X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_refiner%2FnCicMetaSubst.ml;h=60abe85c37c08879ea80d01ededa27c158d0192f;hb=8049c166a37789d7a1b1ca1c3a1174712bbf87ba;hp=12fe977083ec04a2c9ee309c116e2cb22419929b;hpb=e1ffde2ba67b8a2f7d4d97898ba28afd65d96ea7;p=helm.git

diff --git a/helm/software/components/ng_refiner/nCicMetaSubst.ml b/helm/software/components/ng_refiner/nCicMetaSubst.ml
index 12fe97708..60abe85c3 100644
--- a/helm/software/components/ng_refiner/nCicMetaSubst.ml
+++ b/helm/software/components/ng_refiner/nCicMetaSubst.ml
@@ -14,155 +14,27 @@
 exception MetaSubstFailure of string Lazy.t
 exception Uncertain of string Lazy.t
 
-(*
-(*** Functions to apply a substitution ***)
-
-let apply_subst_gen ~appl_fun subst term =
- let rec um_aux =
-  let module C = Cic in
-  let module S = CicSubstitution in 
-   function
-      C.Rel _ as t -> t
-    | C.Var (uri,exp_named_subst) ->
-       let exp_named_subst' =
-         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
-       in
-       C.Var (uri, exp_named_subst')
-    | C.Meta (i, l) -> 
-        (try
-          let (_, t,_) = lookup_subst i subst in
-          um_aux (S.subst_meta l t)
-        with CicUtil.Subst_not_found _ -> 
-	  (* unconstrained variable, i.e. free in subst*)
-          let l' =
-            List.map (function None -> None | Some t -> Some (um_aux t)) l
-          in
-           C.Meta (i,l'))
-    | C.Sort _
-    | C.Implicit _ as t -> t
-    | C.Cast (te,ty) -> C.Cast (um_aux te, um_aux ty)
-    | C.Prod (n,s,t) -> C.Prod (n, um_aux s, um_aux t)
-    | C.Lambda (n,s,t) -> C.Lambda (n, um_aux s, um_aux t)
-    | C.LetIn (n,s,ty,t) -> C.LetIn (n, um_aux s, um_aux ty, um_aux t)
-    | C.Appl (hd :: tl) -> appl_fun um_aux hd tl
-    | C.Appl _ -> assert false
-    | C.Const (uri,exp_named_subst) ->
-       let exp_named_subst' =
-         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
-       in
-       C.Const (uri, exp_named_subst')
-    | C.MutInd (uri,typeno,exp_named_subst) ->
-       let exp_named_subst' =
-         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
-       in
-       C.MutInd (uri,typeno,exp_named_subst')
-    | C.MutConstruct (uri,typeno,consno,exp_named_subst) ->
-       let exp_named_subst' =
-         List.map (fun (uri, t) -> (uri, um_aux t)) exp_named_subst
-       in
-       C.MutConstruct (uri,typeno,consno,exp_named_subst')
-    | C.MutCase (sp,i,outty,t,pl) ->
-       let pl' = List.map um_aux pl in
-       C.MutCase (sp, i, um_aux outty, um_aux t, pl')
-    | C.Fix (i, fl) ->
-       let fl' =
-         List.map (fun (name, i, ty, bo) -> (name, i, um_aux ty, um_aux bo)) fl
-       in
-       C.Fix (i, fl')
-    | C.CoFix (i, fl) ->
-       let fl' =
-         List.map (fun (name, ty, bo) -> (name, um_aux ty, um_aux bo)) fl
-       in
-       C.CoFix (i, fl')
- in
-  um_aux term
-;;
-
-let apply_subst =
-  let appl_fun um_aux he tl =
-    let tl' = List.map um_aux tl in
-    let t' =
-     match um_aux he with
-        Cic.Appl l -> Cic.Appl (l@tl')
-      | he' -> Cic.Appl (he'::tl')
-    in
-     begin
-      match he with
-         Cic.Meta (m,_) -> CicReduction.head_beta_reduce t'
-       | _ -> t'
-     end
-  in
-  fun subst t ->
-(*     incr apply_subst_counter; *)
-match subst with
-   [] -> t
- | _ -> apply_subst_gen ~appl_fun subst t
-;;
-
-let profiler = HExtlib.profile "U/CicMetaSubst.apply_subst"
-let apply_subst s t = 
-  profiler.HExtlib.profile (apply_subst s) t
-
-
-let apply_subst_context subst context =
- match subst with
-    [] -> context
-  | _ ->
-(*
-  incr apply_subst_context_counter;
-  context_length := !context_length + List.length context;
-*)
-  List.fold_right
-    (fun item context ->
-      match item with
-      | Some (n, Cic.Decl t) ->
-          let t' = apply_subst subst t in
-          Some (n, Cic.Decl t') :: context
-      | Some (n, Cic.Def (t, ty)) ->
-          let ty' = apply_subst subst ty in
-          let t' = apply_subst subst t in
-          Some (n, Cic.Def (t', ty')) :: context
-      | None -> None :: context)
-    context []
-
-let apply_subst_metasenv subst metasenv =
-(*
-  incr apply_subst_metasenv_counter;
-  metasenv_length := !metasenv_length + List.length metasenv;
-*)
-match subst with
-   [] -> metasenv
- | _ ->
-  List.map
-    (fun (n, context, ty) ->
-      (n, apply_subst_context subst context, apply_subst subst ty))
-    (List.filter
-      (fun (i, _, _) -> not (List.mem_assoc i subst))
-      metasenv)
-
-let tempi_type_of_aux_subst = ref 0.0;;
-let tempi_subst = ref 0.0;;
-let tempi_type_of_aux = ref 0.0;;
-*)
-
-let newmeta = 
+let newmeta,maxmeta = 
   let maxmeta = ref 0 in
-  fun () -> incr maxmeta; !maxmeta
+  (fun () -> incr maxmeta; !maxmeta),
+  (fun () -> !maxmeta)
 ;;
 
 exception NotInTheList;;
 
-let position n (shift, lc) =
+let position to_skip n (shift, lc) =
   match lc with
+  | NCic.Irl _ when to_skip > 0 -> assert false  (* unclear to me *)
   | NCic.Irl len when n <= shift || n > shift + len -> raise NotInTheList
   | NCic.Irl _ -> n - shift
   | NCic.Ctx tl ->
-      let rec aux k = function 
+      let rec aux to_skip k = function 
          | [] -> raise NotInTheList
+         | _ :: tl when to_skip > 0 -> aux (to_skip - 1) (k+1) tl
          | (NCic.Rel m)::_ when m + shift = n -> k
-         | _::tl -> aux (k+1) tl 
+         | _::tl -> aux to_skip (k+1) tl 
       in
-       aux 1 tl
+       aux to_skip 1 tl
 ;;
 
 let pack_lc orig = 
@@ -200,29 +72,41 @@ let rec force_does_not_occur metasenv subst restrictions t =
         in
         if amount > 0 then ms, NCic.Rel (r - amount) else ms, orig
     | NCic.Meta (n, (shift,lc as l)) as orig ->
-       (* we ignore the subst since restrict will take care of already
-        * instantiated/restricted metavariabels *)
-       let (metasenv,subst as ms), restrictions_for_n, l' =
-         let l = NCicUtils.expand_local_context lc in
-         let ms, _, restrictions_for_n, l =
-          List.fold_right
-            (fun t (ms, i, restrictions_for_n, l) ->
-              try 
-                let ms, t = aux (k-shift) ms t in
-                ms, i-1, restrictions_for_n, t::l
-              with Occur ->
-                ms, i-1, i::restrictions_for_n, l)
-            l (ms, List.length l, [], [])
-         in
-          ms, restrictions_for_n, pack_lc (shift, NCic.Ctx l)
+       let meta_chain =
+        try
+         Some (NCicUtils.lookup_subst n subst)
+        with
+         NCicUtils.Subst_not_found _ -> None
        in
-       if restrictions_for_n = [] then
-         ms, if l = l' then orig else NCic.Meta (n, l')
-       else
-         let metasenv, subst, newmeta = 
-           restrict metasenv subst n restrictions_for_n 
-         in
-           (metasenv, subst), NCic.Meta (newmeta, l')
+        (match meta_chain with
+            Some (_,_,bo,_) ->
+             aux k ms (NCicSubstitution.subst_meta l bo)
+          | None ->
+             (* we ignore the subst since restrict will take care of already
+              * instantiated/restricted metavariabels *)
+             let (metasenv,subst as ms), restrictions_for_n, l' =
+               let l = NCicUtils.expand_local_context lc in
+         
+               let ms, _, restrictions_for_n, l =
+                List.fold_right
+                  (fun t (ms, i, restrictions_for_n, l) ->
+                    try 
+                      let ms, t = aux (k-shift) ms t in
+                      ms, i-1, restrictions_for_n, t::l
+                    with Occur ->
+                      ms, i-1, i::restrictions_for_n, l)
+                  l (ms, List.length l, [], [])
+               in
+                   
+                ms, restrictions_for_n, pack_lc (shift, NCic.Ctx l)
+             in
+             if restrictions_for_n = [] then
+               ms, if l = l' then orig else NCic.Meta (n, l')
+             else
+               let metasenv, subst, newmeta = 
+                 restrict metasenv subst n restrictions_for_n 
+               in
+                 (metasenv, subst), NCic.Meta (newmeta, l'))
     | t -> NCicUntrusted.map_term_fold_a (fun _ k -> k+1) k aux ms t
  in
    aux 0 (metasenv,subst) t 
@@ -322,37 +206,129 @@ and restrict metasenv subst i restrictions =
     | NCicUtils.Meta_not_found _ -> assert false
 ;;
 
+let rec flexible_arg context subst = function 
+  | NCic.Meta (i,_) | NCic.Appl (NCic.Meta (i,_) :: _)-> 
+      (try 
+        let _,_,t,_ = List.assoc i subst in
+        flexible_arg context subst t
+      with Not_found -> true)
+   (* this is a cheap whd, it only performs zeta-reduction.
+    * 
+    * it works when the **omissis** disambiguation algorithm
+    * is run on `let x := K a b in t`, K is substituted for a 
+    * ? and thus in t metavariables have a flexible Rel
+    *)
+  | NCic.Rel i ->
+      (try
+         match List.nth context (i-1)
+         with 
+         | _,NCic.Def (bo,_) ->
+               flexible_arg context subst
+                 (NCicSubstitution.lift i bo)
+         | _ -> false
+      with 
+      | Failure _ -> assert false
+      | Invalid_argument _ -> assert false)
+  | _ -> false
+;;
+
+let in_scope_tag  = "tag:in_scope" ;;
+let out_scope_tag_prefix = "tag:out_scope:" 
+let out_scope_tag n = out_scope_tag_prefix ^ string_of_int n ;;
+let is_out_scope_tag tag =
+   String.length tag > String.length out_scope_tag_prefix &&
+   String.sub tag 0 (String.length out_scope_tag_prefix) = out_scope_tag_prefix 
+;;
+let int_of_out_scope_tag tag = 
+  int_of_string
+   (String.sub tag (String.length out_scope_tag_prefix)
+     (String.length tag - (String.length out_scope_tag_prefix)))
+;;
+
+
+exception Found;;
+
 (* INVARIANT: we suppose that t is not another occurrence of Meta(n,_), 
    otherwise the occur check does not make sense in case of unification
    of ?n with ?n *)
-let delift metasenv subst context n l t =
-  let rec aux k (metasenv, subst as ms) = function
+let delift ~unify metasenv subst context n l t =
+  let is_in_scope_meta subst = function
+    | NCic.Meta (i,_) ->
+        (try 
+           let tag, _, _, _ = NCicUtils.lookup_subst i subst in 
+           tag = Some in_scope_tag 
+        with NCicUtils.Subst_not_found _ -> false)
+    | _ -> false
+  in
+  let contains_in_scope subst t = 
+    let rec aux _ () = function
+      | NCic.Meta _ as t ->
+          if is_in_scope_meta subst t then raise Found
+          else ()
+      | t -> 
+          if is_in_scope_meta subst t then raise Found
+          else NCicUtils.fold (fun _ () -> ()) () aux () t
+    in
+    try aux () () t; false with Found -> true
+  in
+  let unify_list in_scope = 
+    match l with
+    | _, NCic.Irl _ -> fun _ _ _ _ _ -> None
+    | shift, NCic.Ctx l -> fun metasenv subst context k t ->
+       if flexible_arg context subst t || contains_in_scope subst t then None else
+         let lb = List.map (fun t -> t, flexible_arg context subst t) l in
+         HExtlib.list_findopt
+          (fun (li,flexible) i ->
+            if flexible || i < in_scope then None else
+             let li = NCicSubstitution.lift (k+shift) li in
+             match unify metasenv subst context li t with
+             | Some (metasenv,subst) -> 
+                 Some ((metasenv, subst), NCic.Rel (i+1+k))
+             | None -> None)
+          lb
+  in
+  let rec aux (context,k,in_scope) (metasenv, subst as ms) t = 
+   match unify_list in_scope metasenv subst context k t with
+   | Some x -> x
+   | None -> 
+    match t with 
     | NCic.Rel n as t when n <= k -> ms, t
     | NCic.Rel n -> 
         (try
           match List.nth context (n-k-1) with
           | _,NCic.Def (bo,_) -> 
-                (try ms, NCic.Rel ((position (n-k) l) + k)
+                (try ms, NCic.Rel ((position in_scope (n-k) l) + k)
                  with NotInTheList ->
                 (* CSC: This bit of reduction hurts performances since it is
                  * possible to  have an exponential explosion of the size of the
                  * proof. required for nat/nth_prime.ma *)
-                  aux k ms (NCicSubstitution.lift n bo))
-          | _,NCic.Decl _ -> ms, NCic.Rel ((position (n-k) l) + k)
+                  aux (context,k,in_scope) ms (NCicSubstitution.lift n bo))
+          | _,NCic.Decl _ -> ms, NCic.Rel ((position in_scope (n-k) l) + k)
         with Failure _ -> assert false) (*Unbound variable found in delift*)
-    | NCic.Meta (_,(_,(NCic.Irl 0| NCic.Ctx []))) as orig -> ms, orig
+    | NCic.Meta (i,_) when i=n ->
+         raise (MetaSubstFailure (lazy (Printf.sprintf (
+           "Cannot unify the metavariable ?%d with a term that has "^^
+           "as subterm %s in which the same metavariable "^^
+           "occurs (occur check)") i 
+            (NCicPp.ppterm ~context ~metasenv ~subst t))))
     | NCic.Meta (i,l1) as orig ->
         (try
-           let _,_,t,_ = NCicUtils.lookup_subst i subst in
-           aux k ms (NCicSubstitution.subst_meta l1 t)
+           let tag,c,t,ty = NCicUtils.lookup_subst i subst in
+           let in_scope, clear = 
+             match tag with 
+             | Some tag when tag = in_scope_tag -> 0, true
+             | Some tag when is_out_scope_tag tag->int_of_out_scope_tag tag,true
+             | _ -> in_scope, false
+           in
+           let ms = 
+             if not clear then ms
+             else 
+               metasenv, 
+               (i,(None,c,t,ty)) :: List.filter (fun j,_ -> i <> j) subst
+           in
+           aux (context,k,in_scope) ms (NCicSubstitution.subst_meta l1 t)
          with NCicUtils.Subst_not_found _ ->
-           (* see the top level invariant *)
-           if (i = n) then 
-            raise (MetaSubstFailure (lazy (Printf.sprintf (
-              "Cannot unify the metavariable ?%d with a term that has "^^
-              "as subterm %s in which the same metavariable "^^
-              "occurs (occur check)") i 
-               (NCicPp.ppterm ~context ~metasenv ~subst t))))
+           if snd l1 = NCic.Irl 0 || snd l1 = NCic.Ctx [] then ms, orig
            else
               let shift1,lc1 = l1 in
               let shift,lc = l in
@@ -366,21 +342,33 @@ let delift metasenv subst context n l t =
                   in
                   (metasenv, subst), 
                     NCic.Meta (newmeta, (0,NCic.Irl (max 0 (k-shift1))))
-              | NCic.Irl len, NCic.Irl len1 
-                when shift1 < shift || len1 + shift1 > len + shift ->
-                  (* C. Hoare. Premature optimization is the root of all evil*)
-                  let stop = shift + len in
-                  let stop1 = shift1 + len1 in
-                  let low_gap = max 0 (shift - shift1) in
-                  let high_gap = max 0 (stop1 - stop) in
-                  let restrictions = 
-                     HExtlib.list_seq (k+1-shift1) (low_gap + 1) @
-                     HExtlib.list_seq (len1 - high_gap + 1) (len1 + 1)
+              | NCic.Irl len, NCic.Irl len1 ->
+                  let low_restrictions, new_shift = 
+                    if k <= shift1 && shift1 < shift then 
+                      HExtlib.list_seq 1 (shift - shift1 + 1), k
+                    else if shift1 < k (* <= shift *) then
+                      let save_below = k - shift1 in
+                      HExtlib.list_seq (save_below + 1) (shift - shift1 + 1),
+                      shift1
+                    else [], shift1 - shift + k
+                  in
+                  let high_restrictions = 
+                    let last = shift + len in
+                    let last1 = shift1 + len1 in
+                    if last1 > last then
+                      let high_gap = last1 - last in
+                      HExtlib.list_seq (len1 - high_gap + 1) (len1 + 1)
+                    else []
                   in
+                  let restrictions = low_restrictions @ high_restrictions in
+                  if restrictions = [] then
+                    if shift = k then ms, orig
+                    else ms, NCic.Meta (i, (new_shift, lc1))
+                  else
                     let metasenv, subst, newmeta = 
-                       restrict metasenv subst i restrictions 
+                       restrict metasenv subst i restrictions
                     in
-(*
+(* {{{
                   prerr_endline ("RESTRICTIONS FOR: " ^ 
                     NCicPp.ppterm ~metasenv ~subst ~context:[] 
                     (NCic.Meta (i,l1))^" that was part of a term unified with "
@@ -389,22 +377,16 @@ let delift metasenv subst context n l t =
                     string_of_int restrictions) ^ "\nMENV:\n" ^
                     NCicPp.ppmetasenv ~subst metasenv ^ "\nSUBST:\n" ^
                     NCicPp.ppsubst subst ~metasenv);
-*)
-                  let newlc_len = 
-                    len1 - low_gap - high_gap + max 0 (k - shift1) in
-                  assert (if shift1 > k then 
-                    shift1 + low_gap - shift = 0 else true);
-                  let meta = 
-                     NCic.Meta(newmeta,(shift1 + low_gap - shift, 
-                       NCic.Irl newlc_len))
-                  in
-                  let _, cctx, _ = NCicUtils.lookup_meta newmeta metasenv in
-                  assert (List.length cctx = newlc_len);
+}}} *)
+                    let newlc_len = len1 - List.length restrictions in 
+                    let meta = 
+                       NCic.Meta(newmeta,(new_shift, NCic.Irl newlc_len))
+                    in
+                    assert (
+                      let _, cctx, _ = NCicUtils.lookup_meta newmeta metasenv in
+                      List.length cctx = newlc_len);
                     (metasenv, subst), meta
-                  
-              | NCic.Irl _, NCic.Irl _ when shift = 0 -> ms, orig
-              | NCic.Irl _, NCic.Irl _ ->
-                   ms, NCic.Meta (i, (max 0 (shift1 - shift), lc1))
+
               | _ ->
                   let lc1 = NCicUtils.expand_local_context lc1 in
                   let lc1 = List.map (NCicSubstitution.lift shift1) lc1 in
@@ -413,7 +395,7 @@ let delift metasenv subst context n l t =
                     | t::tl ->
                         let ms, tbr, tl = deliftl tbr (j+1) ms tl in
                         try 
-                          let ms, t = aux k ms t in 
+                          let ms, t = aux (context,k,in_scope) ms t in 
                           ms, tbr, t::tl
                         with
                         | NotInTheList | MetaSubstFailure _ -> ms, j::tbr, tl
@@ -436,9 +418,11 @@ let delift metasenv subst context n l t =
                       restrict metasenv subst i to_be_r in
                     (metasenv, subst), NCic.Meta(newmeta,l1))
 
-    | t -> NCicUntrusted.map_term_fold_a (fun _ k -> k+1) k aux ms t
+    | t -> 
+        NCicUntrusted.map_term_fold_a 
+          (fun e (c,k,s) -> (e::c,k+1,s)) (context,k,in_scope) aux ms t
   in
-   try aux 0 (metasenv,subst) t
+   try aux (context,0,0) (metasenv,subst) t
    with NotInTheList ->
       (* This is the case where we fail even first order unification. *)
       (* The reason is that our delift function is weaker than first  *)
@@ -455,184 +439,40 @@ let delift metasenv subst context n l t =
       let lc = NCicUtils.expand_local_context lc in
       let l = List.map (NCicSubstitution.lift shift) lc in
        if
-         List.exists
-          (fun t -> NCicUntrusted.metas_of_term subst context t = [])
-            l
+        List.exists (fun t-> NCicUntrusted.metas_of_term subst context t <> [])l
        then
         raise (Uncertain msg)
        else
         raise (MetaSubstFailure msg)
 ;;
 
-(*
-(* delifts a term t of n levels strating from k, that is changes (Rel m)
- * to (Rel (m - n)) when m > (k + n). if k <= m < k + n delift fails
- *)
-let delift_rels_from subst metasenv k n =
- let rec liftaux subst metasenv k =
-  let module C = Cic in
-   function
-      C.Rel m as t ->
-       if m < k then
-        t, subst, metasenv
-       else if m < k + n then
-         raise DeliftingARelWouldCaptureAFreeVariable
-       else
-        C.Rel (m - n), subst, metasenv
-    | C.Var (uri,exp_named_subst) ->
-       let exp_named_subst',subst,metasenv = 
-        List.fold_right
-         (fun (uri,t) (l,subst,metasenv) ->
-           let t',subst,metasenv = liftaux subst metasenv k t in
-            (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
-       in
-        C.Var (uri,exp_named_subst'),subst,metasenv
-    | C.Meta (i,l) ->
-        (try
-          let (_, t,_) = lookup_subst i subst in
-           liftaux subst metasenv k (CicSubstitution.subst_meta l t)
-         with CicUtil.Subst_not_found _ -> 
-          let l',to_be_restricted,subst,metasenv =
-           let rec aux con l subst metasenv =
-            match l with
-               [] -> [],[],subst,metasenv
-             | he::tl ->
-                let tl',to_be_restricted,subst,metasenv =
-                 aux (con + 1) tl subst metasenv in
-                let he',more_to_be_restricted,subst,metasenv =
-                 match he with
-                    None -> None,[],subst,metasenv
-                  | Some t ->
-                     try
-                      let t',subst,metasenv = liftaux subst metasenv k t in
-                       Some t',[],subst,metasenv
-                     with
-                      DeliftingARelWouldCaptureAFreeVariable ->
-                       None,[i,con],subst,metasenv
-                in
-                 he'::tl',more_to_be_restricted@to_be_restricted,subst,metasenv
-           in
-            aux 1 l subst metasenv in
-          let metasenv,subst = restrict subst to_be_restricted metasenv in
-           C.Meta(i,l'),subst,metasenv)
-    | C.Sort _ as t -> t,subst,metasenv
-    | C.Implicit _ as t -> t,subst,metasenv
-    | C.Cast (te,ty) ->
-       let te',subst,metasenv = liftaux subst metasenv k te in
-       let ty',subst,metasenv = liftaux subst metasenv k ty in
-        C.Cast (te',ty'),subst,metasenv
-    | C.Prod (n,s,t) ->
-       let s',subst,metasenv = liftaux subst metasenv k s in
-       let t',subst,metasenv = liftaux subst metasenv (k+1) t in
-        C.Prod (n,s',t'),subst,metasenv
-    | C.Lambda (n,s,t) ->
-       let s',subst,metasenv = liftaux subst metasenv k s in
-       let t',subst,metasenv = liftaux subst metasenv (k+1) t in
-        C.Lambda (n,s',t'),subst,metasenv
-    | C.LetIn (n,s,ty,t) ->
-       let s',subst,metasenv = liftaux subst metasenv k s in
-       let ty',subst,metasenv = liftaux subst metasenv k ty in
-       let t',subst,metasenv = liftaux subst metasenv (k+1) t in
-        C.LetIn (n,s',ty',t'),subst,metasenv
-    | C.Appl l ->
-       let l',subst,metasenv =
-        List.fold_right
-         (fun t (l,subst,metasenv) ->
-           let t',subst,metasenv = liftaux subst metasenv k t in
-            t'::l,subst,metasenv) l ([],subst,metasenv) in
-       C.Appl l',subst,metasenv
-    | C.Const (uri,exp_named_subst) ->
-       let exp_named_subst',subst,metasenv = 
-        List.fold_right
-         (fun (uri,t) (l,subst,metasenv) ->
-           let t',subst,metasenv = liftaux subst metasenv k t in
-            (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
-       in
-        C.Const (uri,exp_named_subst'),subst,metasenv
-    | C.MutInd (uri,tyno,exp_named_subst) ->
-       let exp_named_subst',subst,metasenv = 
-        List.fold_right
-         (fun (uri,t) (l,subst,metasenv) ->
-           let t',subst,metasenv = liftaux subst metasenv k t in
-            (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
-       in
-        C.MutInd (uri,tyno,exp_named_subst'),subst,metasenv
-    | C.MutConstruct (uri,tyno,consno,exp_named_subst) ->
-       let exp_named_subst',subst,metasenv = 
-        List.fold_right
-         (fun (uri,t) (l,subst,metasenv) ->
-           let t',subst,metasenv = liftaux subst metasenv k t in
-            (uri,t')::l,subst,metasenv) exp_named_subst ([],subst,metasenv)
-       in
-        C.MutConstruct (uri,tyno,consno,exp_named_subst'),subst,metasenv
-    | C.MutCase (sp,i,outty,t,pl) ->
-       let outty',subst,metasenv = liftaux subst metasenv k outty in
-       let t',subst,metasenv = liftaux subst metasenv k t in
-       let pl',subst,metasenv =
-        List.fold_right
-         (fun t (l,subst,metasenv) ->
-           let t',subst,metasenv = liftaux subst metasenv k t in
-            t'::l,subst,metasenv) pl ([],subst,metasenv)
-       in
-        C.MutCase (sp,i,outty',t',pl'),subst,metasenv
-    | C.Fix (i, fl) ->
-       let len = List.length fl in
-       let liftedfl,subst,metasenv =
-        List.fold_right
-         (fun (name, i, ty, bo) (l,subst,metasenv) ->
-           let ty',subst,metasenv = liftaux subst metasenv k ty in
-           let bo',subst,metasenv = liftaux subst metasenv (k+len) bo in
-            (name,i,ty',bo')::l,subst,metasenv
-         ) fl ([],subst,metasenv)
-       in
-        C.Fix (i, liftedfl),subst,metasenv
-    | C.CoFix (i, fl) ->
-       let len = List.length fl in
-       let liftedfl,subst,metasenv =
-        List.fold_right
-         (fun (name, ty, bo) (l,subst,metasenv) ->
-           let ty',subst,metasenv = liftaux subst metasenv k ty in
-           let bo',subst,metasenv = liftaux subst metasenv (k+len) bo in
-            (name,ty',bo')::l,subst,metasenv
-         ) fl ([],subst,metasenv)
-       in
-        C.CoFix (i, liftedfl),subst,metasenv
- in
-  liftaux subst metasenv k
-
-let delift_rels subst metasenv n t =
-  delift_rels_from subst metasenv 1 n t
-*) 
-
 let mk_meta ?name metasenv context ty = 
-  match ty with
-  | `Typeless ->
-    let n = newmeta () in
-    let ty = NCic.Implicit (`Typeof n) in
-    let menv_entry = (n, (name, context, ty)) in
-    menv_entry :: metasenv,NCic.Meta (n, (0,NCic.Irl (List.length context))), ty
-  | `Type 
-  | `Term ->
-    let context_for_ty = if ty = `Type then [] else context in
-    let n = newmeta () in
-    let ty_menv_entry = (n, (name,context_for_ty, NCic.Implicit (`Typeof n))) in
-    let m = newmeta () in
-    let ty = NCic.Meta (n, (0,NCic.Irl (List.length context_for_ty))) in
-    let menv_entry = (m, (name, context, ty)) in
-    menv_entry :: ty_menv_entry :: metasenv, 
-      NCic.Meta (m, (0,NCic.Irl (List.length context))), ty
+  let tyof = function Some s -> Some ("typeof_"^s) | None -> None in
+  let rec mk_meta name n metasenv context = function
   | `WithType ty ->
-    let n = newmeta () in
     let len = List.length context in
     let menv_entry = (n, (name, context, ty)) in
-    menv_entry :: metasenv, NCic.Meta (n, (0,NCic.Irl len)), ty
+    menv_entry :: metasenv, n, NCic.Meta (n, (0,NCic.Irl len)), ty
+  | `Sort ->
+    let ty = NCic.Implicit (`Typeof n) in
+    mk_meta (tyof name) n metasenv [] (`WithType ty)
+  | `Type ->
+    let metasenv, _, ty, _ = 
+      mk_meta (tyof name) (newmeta ()) metasenv context `Sort in
+    mk_meta name n metasenv context (`WithType ty)
+  | `Term ->
+    let metasenv, _, ty, _ = 
+      mk_meta (tyof name) (newmeta ()) metasenv context `Type in
+    mk_meta name n metasenv context (`WithType ty)
+  in
+    mk_meta name (newmeta ()) metasenv context ty
 ;;
 
-let saturate ?(delta=0) metasenv context ty goal_arity =
+let saturate ?(delta=0) metasenv subst context ty goal_arity =
  assert (goal_arity >= 0);
   let rec aux metasenv = function
-   | NCic.Prod (name,s,t) ->
-       let metasenv1, arg,_ = 
+   | NCic.Prod (name,s,t) as ty ->
+       let metasenv1, _, arg,_ = 
           mk_meta ~name:name metasenv context (`WithType s) in            
        let t, metasenv1, args, pno = 
            aux metasenv1 (NCicSubstitution.subst arg t) 
@@ -642,7 +482,7 @@ let saturate ?(delta=0) metasenv context ty goal_arity =
        else
          t, metasenv1, arg::args, pno+1
    | ty ->
-        match NCicReduction.whd context ty ~delta with
+        match NCicReduction.whd ~subst context ty ~delta with
         | NCic.Prod _ as ty -> aux metasenv ty
         | ty -> ty, metasenv, [], 0
   in