain subst_in metasenv =
137 (fun (i,canonical_context,ty) (old_uninst,new_uninst) ->
138 if in_subst_domain i then
139 old_uninst,new_uninst
141 let ty' = subst_in canonical_context ty in
142 let canonical_context' =
144 (fun entry canonical_context' ->
147 Some (n,Cic.Decl s) ->
148 Some (n,Cic.Decl (subst_in canonical_context' s))
149 | Some (n,Cic.Def (s,None)) ->
150 Some (n,Cic.Def ((subst_in canonical_context' s),None))
152 | Some (_,Cic.Def (_,Some _)) -> assert false
154 entry'::canonical_context'
155 ) canonical_context []
158 ((i,canonical_context',ty')::old_uninst),new_uninst
160 old_uninst,((i,canonical_context',ty')::new_uninst)
163 (* Auxiliary function for apply: given a type (a backbone), it returns its *)
164 (* head, a META environment in which there is new a META for each hypothesis,*)
165 (* a list of arguments for the new applications and the indexes of the first *)
166 (* and last new METAs introduced. The nth argument in the list of arguments *)
167 (* is just the nth new META. *)
168 let new_metasenv_for_apply newmeta proof context ty =
169 let module C = Cic in
170 let module S = CicSubstitution in
171 let rec aux newmeta ty =
174 C.Cast (he,_) -> aux newmeta he
175 (* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
176 (* If the expected type is a Type, then also Set is OK ==>
177 * we accept any term of type Type *)
178 (*CSC: BUG HERE: in this way it is possible for the term of
179 * type Type to be different from a Sort!!! *)
180 | C.Prod (name,(C.Sort (C.Type _) as s),t) ->
181 (* TASSI: ask CSC if BUG HERE refers to the C.Cast or C.Propd case *)
183 CicMkImplicit.identity_relocation_list_for_metavariable context
185 let newargument = C.Meta (newmeta+1,irl) in
186 let (res,newmetasenv,arguments,lastmeta) =
187 aux (newmeta + 2) (S.subst newargument t)
190 (newmeta,[],s)::(newmeta+1,context,C.Meta (newmeta,[]))::newmetasenv,
191 newargument::arguments,lastmeta
193 | C.Prod (name,s,t) ->
195 CicMkImplicit.identity_relocation_list_for_metavariable context
197 let newargument = C.Meta (newmeta,irl) in
198 let (res,newmetasenv,arguments,lastmeta) =
199 aux (newmeta + 1) (S.subst newargument t)
201 let s' = CicReduction.normalize ~delta:false context s in
202 res,(newmeta,context,s')::newmetasenv,newargument::arguments,lastmeta
203 (** NORMALIZE RATIONALE
204 * we normalize the target only NOW since we may be in this case:
205 * A1 -> A2 -> T where T = (\lambda x.A3 -> P) k
206 * and we want a mesasenv with ?1:A1 and ?2:A2 and not
207 * ?1, ?2, ?3 (that is the one we whould get if we start from the
208 * beta-normalized A1 -> A2 -> A3 -> P **)
209 | t -> (CicReduction.normalize ~delta:false context t),[],[],newmeta
211 (* WARNING: here we are using the invariant that above the most *)
212 (* recente new_meta() there are no used metas. *)
213 let (res,newmetasenv,arguments,lastmeta) = aux newmeta ty in
214 res,newmetasenv,arguments,lastmeta
216 (* Useful only inside apply_tac *)
218 generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
220 let module C = Cic in
222 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
223 CicUtil.params_of_obj o
225 let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
226 let next_fresh_meta = ref newmeta in
227 let newmetasenvfragment = ref [] in
228 let exp_named_subst_diff = ref [] in
234 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
236 C.Variable (_,_,ty,_,_) ->
237 CicSubstitution.subst_vars !exp_named_subst_diff ty
238 | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
240 (* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
242 C.Sort (C.Type _) as s -> (* TASSI: ?? *)
243 let fresh_meta = !next_fresh_meta in
244 let fresh_meta' = fresh_meta + 1 in
245 next_fresh_meta := !next_fresh_meta + 2 ;
246 let subst_item = uri,C.Meta (fresh_meta',[]) in
247 newmetasenvfragment :=
248 (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
250 (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
251 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
252 subst_item::(aux (tl,[]))
256 CicMkImplicit.identity_relocation_list_for_metavariable context
258 let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
259 newmetasenvfragment :=
260 (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
261 exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
262 incr next_fresh_meta ;
263 subst_item::(aux (tl,[]))(*)*)
264 | uri::tl1,((uri',_) as s)::tl2 ->
265 assert (UriManager.eq uri uri') ;
267 | [],_ -> assert false
269 let exp_named_subst' = aux (params,exp_named_subst) in
270 !exp_named_subst_diff,!next_fresh_meta,
271 List.rev !newmetasenvfragment, exp_named_subst'
273 new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
276 let new_metasenv_and_unify_and_t newmeta' metasenv' proof context term' ty termty =
277 let (consthead,newmetas,arguments,_) =
278 new_metasenv_for_apply newmeta' proof context termty
280 let newmetasenv = metasenv'@newmetas in
281 let subst,newmetasenv',_ =
282 CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
285 if List.length newmetas = 0 then term' else Cic.Appl (term'::arguments)
289 let apply_tac_verbose ~term (proof, goal) =
290 (* Assumption: The term "term" must be closed in the current context *)
291 let module T = CicTypeChecker in
292 let module R = CicReduction in
293 let module C = Cic in
294 let (_,metasenv,_,_) = proof in
295 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
296 let newmeta = new_meta_of_proof ~proof in
297 let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
299 C.Var (uri,exp_named_subst) ->
300 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
301 generalize_exp_named_subst_with_fresh_metas context newmeta uri
304 exp_named_subst_diff,newmeta',newmetasenvfragment,
305 C.Var (uri,exp_named_subst')
306 | C.Const (uri,exp_named_subst) ->
307 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
308 generalize_exp_named_subst_with_fresh_metas context newmeta uri
311 exp_named_subst_diff,newmeta',newmetasenvfragment,
312 C.Const (uri,exp_named_subst')
313 | C.MutInd (uri,tyno,exp_named_subst) ->
314 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
315 generalize_exp_named_subst_with_fresh_metas context newmeta uri
318 exp_named_subst_diff,newmeta',newmetasenvfragment,
319 C.MutInd (uri,tyno,exp_named_subst')
320 | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
321 let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
322 generalize_exp_named_subst_with_fresh_metas context newmeta uri
325 exp_named_subst_diff,newmeta',newmetasenvfragment,
326 C.MutConstruct (uri,tyno,consno,exp_named_subst')
327 | _ -> [],newmeta,[],term
329 let metasenv' = metasenv@newmetasenvfragment in
331 CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph in
333 CicSubstitution.subst_vars exp_named_subst_diff termty
335 let subst,newmetasenv',t =
337 new_metasenv_and_unify_and_t newmeta' metasenv' proof context term' ty
339 with CicUnification.UnificationFailure _ ->
340 new_metasenv_and_unify_and_t newmeta' metasenv' proof context term' ty
341 (CicReduction.whd context termty)
343 let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
344 let apply_subst = CicMetaSubst.apply_subst subst in
345 let old_uninstantiatedmetas,new_uninstantiatedmetas =
346 (* subst_in doesn't need the context. Hence the underscore. *)
347 let subst_in _ = CicMetaSubst.apply_subst subst in
348 classify_metas newmeta in_subst_domain subst_in newmetasenv'
350 let bo' = apply_subst t in
351 let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
352 (* prerr_endline ("me: " ^ CicMetaSubst.ppmetasenv newmetasenv'' subst); *)
354 (* if we just apply the subtitution, the type is irrelevant:
355 we may use Implicit, since it will be dropped *)
356 CicMetaSubst.apply_subst ((metano,(context,bo',Cic.Implicit None))::subst)
358 let (newproof, newmetasenv''') =
359 subst_meta_and_metasenv_in_proof proof metano subst_in newmetasenv''
363 List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
365 let apply_tac ~term status = snd (apply_tac_verbose ~term status)
367 let apply_tac_verbose ~term status =
369 apply_tac_verbose ~term status
370 (* TODO cacciare anche altre eccezioni? *)
371 with CicUnification.UnificationFailure _ as e ->
372 raise (Fail (Printexc.to_string e))
374 (* TODO per implementare i tatticali e' necessario che tutte le tattiche
375 sollevino _solamente_ Fail *)
376 let apply_tac ~term =
377 let apply_tac ~term status =
379 apply_tac ~term status
380 (* TODO cacciare anche altre eccezioni? *)
381 with CicUnification.UnificationFailure _ as e ->
382 raise (Fail (Printexc.to_string e))
384 mk_tactic (apply_tac ~term)
386 let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
388 ?(mk_fresh_name_callback = (FreshNamesGenerator.mk_fresh_name ~subst:[])) ()
391 let module C = Cic in
392 let module R = CicReduction in
393 let (_,metasenv,_,_) = proof in
394 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
395 let newmeta = new_meta_of_proof ~proof in
396 let (context',ty',bo') =
397 lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
400 subst_meta_in_proof proof metano bo' [newmeta,context',ty']
402 (newproof, [newmeta])
404 mk_tactic (intros_tac ~mk_fresh_name_callback ())
406 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
408 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
411 let module C = Cic in
412 let curi,metasenv,pbo,pty = proof in
413 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
414 let newmeta1 = new_meta_of_proof ~proof in
415 let newmeta2 = newmeta1 + 1 in
417 mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
418 let context_for_newmeta1 =
419 (Some (fresh_name,C.Decl term))::context in
421 CicMkImplicit.identity_relocation_list_for_metavariable
425 CicMkImplicit.identity_relocation_list_for_metavariable context
427 let newmeta1ty = CicSubstitution.lift 1 ty in
430 [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
431 C.Meta (newmeta2,irl2)]
434 subst_meta_in_proof proof metano bo'
435 [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
437 (newproof, [newmeta1 ; newmeta2])
439 mk_tactic (cut_tac ~mk_fresh_name_callback term)
441 let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
443 ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
446 let module C = Cic in
447 let curi,metasenv,pbo,pty = proof in
448 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
449 let _,_ = (* TASSI: FIXME *)
450 CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
451 let newmeta = new_meta_of_proof ~proof in
453 mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
454 let context_for_newmeta =
455 (Some (fresh_name,C.Def (term,None)))::context in
457 CicMkImplicit.identity_relocation_list_for_metavariable
460 let newmetaty = CicSubstitution.lift 1 ty in
461 let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
464 proof metano bo'[newmeta,context_for_newmeta,newmetaty]
466 (newproof, [newmeta])
468 mk_tactic (letin_tac ~mk_fresh_name_callback term)
470 (** functional part of the "exact" tactic *)
471 let exact_tac ~term =
472 let exact_tac ~term (proof, goal) =
473 (* Assumption: the term bo must be closed in the current context *)
474 let (_,metasenv,_,_) = proof in
475 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
476 let module T = CicTypeChecker in
477 let module R = CicReduction in
478 let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
479 let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
482 let (newproof, metasenv') =
483 subst_meta_in_proof proof metano term [] in
487 raise (Fail "The type of the provided term is not the one expected.")
489 mk_tactic (exact_tac ~term)
491 (* not really "primitive" tactics .... *)
493 let elim_tac ~term (proof, goal) =
494 let module T = CicTypeChecker in
495 let module U = UriManager in
496 let module R = CicReduction in
497 let module C = Cic in
498 let (curi,metasenv,proofbo,proofty) = proof in
499 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
500 let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
502 let uri,exp_named_subst,typeno,args =
504 C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
505 | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
506 (uri,exp_named_subst,typeno,args)
507 | _ -> raise NotAnInductiveTypeToEliminate
510 let buri = U.buri_of_uri uri in
512 let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
514 C.InductiveDefinition (tys,_,_,_) ->
515 let (name,_,_,_) = List.nth tys typeno in
519 let ty_ty,_ = T.type_of_aux' metasenv context ty CicUniv.empty_ugraph in
523 C.Sort C.Prop -> "_ind"
524 | C.Sort C.Set -> "_rec"
525 | C.Sort C.CProp -> "_rec"
526 | C.Sort (C.Type _)-> "_rect"
527 | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
530 U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
532 let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) in
534 T.type_of_aux' metasenv context eliminator_ref CicUniv.empty_ugraph in
535 let rec find_args_no =
537 C.Prod (_,_,t) -> 1 + find_args_no t
538 | C.Cast (s,_) -> find_args_no s
539 | C.LetIn (_,_,t) -> 0 + find_args_no t
542 let args_no = find_args_no ety in
544 let rec make_tl base_case =
547 | n -> (C.Implicit None)::(make_tl base_case (n - 1))
549 C.Appl (eliminator_ref :: make_tl term (args_no - 1))
551 let metasenv', term_to_refine' =
552 CicMkImplicit.expand_implicits metasenv [] context term_to_refine in
553 let refined_term,_,metasenv'',_ = (* TASSI: FIXME *)
554 CicRefine.type_of_aux' metasenv' context term_to_refine'
558 ProofEngineHelpers.compare_metasenvs
559 ~oldmetasenv:metasenv ~newmetasenv:metasenv''
561 let proof' = curi,metasenv'',proofbo,proofty in
562 let proof'', new_goals' =
563 apply_tactic (apply_tac ~term:refined_term) (proof',goal)
565 (* The apply_tactic can have closed some of the new_goals *)
566 let patched_new_goals =
567 let (_,metasenv''',_,_) = proof'' in
569 (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
570 ) new_goals @ new_goals'
572 proof'', patched_new_goals
574 mk_tactic (elim_tac ~term)
577 let elim_intros_tac ~term =
578 Tacticals.then_ ~start:(elim_tac ~term)
579 ~continuation:(intros_tac ())
582 (* The simplification is performed only on the conclusion *)
583 let elim_intros_simpl_tac ~term =
584 Tacticals.then_ ~start:(elim_tac ~term)
587 ~start:(intros_tac ())
589 [ReductionTactics.simpl_tac ~pattern:ProofEngineTypes.goal_pattern])
592 exception NotConvertible
594 (*CSC: Bug (or feature?). [with_what] is parsed in the context of the goal, *)
595 (*CSC: while [what] can have a richer context (because of binders) *)
596 (*CSC: So it is _NOT_ possible to use those binders in the [with_what] term. *)
597 (*CSC: Is that evident? Is that right? Or should it be changed? *)
598 let change_tac ~what ~with_what =
599 let change_tac ~what ~with_what (proof, goal) =
600 let curi,metasenv,pbo,pty = proof in
601 let metano,context,ty = CicUtil.lookup_meta goal metasenv in
602 (* are_convertible works only on well-typed terms *)
604 CicTypeChecker.type_of_aux' metasenv context with_what
606 in (* TASSI: FIXME *)
608 CicReduction.are_convertible context what with_what u
613 ProofEngineReduction.replace
614 ~equality:(==) ~what:[what] ~with_what:[with_what]
616 let ty' = replace ty in
620 Some (name,Cic.Def (t,None))->
621 Some (name,Cic.Def ((replace t),None))
622 | Some (name,Cic.Decl t) -> Some (name,Cic.Decl (replace t))
624 | Some (_,Cic.Def (_,Some _)) -> assert false
630 (n,_,_) when n = metano -> (metano,context',ty')
634 (curi,metasenv',pbo,pty), [metano]
637 raise (ProofEngineTypes.Fail "Not convertible")
639 mk_tactic (change_tac ~what ~with_what)