X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=helm%2Focaml%2Ftactics%2FprimitiveTactics.ml;fp=helm%2Focaml%2Ftactics%2FprimitiveTactics.ml;h=7a732a57257304dd89835b7e31aac819f047bea2;hp=0000000000000000000000000000000000000000;hb=792b5d29ebae8f917043d9dd226692919b5d6ca1;hpb=a14a8c7637fd0b95e9d4deccb20c6abc98e8f953

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+(* Copyright (C) 2002, HELM Team.
+ * 
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ * 
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ * 
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA  02111-1307, USA.
+ * 
+ * For details, see the HELM World-Wide-Web page,
+ * http://cs.unibo.it/helm/.
+ *)
+
+(* $Id$ *)
+
+open ProofEngineHelpers
+open ProofEngineTypes
+
+exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
+exception NotAnInductiveTypeToEliminate
+exception WrongUriToVariable of string
+
+(* lambda_abstract newmeta ty *)
+(* returns a triple [bo],[context],[ty'] where              *)
+(* [ty] = Pi/LetIn [context].[ty'] ([context] is a vector!) *)
+(* and [bo] = Lambda/LetIn [context].(Meta [newmeta])       *)
+(* So, lambda_abstract is the core of the implementation of *)
+(* the Intros tactic.                                       *)
+(* howmany = -1 means Intros, howmany > 0 means Intros n    *)
+let lambda_abstract ?(howmany=(-1)) metasenv context newmeta ty mk_fresh_name =
+ let module C = Cic in
+  let rec collect_context context howmany ty =
+   match howmany with
+   | 0 ->  
+        let irl =
+          CicMkImplicit.identity_relocation_list_for_metavariable context
+        in
+         context, ty, (C.Meta (newmeta,irl))
+   | _ -> 
+      match ty with 
+        C.Cast (te,_)   -> collect_context context howmany te 
+      | C.Prod (n,s,t)  ->
+         let n' = mk_fresh_name metasenv context n ~typ:s in
+          let (context',ty,bo) =
+           collect_context ((Some (n',(C.Decl s)))::context) (howmany - 1) t 
+          in
+           (context',ty,C.Lambda(n',s,bo))
+      | C.LetIn (n,s,t) ->
+         let (context',ty,bo) =
+          collect_context ((Some (n,(C.Def (s,None))))::context) (howmany - 1) t
+         in
+          (context',ty,C.LetIn(n,s,bo))
+      | _ as t ->
+        if howmany <= 0 then
+         let irl =
+          CicMkImplicit.identity_relocation_list_for_metavariable context
+         in
+          context, t, (C.Meta (newmeta,irl))
+        else
+         raise (Fail (lazy "intro(s): not enough products or let-ins"))
+  in
+   collect_context context howmany ty 
+
+let eta_expand metasenv context t arg =
+ let module T = CicTypeChecker in
+ let module S = CicSubstitution in
+ let module C = Cic in
+  let rec aux n =
+   function
+      t' when t' = S.lift n arg -> C.Rel (1 + n)
+    | C.Rel m  -> if m <= n then C.Rel m else C.Rel (m+1)
+    | C.Var (uri,exp_named_subst) ->
+       let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
+        C.Var (uri,exp_named_subst')
+    | C.Meta (i,l) ->
+       let l' =
+        List.map (function None -> None | Some t -> Some (aux n t)) l
+       in
+        C.Meta (i, l')
+    | C.Sort _
+    | C.Implicit _ as t -> t
+    | C.Cast (te,ty) -> C.Cast (aux n te, aux n ty)
+    | C.Prod (nn,s,t) -> C.Prod (nn, aux n s, aux (n+1) t)
+    | C.Lambda (nn,s,t) -> C.Lambda (nn, aux n s, aux (n+1) t)
+    | C.LetIn (nn,s,t) -> C.LetIn (nn, aux n s, aux (n+1) t)
+    | C.Appl l -> C.Appl (List.map (aux n) l)
+    | C.Const (uri,exp_named_subst) ->
+       let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
+        C.Const (uri,exp_named_subst')
+    | C.MutInd (uri,i,exp_named_subst) ->
+       let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
+        C.MutInd (uri,i,exp_named_subst')
+    | C.MutConstruct (uri,i,j,exp_named_subst) ->
+       let exp_named_subst' = aux_exp_named_subst n exp_named_subst in
+        C.MutConstruct (uri,i,j,exp_named_subst')
+    | C.MutCase (sp,i,outt,t,pl) ->
+       C.MutCase (sp,i,aux n outt, aux n t,
+        List.map (aux n) pl)
+    | C.Fix (i,fl) ->
+       let tylen = List.length fl in
+        let substitutedfl =
+         List.map
+          (fun (name,i,ty,bo) -> (name, i, aux n ty, aux (n+tylen) bo))
+           fl
+        in
+         C.Fix (i, substitutedfl)
+    | C.CoFix (i,fl) ->
+       let tylen = List.length fl in
+        let substitutedfl =
+         List.map
+          (fun (name,ty,bo) -> (name, aux n ty, aux (n+tylen) bo))
+           fl
+        in
+         C.CoFix (i, substitutedfl)
+  and aux_exp_named_subst n =
+   List.map (function uri,t -> uri,aux n t)
+  in
+   let argty,_ = 
+    T.type_of_aux' metasenv context arg CicUniv.empty_ugraph (* TASSI: FIXME *)
+   in
+    let fresh_name =
+     FreshNamesGenerator.mk_fresh_name ~subst:[]
+      metasenv context (Cic.Name "Heta") ~typ:argty
+    in
+     (C.Appl [C.Lambda (fresh_name,argty,aux 0 t) ; arg])
+
+(*CSC: ma serve solamente la prima delle new_uninst e l'unione delle due!!! *)
+let classify_metas newmeta in_subst_domain subst_in metasenv =
+ List.fold_right
+  (fun (i,canonical_context,ty) (old_uninst,new_uninst) ->
+    if in_subst_domain i then
+     old_uninst,new_uninst
+    else
+     let ty' = subst_in canonical_context ty in
+      let canonical_context' =
+       List.fold_right
+        (fun entry canonical_context' ->
+          let entry' =
+           match entry with
+              Some (n,Cic.Decl s) ->
+               Some (n,Cic.Decl (subst_in canonical_context' s))
+            | Some (n,Cic.Def (s,None)) ->
+               Some (n,Cic.Def ((subst_in canonical_context' s),None))
+            | None -> None
+            | Some (n,Cic.Def (bo,Some ty)) ->
+               Some
+                (n,
+                  Cic.Def
+                   (subst_in canonical_context' bo,
+                    Some (subst_in canonical_context' ty)))
+          in
+           entry'::canonical_context'
+        ) canonical_context []
+     in
+      if i < newmeta then
+       ((i,canonical_context',ty')::old_uninst),new_uninst
+      else
+       old_uninst,((i,canonical_context',ty')::new_uninst)
+  ) metasenv ([],[])
+
+(* Useful only inside apply_tac *)
+let
+ generalize_exp_named_subst_with_fresh_metas context newmeta uri exp_named_subst
+=
+ let module C = Cic in
+  let params =
+    let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+    CicUtil.params_of_obj o
+  in
+   let exp_named_subst_diff,new_fresh_meta,newmetasenvfragment,exp_named_subst'=
+    let next_fresh_meta = ref newmeta in
+    let newmetasenvfragment = ref [] in
+    let exp_named_subst_diff = ref [] in
+     let rec aux =
+      function
+         [],[] -> []
+       | uri::tl,[] ->
+          let ty =
+            let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+              match o with
+                  C.Variable (_,_,ty,_,_) ->
+                    CicSubstitution.subst_vars !exp_named_subst_diff ty
+                | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
+          in
+(* CSC: patch to generate ?1 : ?2 : Type in place of ?1 : Type to simulate ?1 :< Type
+           (match ty with
+               C.Sort (C.Type _) as s -> (* TASSI: ?? *)
+                 let fresh_meta = !next_fresh_meta in
+                 let fresh_meta' = fresh_meta + 1 in
+                  next_fresh_meta := !next_fresh_meta + 2 ;
+                  let subst_item = uri,C.Meta (fresh_meta',[]) in
+                   newmetasenvfragment :=
+                    (fresh_meta,[],C.Sort (C.Type (CicUniv.fresh()))) ::
+                     (* TASSI: ?? *)
+                     (fresh_meta',[],C.Meta (fresh_meta,[])) :: !newmetasenvfragment ;
+                   exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
+                   subst_item::(aux (tl,[]))
+             | _ ->
+*)
+              let irl =
+                CicMkImplicit.identity_relocation_list_for_metavariable context
+              in
+              let subst_item = uri,C.Meta (!next_fresh_meta,irl) in
+               newmetasenvfragment :=
+                (!next_fresh_meta,context,ty)::!newmetasenvfragment ;
+               exp_named_subst_diff := !exp_named_subst_diff @ [subst_item] ;
+               incr next_fresh_meta ;
+               subst_item::(aux (tl,[]))(*)*)
+       | uri::tl1,((uri',_) as s)::tl2 ->
+          assert (UriManager.eq uri uri') ;
+          s::(aux (tl1,tl2))
+       | [],_ -> assert false
+     in
+      let exp_named_subst' = aux (params,exp_named_subst) in
+       !exp_named_subst_diff,!next_fresh_meta,
+        List.rev !newmetasenvfragment, exp_named_subst'
+   in
+    new_fresh_meta,newmetasenvfragment,exp_named_subst',exp_named_subst_diff
+;;
+
+let new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty termty goal_arity =
+  let (consthead,newmetasenv,arguments,_) =
+   saturate_term newmeta' metasenv' context termty goal_arity in
+  let subst,newmetasenv',_ = 
+   CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
+  in
+  let t = 
+    if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
+  in
+  subst,newmetasenv',t
+
+let rec count_prods context ty =
+ match CicReduction.whd context ty with
+    Cic.Prod (n,s,t) -> 1 + count_prods (Some (n,Cic.Decl s)::context) t
+  | _ -> 0
+
+let apply_tac_verbose_with_subst ~term (proof, goal) =
+  (* Assumption: The term "term" must be closed in the current context *)
+ let module T = CicTypeChecker in
+ let module R = CicReduction in
+ let module C = Cic in
+  let (_,metasenv,_,_) = proof in
+  let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+  let newmeta = new_meta_of_proof ~proof in
+   let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
+    match term with
+       C.Var (uri,exp_named_subst) ->
+        let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
+         generalize_exp_named_subst_with_fresh_metas context newmeta uri
+          exp_named_subst
+        in
+         exp_named_subst_diff,newmeta',newmetasenvfragment,
+          C.Var (uri,exp_named_subst')
+     | C.Const (uri,exp_named_subst) ->
+        let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
+         generalize_exp_named_subst_with_fresh_metas context newmeta uri
+          exp_named_subst
+        in
+         exp_named_subst_diff,newmeta',newmetasenvfragment,
+          C.Const (uri,exp_named_subst')
+     | C.MutInd (uri,tyno,exp_named_subst) ->
+        let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
+         generalize_exp_named_subst_with_fresh_metas context newmeta uri
+          exp_named_subst
+        in
+         exp_named_subst_diff,newmeta',newmetasenvfragment,
+          C.MutInd (uri,tyno,exp_named_subst')
+     | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
+        let newmeta',newmetasenvfragment,exp_named_subst',exp_named_subst_diff =
+         generalize_exp_named_subst_with_fresh_metas context newmeta uri
+          exp_named_subst
+        in
+         exp_named_subst_diff,newmeta',newmetasenvfragment,
+          C.MutConstruct (uri,tyno,consno,exp_named_subst')
+     | _ -> [],newmeta,[],term
+   in
+   let metasenv' = metasenv@newmetasenvfragment in
+   let termty,_ = 
+     CicTypeChecker.type_of_aux' metasenv' context term' CicUniv.empty_ugraph
+   in
+   let termty =
+     CicSubstitution.subst_vars exp_named_subst_diff termty in
+   let goal_arity = count_prods context ty in
+   let subst,newmetasenv',t = 
+    let rec add_one_argument n =
+     try
+      new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty
+        termty n
+     with CicUnification.UnificationFailure _ when n > 0 ->
+      add_one_argument (n - 1)
+    in
+     add_one_argument goal_arity
+   in
+   let in_subst_domain i = List.exists (function (j,_) -> i=j) subst in
+   let apply_subst = CicMetaSubst.apply_subst subst in
+   let old_uninstantiatedmetas,new_uninstantiatedmetas =
+     (* subst_in doesn't need the context. Hence the underscore. *)
+     let subst_in _ = CicMetaSubst.apply_subst subst in
+     classify_metas newmeta in_subst_domain subst_in newmetasenv'
+   in
+   let bo' = apply_subst t in
+   let newmetasenv'' = new_uninstantiatedmetas@old_uninstantiatedmetas in
+   let subst_in =
+     (* if we just apply the subtitution, the type is irrelevant:
+              we may use Implicit, since it will be dropped *)
+     CicMetaSubst.apply_subst ((metano,(context,bo',Cic.Implicit None))::subst)
+   in
+   let (newproof, newmetasenv''') = 
+     subst_meta_and_metasenv_in_proof proof metano subst_in newmetasenv''
+   in
+   (((metano,(context,bo',Cic.Implicit None))::subst)(* subst_in *), (* ALB *)
+    (newproof, 
+     List.map (function (i,_,_) -> i) new_uninstantiatedmetas))
+
+
+(* ALB *)
+let apply_tac_verbose_with_subst ~term status =
+  try
+(*     apply_tac_verbose ~term status *)
+    apply_tac_verbose_with_subst ~term status
+      (* TODO cacciare anche altre eccezioni? *)
+  with 
+  | CicUnification.UnificationFailure msg
+  | CicTypeChecker.TypeCheckerFailure msg ->
+      raise (Fail msg)
+
+(* ALB *)
+let apply_tac_verbose ~term status =
+  let subst, status = apply_tac_verbose_with_subst ~term status in
+  (CicMetaSubst.apply_subst subst), status
+
+let apply_tac ~term status = snd (apply_tac_verbose ~term status)
+
+  (* TODO per implementare i tatticali e' necessario che tutte le tattiche
+  sollevino _solamente_ Fail *)
+let apply_tac ~term =
+ let apply_tac ~term status =
+  try
+    apply_tac ~term status
+      (* TODO cacciare anche altre eccezioni? *)
+  with 
+  | CicUnification.UnificationFailure msg
+  | CicTypeChecker.TypeCheckerFailure msg ->
+      raise (Fail msg)
+ in
+  mk_tactic (apply_tac ~term)
+
+let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) ()=
+ let intros_tac
+  ?(mk_fresh_name_callback = (FreshNamesGenerator.mk_fresh_name ~subst:[])) ()
+  (proof, goal)
+ =
+  let module C = Cic in
+  let module R = CicReduction in
+   let (_,metasenv,_,_) = proof in
+   let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+    let newmeta = new_meta_of_proof ~proof in
+     let (context',ty',bo') =
+      lambda_abstract ?howmany metasenv context newmeta ty mk_fresh_name_callback
+     in
+      let (newproof, _) =
+        subst_meta_in_proof proof metano bo' [newmeta,context',ty']
+      in
+       (newproof, [newmeta])
+ in
+  mk_tactic (intros_tac ~mk_fresh_name_callback ())
+  
+let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
+ let cut_tac
+  ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
+  term (proof, goal)
+ =
+  let module C = Cic in
+   let curi,metasenv,pbo,pty = proof in
+   let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+    let newmeta1 = new_meta_of_proof ~proof in
+    let newmeta2 = newmeta1 + 1 in
+    let fresh_name =
+     mk_fresh_name_callback metasenv context (Cic.Name "Hcut") ~typ:term in
+    let context_for_newmeta1 =
+     (Some (fresh_name,C.Decl term))::context in
+    let irl1 =
+     CicMkImplicit.identity_relocation_list_for_metavariable
+      context_for_newmeta1
+    in
+    let irl2 =
+      CicMkImplicit.identity_relocation_list_for_metavariable context
+    in
+     let newmeta1ty = CicSubstitution.lift 1 ty in
+     let bo' =
+      C.Appl
+       [C.Lambda (fresh_name,term,C.Meta (newmeta1,irl1)) ;
+        C.Meta (newmeta2,irl2)]
+     in
+      let (newproof, _) =
+       subst_meta_in_proof proof metano bo'
+        [newmeta2,context,term; newmeta1,context_for_newmeta1,newmeta1ty];
+      in
+       (newproof, [newmeta1 ; newmeta2])
+ in
+  mk_tactic (cut_tac ~mk_fresh_name_callback term)
+
+let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
+ let letin_tac
+  ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
+  term (proof, goal)
+ =
+  let module C = Cic in
+   let curi,metasenv,pbo,pty = proof in
+   let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+    let _,_ = (* TASSI: FIXME *)
+      CicTypeChecker.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+     let newmeta = new_meta_of_proof ~proof in
+     let fresh_name =
+      mk_fresh_name_callback metasenv context (Cic.Name "Hletin") ~typ:term in
+     let context_for_newmeta =
+      (Some (fresh_name,C.Def (term,None)))::context in
+     let irl =
+      CicMkImplicit.identity_relocation_list_for_metavariable
+       context_for_newmeta
+     in
+      let newmetaty = CicSubstitution.lift 1 ty in
+      let bo' = C.LetIn (fresh_name,term,C.Meta (newmeta,irl)) in
+       let (newproof, _) =
+         subst_meta_in_proof
+           proof metano bo'[newmeta,context_for_newmeta,newmetaty]
+       in
+        (newproof, [newmeta])
+ in
+  mk_tactic (letin_tac ~mk_fresh_name_callback term)
+
+  (** functional part of the "exact" tactic *)
+let exact_tac ~term =
+ let exact_tac ~term (proof, goal) =
+  (* Assumption: the term bo must be closed in the current context *)
+  let (_,metasenv,_,_) = proof in
+  let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+  let module T = CicTypeChecker in
+  let module R = CicReduction in
+  let ty_term,u = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+  let b,_ = R.are_convertible context ty_term ty u in (* TASSI: FIXME *)
+  if b then
+   begin
+    let (newproof, metasenv') =
+      subst_meta_in_proof proof metano term [] in
+    (newproof, [])
+   end
+  else
+   raise (Fail (lazy "The type of the provided term is not the one expected."))
+ in
+  mk_tactic (exact_tac ~term)
+
+(* not really "primitive" tactics .... *)
+let elim_tac ~term = 
+ let elim_tac ~term (proof, goal) =
+  let module T = CicTypeChecker in
+  let module U = UriManager in
+  let module R = CicReduction in
+  let module C = Cic in
+   let (curi,metasenv,proofbo,proofty) = proof in
+   let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+    let termty,_ = T.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+    let (termty,metasenv',arguments,fresh_meta) =
+     ProofEngineHelpers.saturate_term
+      (ProofEngineHelpers.new_meta_of_proof proof) metasenv context termty 0 in
+    let term = if arguments = [] then term else Cic.Appl (term::arguments) in
+    let uri,exp_named_subst,typeno,args =
+     match termty with
+        C.MutInd (uri,typeno,exp_named_subst) -> (uri,exp_named_subst,typeno,[])
+      | C.Appl ((C.MutInd (uri,typeno,exp_named_subst))::args) ->
+          (uri,exp_named_subst,typeno,args)
+      | _ -> raise NotAnInductiveTypeToEliminate
+    in
+     let eliminator_uri =
+      let buri = U.buri_of_uri uri in
+      let name = 
+        let o,_ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
+       match o with
+          C.InductiveDefinition (tys,_,_,_) ->
+           let (name,_,_,_) = List.nth tys typeno in
+            name
+        | _ -> assert false
+      in
+      let ty_ty,_ = T.type_of_aux' metasenv' context ty CicUniv.empty_ugraph in
+      let ext =
+       match ty_ty with
+          C.Sort C.Prop -> "_ind"
+        | C.Sort C.Set  -> "_rec"
+        | C.Sort C.CProp -> "_rec"
+        | C.Sort (C.Type _)-> "_rect" 
+        | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
+        | _ -> assert false
+      in
+       U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
+     in
+      let eliminator_ref = C.Const (eliminator_uri,exp_named_subst) in
+       let ety,_ = 
+         T.type_of_aux' metasenv' context eliminator_ref CicUniv.empty_ugraph in
+        let rec find_args_no =
+         function
+            C.Prod (_,_,t) -> 1 + find_args_no t
+          | C.Cast (s,_) -> find_args_no s
+          | C.LetIn (_,_,t) -> 0 + find_args_no t
+          | _ -> 0
+        in
+         let args_no = find_args_no ety in
+         let term_to_refine =
+          let rec make_tl base_case =
+           function
+              0 -> [base_case]
+            | n -> (C.Implicit None)::(make_tl base_case (n - 1))
+          in
+           C.Appl (eliminator_ref :: make_tl term (args_no - 1))
+         in
+          let refined_term,_,metasenv'',_ = 
+           CicRefine.type_of_aux' metasenv' context term_to_refine
+             CicUniv.empty_ugraph
+          in
+           let new_goals =
+            ProofEngineHelpers.compare_metasenvs
+             ~oldmetasenv:metasenv ~newmetasenv:metasenv''
+           in
+           let proof' = curi,metasenv'',proofbo,proofty in
+            let proof'', new_goals' =
+             apply_tactic (apply_tac ~term:refined_term) (proof',goal)
+            in
+             (* The apply_tactic can have closed some of the new_goals *)
+             let patched_new_goals =
+              let (_,metasenv''',_,_) = proof'' in
+               List.filter
+                (function i -> List.exists (function (j,_,_) -> j=i) metasenv'''
+                ) new_goals @ new_goals'
+             in
+              proof'', patched_new_goals
+ in
+  mk_tactic (elim_tac ~term)
+;;
+
+let elim_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) 
+                    ?depth ?using what =
+ Tacticals.then_ ~start:(elim_tac ~term:what)
+  ~continuation:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
+;;
+
+(* The simplification is performed only on the conclusion *)
+let elim_intros_simpl_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[])
+                          ?depth ?using what =
+ Tacticals.then_ ~start:(elim_tac ~term:what)
+  ~continuation:
+   (Tacticals.thens
+     ~start:(intros_tac ~mk_fresh_name_callback ?howmany:depth ())
+     ~continuations:
+       [ReductionTactics.simpl_tac
+         ~pattern:(ProofEngineTypes.conclusion_pattern None)])
+;;