X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Ftactics%2FprimitiveTactics.ml;h=e17d6cb7b68f16c5f4bac08b75fe91d3bdda4506;hb=3990759a81db3ce45bf4ec56e1985e532151f6e0;hp=6646157240d93ab648ed54386908b03b51da1a28;hpb=acc9067d3263ffced81c52539f918d47d418d5c7;p=helm.git

diff --git a/helm/software/components/tactics/primitiveTactics.ml b/helm/software/components/tactics/primitiveTactics.ml
index 664615724..e17d6cb7b 100644
--- a/helm/software/components/tactics/primitiveTactics.ml
+++ b/helm/software/components/tactics/primitiveTactics.ml
@@ -25,13 +25,13 @@
 
 (* $Id$ *)
 
-open ProofEngineTypes
-
 exception TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
 exception NotAnInductiveTypeToEliminate
 exception WrongUriToVariable of string
 exception NotAnEliminator
 
+module PET = ProofEngineTypes
+
 (* lambda_abstract newmeta ty *)
 (* returns a triple [bo],[context],[ty'] where              *)
 (* [ty] = Pi/LetIn [context].[ty'] ([context] is a vector!) *)
@@ -52,9 +52,14 @@ let lambda_abstract ?(howmany=(-1)) metasenv context newmeta ty mk_fresh_name =
       match ty with 
         C.Cast (te,_)   -> collect_context context howmany do_whd te 
       | C.Prod (n,s,t)  ->
-         let n' = mk_fresh_name metasenv context n ~typ:s in
+	 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) do_whd t 
+           let entry = match n' with
+	      | C.Name _    -> Some (n',(C.Decl s))
+	      | C.Anonymous -> None
+	   in
+	   let ctx = entry :: context in
+           collect_context ctx (howmany - 1) do_whd t 
           in
            (context',ty,C.Lambda(n',s,bo))
       | C.LetIn (n,s,t) ->
@@ -72,7 +77,7 @@ let lambda_abstract ?(howmany=(-1)) metasenv context newmeta ty mk_fresh_name =
 	  let t = CicReduction.whd ~delta:true context t in
 	  collect_context context howmany false t
 	else
-         raise (Fail (lazy "intro(s): not enough products or let-ins"))
+         raise (PET.Fail (lazy "intro(s): not enough products or let-ins"))
   in
    collect_context context howmany true ty 
 
@@ -233,12 +238,13 @@ let
     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 new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty termty goal_arity =
   let (consthead,newmetasenv,arguments,_) =
    TermUtil.saturate_term newmeta' metasenv' context termty
     goal_arity in
   let subst,newmetasenv',_ = 
-   CicUnification.fo_unif newmetasenv context consthead ty CicUniv.empty_ugraph
+   CicUnification.fo_unif_subst 
+     subst context newmetasenv consthead ty CicUniv.empty_ugraph
   in
   let t = 
     if List.length arguments = 0 then term' else Cic.Appl (term'::arguments)
@@ -255,7 +261,7 @@ let apply_with_subst ~term ~subst ~maxmeta (proof, goal) =
  let module T = CicTypeChecker in
  let module R = CicReduction in
  let module C = Cic in
-  let (_,metasenv,_,_, _) = proof in
+  let (_,metasenv,_subst,_,_, _) = proof in
   let metano,context,ty = CicUtil.lookup_meta goal metasenv in
   let newmeta = max (CicMkImplicit.new_meta metasenv subst) maxmeta in
    let exp_named_subst_diff,newmeta',newmetasenvfragment,term' =
@@ -300,7 +306,7 @@ let apply_with_subst ~term ~subst ~maxmeta (proof, goal) =
    let subst,newmetasenv',t = 
     let rec add_one_argument n =
      try
-      new_metasenv_and_unify_and_t newmeta' metasenv' context term' ty
+      new_metasenv_and_unify_and_t newmeta' metasenv' subst context term' ty
         termty n
      with CicUnification.UnificationFailure _ when n > 0 ->
       add_one_argument (n - 1)
@@ -319,13 +325,13 @@ let apply_with_subst ~term ~subst ~maxmeta (proof, goal) =
    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)
+      ((metano,(context,bo',Cic.Implicit None))::subst)
    in
    let (newproof, newmetasenv''') = 
     ProofEngineHelpers.subst_meta_and_metasenv_in_proof proof metano subst_in
      newmetasenv''
    in
-   let subst = ((metano,(context,bo',Cic.Implicit None))::subst) in
+   let subst = ((metano,(context,bo',ty))::subst) in
    subst,
    (newproof, List.map (function (i,_,_) -> i) new_uninstantiatedmetas),
    max maxmeta (CicMkImplicit.new_meta newmetasenv''' subst)
@@ -339,7 +345,7 @@ let apply_with_subst ~term ?(subst=[]) ?(maxmeta=0) status =
       (* TODO cacciare anche altre eccezioni? *)
   with 
   | CicUnification.UnificationFailure msg
-  | CicTypeChecker.TypeCheckerFailure msg -> raise (Fail msg)
+  | CicTypeChecker.TypeCheckerFailure msg -> raise (PET.Fail msg)
 
 (* ALB *)
 let apply_tac_verbose ~term status =
@@ -358,18 +364,16 @@ let apply_tac ~term =
   with 
   | CicUnification.UnificationFailure msg
   | CicTypeChecker.TypeCheckerFailure msg ->
-      raise (Fail msg)
+      raise (PET.Fail msg)
  in
-  mk_tactic (apply_tac ~term)
+  PET.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 intros_tac (proof, goal)
  =
   let module C = Cic in
   let module R = CicReduction in
-   let (_,metasenv,_,_, _) = proof in
+   let (_,metasenv,_subst,_,_, _) = proof in
    let metano,context,ty = CicUtil.lookup_meta goal metasenv in
     let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
      let (context',ty',bo') =
@@ -381,7 +385,7 @@ let intros_tac ?howmany ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_
       in
        (newproof, [newmeta])
  in
-  mk_tactic (intros_tac ~mk_fresh_name_callback ())
+  PET.mk_tactic intros_tac
   
 let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
  let cut_tac
@@ -389,7 +393,7 @@ 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, attrs = proof in
+   let curi,metasenv,_subst,pbo,pty, attrs = proof in
    let metano,context,ty = CicUtil.lookup_meta goal metasenv in
     let newmeta1 = ProofEngineHelpers.new_meta_of_proof ~proof in
     let newmeta2 = newmeta1 + 1 in
@@ -416,7 +420,7 @@ let cut_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:
       in
        (newproof, [newmeta1 ; newmeta2])
  in
-  mk_tactic (cut_tac ~mk_fresh_name_callback term)
+  PET.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
@@ -424,7 +428,7 @@ 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, attrs = proof in
+   let curi,metasenv,_subst,pbo,pty, attrs = proof in
    (* occur check *)
    let occur i t =
      let m = CicUtil.metas_of_term t in 
@@ -454,13 +458,13 @@ let letin_tac ?(mk_fresh_name_callback=FreshNamesGenerator.mk_fresh_name ~subst:
        in
         (newproof, [newmeta])
  in
-  mk_tactic (letin_tac ~mk_fresh_name_callback term)
+  PET.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 (_,metasenv,_subst,_,_, _) = proof in
   let metano,context,ty = CicUtil.lookup_meta goal metasenv in
   let module T = CicTypeChecker in
   let module R = CicReduction in
@@ -473,17 +477,16 @@ let exact_tac ~term =
     (newproof, [])
    end
   else
-   raise (Fail (lazy "The type of the provided term is not the one expected."))
+   raise (PET.Fail (lazy "The type of the provided term is not the one expected."))
  in
-  mk_tactic (exact_tac ~term)
+  PET.mk_tactic (exact_tac ~term)
 
 (* not really "primitive" tactics .... *)
   
 module TC  = CicTypeChecker
-module U   = UriManager
+module UM  = UriManager
 module R   = CicReduction
 module C   = Cic
-module PET = ProofEngineTypes
 module PEH = ProofEngineHelpers
 module PER = ProofEngineReduction
 module MS  = CicMetaSubst 
@@ -491,24 +494,138 @@ module S   = CicSubstitution
 module T   = Tacticals
 module RT  = ReductionTactics
 
+let rec args_init n f =
+   if n <= 0 then [] else f n :: args_init (pred n) f
+
+let mk_predicate_for_elim 
+ ~context ~metasenv ~ugraph ~goal ~arg ~using ~cpattern ~args_no = 
+   let instantiated_eliminator =
+      let f n = if n = 1 then arg else C.Implicit None in
+      C.Appl (using :: args_init args_no f)
+   in
+   let _actual_arg, iety, _metasenv', _ugraph = 
+      CicRefine.type_of_aux' metasenv context instantiated_eliminator ugraph
+   in
+   let _actual_meta, actual_args = match iety with
+      | C.Meta (i, _)                  -> i, []
+      | C.Appl (C.Meta (i, _) :: args) -> i, args
+      | _                              -> assert false
+   in
+(* let _, upto = PEH.split_with_whd (List.nth splits pred_pos) in *)
+   let rec mk_pred metasenv context' pred arg' = function
+      | []           -> metasenv, pred, arg'
+      | arg :: tail -> 
+(* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
+         let argty, _ugraph = TC.type_of_aux' metasenv context' arg ugraph in
+         let argty = CicReduction.whd context' argty in         
+	       let fresh_name = 
+            FreshNamesGenerator.mk_fresh_name 
+            ~subst:[] metasenv context' C.Anonymous ~typ:argty
+         in
+	 let hyp = Some (fresh_name, C.Decl argty) in
+         let lazy_term c m u =  
+            let distance  = List.length c - List.length context in
+            S.lift distance arg, m, u
+         in
+         let pattern = Some lazy_term, [], Some cpattern in
+         let subst, metasenv, _ugraph, _conjecture, selected_terms =
+            ProofEngineHelpers.select
+            ~metasenv ~ugraph ~conjecture:(0, context, pred) ~pattern
+         in
+         let metasenv = MS.apply_subst_metasenv subst metasenv in  
+         let map (_context_of_t, t) l = t :: l in
+         let what = List.fold_right map selected_terms [] in
+         let arg' = MS.apply_subst subst arg' in
+         let argty = MS.apply_subst subst argty in
+         let pred = PER.replace_with_rel_1_from ~equality:(==) ~what 1 pred in
+         let pred = MS.apply_subst subst pred in
+         let pred = C.Lambda (fresh_name, argty, pred) in
+         mk_pred metasenv (hyp :: context') pred arg' tail 
+   in
+   let metasenv, pred, arg = mk_pred metasenv context goal arg actual_args in
+   HLog.debug ("PRED: " ^ CicPp.ppterm ~metasenv pred ^ " ARGS: " ^ String.concat " " (List.map (CicPp.ppterm ~metasenv) actual_args));
+   metasenv, pred, arg, actual_args
+
+let beta_after_elim_tac upto predicate =
+   let beta_after_elim_tac status =
+      let proof, goal = status in
+      let _, metasenv, _subst, _, _, _ = proof in
+      let _, _, ty = CicUtil.lookup_meta goal metasenv in
+      let mk_pattern ~equality ~upto ~predicate ty =
+         (* code adapted from ProceduralConversion.generalize *)
+	 let meta = C.Implicit None in
+         let hole = C.Implicit (Some `Hole) in
+	 let anon = C.Anonymous in
+         let is_meta =
+            let map b = function
+               | C.Implicit None when b -> b
+	       | _                      -> false
+            in
+            List.fold_left map true
+         in
+         let rec gen_fix len k (name, i, ty, bo) =
+            name, i, gen_term k ty, gen_term (k + len) bo
+         and gen_cofix len k (name, ty, bo) =
+            name, gen_term k ty, gen_term (k + len) bo
+         and gen_term k = function
+            | C.Sort _ 
+            | C.Implicit _
+            | C.Const (_, _)
+            | C.Var (_, _)
+            | C.MutInd (_, _, _)
+            | C.MutConstruct (_, _, _, _)
+            | C.Meta (_, _) 
+            | C.Rel _ -> meta
+            | C.Appl (hd :: tl) when equality hd (S.lift k predicate) ->
+	       assert (List.length tl = upto);
+	       hole
+	    | C.Appl ts -> 
+               let ts = List.map (gen_term k) ts in
+               if is_meta ts then meta else C.Appl ts
+            | C.Cast (te, ty) -> 
+               let te, ty = gen_term k te, gen_term k ty in
+	       if is_meta [te; ty] then meta else C.Cast (te, ty)
+            | C.MutCase (sp, i, outty, t, pl) ->         
+	       let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
+	       if is_meta (outty :: t :: pl) then meta else hole (* C.MutCase (sp, i, outty, t, pl) *)
+            | C.Prod (_, s, t) -> 
+               let s, t = gen_term k s, gen_term (succ k) t in
+               if is_meta [s; t] then meta else C.Prod (anon, s, t)
+            | C.Lambda (_, s, t) ->
+               let s, t = gen_term k s, gen_term (succ k) t in
+               if is_meta [s; t] then meta else C.Lambda (anon, s, t)
+            | C.LetIn (_, s, t) -> 
+               let s, t = gen_term k s, gen_term (succ k) t in
+               if is_meta [s; t] then meta else C.LetIn (anon, s, t)
+            | C.Fix (i, fl) -> C.Fix (i, List.map (gen_fix (List.length fl) k) fl)
+            | C.CoFix (i, fl) -> C.CoFix (i, List.map (gen_cofix (List.length fl) k) fl)
+         in
+         None, [], Some (gen_term 0 ty)
+      in
+      let equality = CicUtil.alpha_equivalence in
+      let pattern = mk_pattern ~equality ~upto ~predicate ty in
+      let tactic = RT.head_beta_reduce_tac ~delta:false ~upto ~pattern in
+      PET.apply_tactic tactic status
+   in
+   PET.mk_tactic beta_after_elim_tac
+   
 let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term = 
  let elim_tac (proof, goal) =
+   let cpattern = match pattern with 
+      | None, [], Some cpattern -> cpattern
+      | _                       -> raise (PET.Fail (lazy "not implemented"))
+   in    
    let ugraph = CicUniv.empty_ugraph in
-   let curi, metasenv, proofbo, proofty, attrs = proof in
+   let curi, metasenv, _subst, proofbo, proofty, attrs = proof in
    let conjecture = CicUtil.lookup_meta goal metasenv in
-   let metano, context, ty = conjecture in
-(*    let (term, metasenv, _ugraph), cpatt = match pattern with 
-       | Some f, [], Some cpatt -> f context metasenv ugraph, cpatt
-       | _                      -> assert false
-    in
-*)    
+   let metano, context, ty = conjecture in 
     let termty,_ugraph = TC.type_of_aux' metasenv context term ugraph in
     let termty = CicReduction.whd context termty in
-    let (termty,metasenv',arguments,_fresh_meta) =
+    let termty, metasenv', arguments, _fresh_meta =
      TermUtil.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 =
+    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) ->
@@ -516,7 +633,7 @@ let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
       | _ -> raise NotAnInductiveTypeToEliminate
     in
      let eliminator_uri =
-      let buri = U.buri_of_uri uri in
+      let buri = UM.buri_of_uri uri in
       let name = 
         let o,_ugraph = CicEnvironment.get_obj ugraph uri in
        match o with
@@ -535,202 +652,199 @@ let elim_tac ?using ?(pattern = PET.conclusion_pattern None) term =
         | C.Meta (_,_) -> raise TheTypeOfTheCurrentGoalIsAMetaICannotChooseTheRightElimiantionPrinciple
         | _ -> assert false
       in
-       U.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
+       UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con")
      in
       let eliminator_ref = match using with
-         | None   -> C.Const (eliminator_uri,exp_named_subst)
+         | None   -> C.Const (eliminator_uri, exp_named_subst)
          | Some t -> t 
        in
-       let ety,_ugraph = 
+       let ety, _ugraph = 
          TC.type_of_aux' metasenv' context eliminator_ref ugraph in
 (* FG: ADDED PART ***********************************************************)
 (* FG: we can not assume eliminator is the default eliminator ***************)
-   let add_lambdas n t =
-      let rec aux n t =
-         if n <= 0 then t 
-	 else C.Lambda (C.Anonymous, C.Implicit None, aux (pred n) t)
-      in
-      aux n (S.lift n t)
-   in
-   let rec args_init n f =
-      if n <= 0 then [] else f n :: args_init (pred n) f
-   in
    let splits, args_no = PEH.split_with_whd (context, ety) in
    let pred_pos = match List.hd splits with
       | _, C.Rel i when i > 1 && i <= args_no -> i
       | _, C.Appl (C.Rel i :: _) when i > 1 && i <= args_no -> i
       | _ -> raise NotAnEliminator
    in
-   let _, lambdas = PEH.split_with_whd (List.nth splits pred_pos) in
-   let termty_ty =
-      let termty_ty,_ugraph = TC.type_of_aux' metasenv' context termty ugraph in
-      CicReduction.whd context termty_ty
-   in
-(*   
-   let metasenv', term, pred, upto = match cpatt, termty_ty with
-      | C.Implicit (Some `Hole), _ 
-      | _, C.Sort C.Prop when lambdas = 0 -> metasenv', term, C.Implicit None, 0
-      | _                                 ->
-(* FG: we find the predicate for the eliminator as in the rewrite tactic ****)
-         let fresh_name = 
-             FreshNamesGenerator.mk_fresh_name 
-             ~subst:[] metasenv' context C.Anonymous ~typ:termty
-         in
-         let lazy_term c m u =  
-            let distance  = List.length c - List.length context in
-            S.lift distance term, m, u
-         in
-         let pattern = Some lazy_term, [], Some cpatt in
-         let subst, metasenv', _ugraph, _conjecture, selected_terms =
-            ProofEngineHelpers.select
-            ~metasenv:metasenv' ~ugraph ~conjecture ~pattern
-         in
-         let metasenv' = MS.apply_subst_metasenv subst metasenv' in  
-         let map (_context_of_t, t) l = t :: l in
-         let what = List.fold_right map selected_terms [] in
-         let ty = MS.apply_subst subst ty in
-         let term = MS.apply_subst subst term in
-         let termty = MS.apply_subst subst termty in
-         let abstr_ty = PER.replace_with_rel_1_from ~equality:(==) ~what 1 ty in
-         let abstr_ty = MS.apply_subst subst abstr_ty in
-         let pred_body = C.Lambda (fresh_name, termty, abstr_ty) in
-	 metasenv', term, add_lambdas (pred lambdas) pred_body, lambdas 
+   let metasenv', pred, term, actual_args = match pattern with 
+      | None, [], Some (C.Implicit (Some `Hole)) ->
+         metasenv', C.Implicit None, term, []
+      | _                                        ->
+         mk_predicate_for_elim 
+	    ~args_no ~context ~ugraph ~cpattern
+	    ~metasenv:metasenv' ~arg:term ~using:eliminator_ref ~goal:ty
    in
 (* FG: END OF ADDED PART ****************************************************)
-*)
-         let pred, upto = C.Implicit None, 0 in
-	 
-	 let term_to_refine =
-          let f n =
-	   if n = pred_pos then pred else
-	   if n = 1 then term else C.Implicit None
-	  in
-           C.Appl (eliminator_ref :: args_init args_no f)
+      let term_to_refine =
+         let f n =
+            if n = pred_pos then pred else
+            if n = 1 then term else C.Implicit None
          in
-          let refined_term,_refined_termty,metasenv'',_ugraph = 
-           CicRefine.type_of_aux' metasenv' context term_to_refine
-             ugraph
-          in
-           let new_goals =
-            ProofEngineHelpers.compare_metasenvs
-             ~oldmetasenv:metasenv ~newmetasenv:metasenv''
-           in
-           let proof' = curi,metasenv'',proofbo,proofty, attrs 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
-              let res = proof'', patched_new_goals in
-               if upto = 0 then res else 
-		let pattern = PET.conclusion_pattern None in
-	        let continuation =
-		 RT.simpl_tac ~pattern
-		 (* RT.head_beta_reduce_tac ~delta:false ~upto ~pattern *)
-		in
-		 let dummy_status = proof,goal in
-		  PET.apply_tactic
-		   (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
-                   dummy_status
- in
-  mk_tactic elim_tac
+         C.Appl (eliminator_ref :: args_init args_no f)
+      in
+      let refined_term,_refined_termty,metasenv'',_ugraph = 
+         CicRefine.type_of_aux' metasenv' context term_to_refine ugraph
+      in
+      let new_goals =
+         ProofEngineHelpers.compare_metasenvs
+            ~oldmetasenv:metasenv ~newmetasenv:metasenv''
+      in
+      let proof' = curi,metasenv'',_subst,proofbo,proofty, attrs in
+      let proof'', new_goals' =
+         PET.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''',_subst,_,_, _) = proof'' in
+         List.filter
+            (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
+	    new_goals @ new_goals'
+      in
+      let res = proof'', patched_new_goals in
+      let upto = List.length actual_args in
+      if upto = 0 then res else 
+      let continuation = beta_after_elim_tac upto pred in
+      let dummy_status = proof,goal in
+      PET.apply_tactic
+         (T.then_ ~start:(PET.mk_tactic (fun _ -> res)) ~continuation)
+         dummy_status
+   in
+   PET.mk_tactic elim_tac
 ;;
 
-let cases_intros_tac ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
+let cases_intros_tac ?(howmany=(-1)) ?(mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[]) term =
  let cases_tac ~term (proof, goal) =
   let module TC = CicTypeChecker in
   let module U = UriManager in
   let module R = CicReduction in
   let module C = Cic in
-   let (curi,metasenv,proofbo,proofty, attrs) = proof in
-   let metano,context,ty = CicUtil.lookup_meta goal metasenv in
-    let termty,_ = TC.type_of_aux' metasenv context term CicUniv.empty_ugraph in
-    let termty = CicReduction.whd context termty in
-    let (termty,metasenv',arguments,fresh_meta) =
-     TermUtil.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 paramsno,itty,patterns =
-      match CicEnvironment.get_obj CicUniv.empty_ugraph uri with
-         C.InductiveDefinition (tys,_,paramsno,_),_ ->
-          let _,_,itty,cl = List.nth tys typeno in
-          let rec aux n context t =
-           match n,CicReduction.whd context t with
-              0,C.Prod (name,source,target) ->
-               let fresh_name =
-                mk_fresh_name_callback metasenv' context name
-                 (*CSC: WRONG TYPE HERE: I can get a "bad" name*)
-                 ~typ:source
-               in
-                C.Lambda (fresh_name,C.Implicit None,
-                 aux 0 (Some (fresh_name,C.Decl source)::context) target)
-            | n,C.Prod (name,source,target) ->
-               let fresh_name =
-                mk_fresh_name_callback metasenv' context name
-                 (*CSC: WRONG TYPE HERE: I can get a "bad" name*)
-                 ~typ:source
-               in
-                aux (n-1) (Some (fresh_name,C.Decl source)::context) target
-            | 0,_ -> C.Implicit None
-            | _,_ -> assert false
-          in
-           paramsno,itty,
-           List.map (function (_,cty) -> aux paramsno context cty) cl 
-       | _ -> assert false
-     in
-      let outtype =
-       let target =
-        C.Lambda (C.Name "fixme",C.Implicit None,
-         ProofEngineReduction.replace_lifting
-          ~equality:(ProofEngineReduction.alpha_equivalence)
-          ~what:[CicSubstitution.lift (paramsno+1) term]
-          ~with_what:[C.Rel (paramsno+1)]
-          ~where:(CicSubstitution.lift (paramsno+1) ty))
+  let (curi,metasenv,_subst, proofbo,proofty, attrs) = proof in
+  let metano,context,ty = CicUtil.lookup_meta goal metasenv in
+  let termty,_ = TC.type_of_aux' metasenv context term CicUniv.empty_ugraph in
+  let termty = CicReduction.whd context termty in
+  let (termty,metasenv',arguments,fresh_meta) =
+   TermUtil.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 paramsno,itty,patterns,right_args =
+    match CicEnvironment.get_obj CicUniv.empty_ugraph uri with
+    | C.InductiveDefinition (tys,_,paramsno,_),_ ->
+       let _,left_parameters,right_args = 
+         List.fold_right 
+           (fun x (n,acc1,acc2) -> 
+             if n > 0 then (n-1,acc1,x::acc2) else (n,x::acc1,acc2)) 
+           args (List.length args - paramsno, [],[])
        in
-        let rec add_lambdas =
-         function
-            0 -> target
-          | n -> C.Lambda (C.Name "fixme",C.Implicit None,add_lambdas (n-1))
-        in
-         add_lambdas (count_prods context itty - paramsno)
-      in
-       let term_to_refine =
-        C.MutCase (uri,typeno,outtype,term,patterns)
+       let _,_,itty,cl = List.nth tys typeno in
+       let rec aux left_parameters context t =
+         match left_parameters,CicReduction.whd context t with
+         | [],C.Prod (name,source,target) ->
+            let fresh_name =
+              mk_fresh_name_callback metasenv' context name ~typ:source
+            in
+             C.Lambda (fresh_name,C.Implicit None,
+             aux [] (Some (fresh_name,C.Decl source)::context) target)
+         | hd::tl,C.Prod (name,source,target) ->
+             (* left parameters instantiation *)
+             aux tl context (CicSubstitution.subst hd target)
+         | [],_ -> C.Implicit None
+         | _ -> assert false
        in
-        let refined_term,_,metasenv'',_ = 
-         CicRefine.type_of_aux' metasenv' context term_to_refine
-           CicUniv.empty_ugraph
+        paramsno,itty,
+        List.map (function (_,cty) -> aux left_parameters context cty) cl,
+        right_args
+    | _ -> assert false
+  in
+  let outtype =
+    let n_right_args = List.length right_args in
+    let n_lambdas = n_right_args + 1 in
+    let lifted_ty = CicSubstitution.lift n_lambdas ty in
+    let captured_ty = 
+      let what = 
+        List.map (CicSubstitution.lift n_lambdas) (right_args)
+      in
+      let with_what meta = 
+        let rec mkargs = function 
+          | 0 -> assert false
+          | 1 -> []
+          | n -> 
+              (if meta then Cic.Implicit None else Cic.Rel n)::(mkargs (n-1)) 
         in
-         let new_goals =
-          ProofEngineHelpers.compare_metasenvs
-           ~oldmetasenv:metasenv ~newmetasenv:metasenv''
-         in
-         let proof' = curi,metasenv'',proofbo,proofty, attrs 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 (cases_tac ~term)
+        mkargs n_lambdas 
+      in
+      let replaced = ref false in
+      let replace = ProofEngineReduction.replace_lifting
+       ~equality:(fun _ a b -> let rc = CicUtil.alpha_equivalence a b in 
+                  if rc then replaced := true; rc)
+       ~context:[]
+      in
+      let captured = 
+        replace ~what:[CicSubstitution.lift n_lambdas term] 
+          ~with_what:[Cic.Rel 1] ~where:lifted_ty
+      in
+      if not !replaced then
+        (* this means the matched term is not there, 
+         * but maybe right params are: we user rels (to right args lambdas) *)
+        replace ~what ~with_what:(with_what false) ~where:captured
+      else
+        (* since the matched is there, rights should be inferrable *)
+        replace ~what ~with_what:(with_what true) ~where:captured
+    in
+    let captured_term_ty = 
+      let term_ty = CicSubstitution.lift n_right_args termty in
+      let rec mkrels = function 0 -> []|n -> (Cic.Rel n)::(mkrels (n-1)) in
+      let rec fstn acc l n = 
+        if n = 0 then acc else fstn (acc@[List.hd l]) (List.tl l) (n-1) 
+      in
+      match term_ty with
+      | C.MutInd _ -> term_ty
+      | C.Appl ((C.MutInd (a,b,c))::args) -> 
+           C.Appl ((C.MutInd (a,b,c))::
+               fstn [] args paramsno @ mkrels n_right_args)
+      | _ -> raise NotAnInductiveTypeToEliminate
+    in
+    let rec add_lambdas = function
+      | 0 -> captured_ty
+      | 1 -> 
+          C.Lambda (C.Name "matched", captured_term_ty, (add_lambdas 0))
+      | n -> 
+           C.Lambda (C.Name ("right_"^(string_of_int (n-1))),
+                     C.Implicit None, (add_lambdas (n-1)))
+    in
+    add_lambdas n_lambdas
+  in
+  let term_to_refine = C.MutCase (uri,typeno,outtype,term,patterns) 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'',_subst,proofbo,proofty, attrs in
+  let proof'', new_goals' =
+    PET.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''',_subst,_,_,_) = proof'' in
+      List.filter
+        (function i -> List.exists (function (j,_,_) -> j=i) metasenv''')
+        new_goals @ new_goals'
+    in
+    proof'', patched_new_goals
+  in
+  PET.mk_tactic (cases_tac ~term)
 ;;
 
 
@@ -758,7 +872,7 @@ let letout_tac =
    let mk_fresh_name_callback = FreshNamesGenerator.mk_fresh_name ~subst:[] in
    let term = C.Sort C.Set in
    let letout_tac (proof, goal) =
-      let curi, metasenv, pbo, pty, attrs = proof in
+      let curi, metasenv, _subst, pbo, pty, attrs = proof in
       let metano, context, ty = CicUtil.lookup_meta goal metasenv in
       let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
       let fresh_name = mk_fresh_name_callback metasenv context (Cic.Name "hole") ~typ:term in
@@ -769,4 +883,4 @@ let letout_tac =
       let newproof, _ = ProofEngineHelpers.subst_meta_in_proof proof metano bo'[newmeta,context_for_newmeta,newmetaty] in
       newproof, [newmeta]
    in
-   mk_tactic letout_tac
+   PET.mk_tactic letout_tac