X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_refiner%2FnCicUnification.ml;h=13744017acc9d98125676b5bc8717a149be51af2;hb=53b957fd45c47b20d698503c9bb67e2ef3ab98e1;hp=d48dfaf460a4967a02aada9d8f7ee5f8bdecd03c;hpb=1f30bba33513dc8257a7c89e64038c096fa21072;p=helm.git

diff --git a/helm/software/components/ng_refiner/nCicUnification.ml b/helm/software/components/ng_refiner/nCicUnification.ml
index d48dfaf46..13744017a 100644
--- a/helm/software/components/ng_refiner/nCicUnification.ml
+++ b/helm/software/components/ng_refiner/nCicUnification.ml
@@ -14,20 +14,17 @@
 exception UnificationFailure of string Lazy.t;;
 exception Uncertain of string Lazy.t;;
 exception AssertFailure of string Lazy.t;;
+exception KeepReducing of string Lazy.t;;
+exception KeepReducingThis of 
+  string Lazy.t * (NCicReduction.machine * bool) * 
+                  (NCicReduction.machine * bool) ;;
 
 let (===) x y = Pervasives.compare x y = 0 ;;
 
-let uncert_exc metasenv subst context t1 t2 = 
-  Uncertain (lazy (
+let mk_msg metasenv subst context t1 t2 =
+ (lazy (
   "Can't unify " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^
   " with " ^ NCicPp.ppterm ~metasenv ~subst ~context t2))
-;;
-
-let fail_exc metasenv subst context t1 t2 = 
-  UnificationFailure (lazy (
-  "Can't unify " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^
-  " with " ^ NCicPp.ppterm ~metasenv ~subst ~context t2));
-;;
 
 let mk_appl ~upto hd tl =
   NCicReduction.head_beta_reduce ~upto
@@ -53,7 +50,7 @@ let eta_reduce subst t =
           let _,_,t,_ = NCicUtils.lookup_subst i subst in
           let t = NCicSubstitution.subst_meta lc t in
           eat_lambdas ctx t
-        with Not_found -> ctx, t)
+        with NCicUtils.Subst_not_found _ -> ctx, t)
     | t -> ctx, t
   in
   let context_body = eat_lambdas [] t in
@@ -78,25 +75,37 @@ let eta_reduce subst t =
 module C = NCic;;
 module Ref = NReference;;
 
-let debug = false;;
+let debug = ref false;;
 let indent = ref "";;
-let pp =
- if debug then
-  fun s -> prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s)
- else 
-  fun _ -> ()
+let times = ref [];;
+let pp s =
+ if !debug then
+  prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s)
 ;;
 let inside c =
- indent := !indent ^ String.make 1 c;
- if debug then prerr_endline ("{{{" ^ !indent ^ " ")
+ if !debug then
+  begin
+   let time1 = Unix.gettimeofday () in
+   indent := !indent ^ String.make 1 c;
+   times := time1 :: !times;
+   prerr_endline ("{{{" ^ !indent ^ " ")
+  end
 ;;
-let outside ok =
- if debug then prerr_endline "}}}";
- if not ok then pp (lazy "exception raised!");
- try
-  indent := String.sub !indent 0 (String.length !indent -1)
- with
-  Invalid_argument _ -> indent := "??"; ()
+let outside exc_opt =
+ if !debug then
+  begin
+   let time2 = Unix.gettimeofday () in
+   let time1 =
+    match !times with time1::tl -> times := tl; time1 | [] -> assert false in
+   prerr_endline ("}}} " ^ !indent ^ " " ^ string_of_float (time2 -. time1));
+   (match exc_opt with
+   | Some e ->  prerr_endline ("exception raised: " ^ Printexc.to_string e)
+   | None -> ());
+   try
+    indent := String.sub !indent 0 (String.length !indent -1)
+   with
+    Invalid_argument _ -> indent := "??"; ()
+  end
 ;;
 
 let ppcontext ~metasenv ~subst c = 
@@ -106,26 +115,8 @@ let ppmetasenv ~subst m = "\nmenv:\n" ^ NCicPp.ppmetasenv ~subst m;;
 
 let ppcontext ~metasenv:_metasenv ~subst:_subst _context = "";;
 let ppmetasenv ~subst:_subst _metasenv = "";;
-
-let fix_sorts swap exc t =
-  let rec aux () = function
-    | NCic.Sort (NCic.Type u) as orig ->
-        if swap then
-         match NCicEnvironment.sup u with
-         | None ->
-            prerr_endline ("no sup for " ^ NCicPp.ppterm ~metasenv:[] ~subst:[] ~context:[] orig) ;
-            raise exc
-         | Some u1 -> if u = u1 then orig else NCic.Sort (NCic.Type u1)
-        else
-         NCic.Sort (NCic.Type (
-           match NCicEnvironment.sup NCicEnvironment.type0 with 
-           | Some x -> x
-           | _ -> assert false))
-    | NCic.Meta _ as orig -> orig
-    | t -> NCicUtils.map (fun _ _ -> ()) () aux t
-  in
-    aux () t
-;;
+let ppterm ~metasenv ~subst ~context = NCicPp.ppterm ~metasenv ~subst ~context;;
+(* let ppterm ~metasenv:_ ~subst:_ ~context:_ _ = "";; *)
 
 let is_locked n subst =
    try
@@ -135,10 +126,9 @@ let is_locked n subst =
    with NCicUtils.Subst_not_found _ -> false
 ;;
 
-let rec mk_irl =
- function
-    0 -> []
-  | n -> NCic.Rel n :: mk_irl (n-1)
+let rec mk_irl stop base =
+  if base > stop then []
+  else (NCic.Rel base) :: mk_irl stop (base+1) 
 ;;
 
 (* the argument must be a term in whd *)
@@ -153,226 +143,309 @@ let rec could_reduce =
   | C.Appl [] | C.LetIn _ | C.Implicit _ -> assert false
 ;;
 
-let rec lambda_intros rdb metasenv subst context t args =
- let tty = NCicTypeChecker.typeof ~metasenv ~subst context t in
- let argsty =
-  List.map
-  (fun arg -> arg, NCicTypeChecker.typeof ~metasenv ~subst context arg) args in
- let context_of_args = context in
- let rec mk_lambda metasenv subst context n processed_args = function
-   | [] ->
+let rec lambda_intros rdb metasenv subst context argsno ty =
+ pp (lazy ("LAMBDA INTROS: " ^ ppterm ~metasenv ~subst ~context ty));
+ match argsno with
+    0 -> 
        let metasenv, _, bo, _ = 
-         NCicMetaSubst.mk_meta metasenv context 
-           (`WithType (NCicSubstitution.lift n tty))
-       in
-       metasenv, subst, bo
-   | (arg,ty)::tail ->
-       pp(lazy("arg{ " ^ 
-         NCicPp.ppterm ~metasenv ~subst ~context:context_of_args arg ^  ":" ^
-         NCicPp.ppterm ~metasenv ~subst ~context:context_of_args ty));
-       let metasenv, subst, telescopic_ty = 
-         if processed_args = [] then metasenv, subst, ty else
-         let _ = pp(lazy("delift")) in
-         delift_type_wrt_terms rdb metasenv subst context_of_args ty 
-           (List.rev processed_args)
-       in
-       pp(lazy("arg}"));
-       let name = "HBeta"^string_of_int n in
-       let metasenv, subst, bo =
-        mk_lambda metasenv subst ((name,NCic.Decl telescopic_ty)::context) (n+1)
-         (arg::processed_args) tail
-       in
-        metasenv, subst, NCic.Lambda (name, telescopic_ty, bo)
- in
- pp(lazy("LAMBDA_INTROS{ " ^ 
-   NCicPp.ppterm ~metasenv ~subst ~context t ^  ":" ^
-   NCicPp.ppterm ~metasenv ~subst ~context tty ^ " over " ^ 
-   String.concat "," (List.map (NCicPp.ppterm ~metasenv ~subst ~context)args)));
- let rc = mk_lambda metasenv subst context 0 [] argsty in
- pp(lazy("LAMBDA_INTROS}"));
- rc
-
-and instantiate rdb test_eq_only metasenv subst context n lc t swap =
- (*D*)  inside 'I'; try let rc =  
-         pp (lazy(string_of_int n ^ " :=?= "^
-           NCicPp.ppterm ~metasenv ~subst ~context t));
-  let unify test_eq_only m s c t1 t2 = 
-    if swap then unify rdb test_eq_only m s c t2 t1 
-    else unify rdb test_eq_only m s c t1 t2
-  in
-  let has_tag = List.exists in
-  let tags, _, ty = NCicUtils.lookup_meta n metasenv in
-  (* on the types *)
-  let metasenv, subst, t = 
-    match ty with 
-    | NCic.Implicit (`Typeof _) -> 
-         pp(lazy("meta with no type"));
-         assert(has_tag ((=)`IsSort) tags); 
-         metasenv, subst, t
-    | _ ->
-       let exc_to_be = fail_exc metasenv subst context (NCic.Meta (n,lc)) t in
-       let t, ty_t = 
-         try t, NCicTypeChecker.typeof ~subst ~metasenv context t 
-         with 
-         | NCicTypeChecker.AssertFailure msg as exn -> 
-              pp(lazy("we try to fix the sort\n"^
-                Lazy.force msg^"\n"^NCicPp.ppmetasenv ~subst metasenv));
-              let ft = fix_sorts swap exc_to_be t in
-              pp(lazy("unable to fix the sort"));
-              if ft == t then raise exn;
-              (try ft, NCicTypeChecker.typeof ~subst ~metasenv context ft 
-               with NCicTypeChecker.AssertFailure _ -> raise exn)
-         | NCicTypeChecker.TypeCheckerFailure msg ->
-              prerr_endline (Lazy.force msg);
-              prerr_endline (NCicPp.ppterm ~metasenv ~subst ~context t);
-              prerr_endline (ppcontext ~metasenv ~subst context); 
-              prerr_endline (ppmetasenv ~subst metasenv);
-              assert false
+         NCicMetaSubst.mk_meta metasenv context ~with_type:ty `IsTerm
        in
-       match ty_t with
-       | NCic.Implicit (`Typeof _) -> 
-           raise (UnificationFailure(lazy "trying to unify a term with a type"))
-       | _ -> 
-          let lty = NCicSubstitution.subst_meta lc ty in
-          pp (lazy ("On the types: " ^
-              NCicPp.ppterm ~metasenv ~subst ~context lty ^ " === " ^ 
-              NCicPp.ppterm ~metasenv ~subst ~context ty_t)); 
-          let metasenv,subst = 
-           try unify test_eq_only metasenv subst context lty ty_t
-           with NCicEnvironment.BadConstraint _ as exc ->
-            let ty_t = fix_sorts swap exc_to_be ty_t in 
-             try unify test_eq_only metasenv subst context lty ty_t
-             with 
-             | NCicEnvironment.BadConstraint _ 
-             | UnificationFailure _ -> raise exc 
+       metasenv, bo
+  | _ ->
+     (match NCicReduction.whd ~subst context ty with
+         C.Prod (n,so,ta) ->
+          let metasenv,bo =
+           lambda_intros rdb metasenv subst
+            ((n,C.Decl so)::context) (argsno - 1) ta
           in
-           metasenv, subst, t
-  in 
-  (* viral sortification *)
-  let is_sort metasenv subst context t = 
-    match NCicReduction.whd ~subst context t with
-    | NCic.Meta (i,_) ->
-         let tags, _, _ = NCicUtils.lookup_meta i metasenv in
-         has_tag ((=) `IsSort) tags
-    | NCic.Sort _ -> true
-    | _ -> false
-  in
-  let rec sortify metasenv subst = function
-    | NCic.Implicit (`Typeof _) -> assert false 
-    | NCic.Sort _ as t -> metasenv, subst, t, 0
-    | NCic.Meta (i,_) as t -> 
-         let tags, context, ty = NCicUtils.lookup_meta i metasenv in
-         if has_tag ((=) `IsSort) tags then metasenv, subst, t, i
-         else
-           let ty = NCicReduction.whd ~subst context ty in
-           let metasenv, subst, ty, _ = sortify metasenv subst ty in
-           let metasenv, j, m, _ = 
-             NCicMetaSubst.mk_meta metasenv ~attrs:[`IsSort] [] (`WithType ty)
-           in
-           pp(lazy("rimpiazzo " ^ string_of_int i^" con "^string_of_int j));
-           let subst_entry = i, (tags, context, m, ty) in
-           let subst = subst_entry :: subst in
-           let metasenv = List.filter (fun x,_ -> i <> x) metasenv in
-           metasenv, subst, m, j 
-    | NCic.Appl (NCic.Meta _ as hd :: args) as t -> 
-           let metasenv, subst, lambda_Mj =
-             lambda_intros rdb metasenv subst context t args
-           in
-           let metasenv,subst= unify true metasenv subst context hd lambda_Mj in
-           let t = NCicReduction.whd ~subst context t in
-           let _result = sortify metasenv subst t in       
-           (* untested, maybe dead, code *) assert false;
-    | t -> 
-         if could_reduce t then raise (Uncertain(lazy "not a sort"))
-         else raise (UnificationFailure(lazy "not a sort"))
-  in
-  let metasenv, subst, _, n = 
-    if has_tag ((=) `IsSort) tags then
-      let m,s,x,_ = sortify metasenv subst (NCicReduction.whd ~subst context t)
-      in m,s,x,n
-    else if is_sort metasenv subst context t then
-      sortify metasenv subst (NCic.Meta (n,lc))
-    else
-      metasenv, subst, NCic.Rel ~-1,n
+           metasenv,C.Lambda (n,so,bo)
+       | _ -> assert false)
+;;
+  
+let unopt exc = function None -> raise exc | Some x -> x ;;
+
+let fix metasenv subst is_sup test_eq_only exc t =
+  (*D*)  inside 'f'; try let rc =  
+  pp (lazy (NCicPp.ppterm ~metasenv ~subst ~context:[] t));
+  let rec aux test_eq_only metasenv = function
+    | NCic.Prod (n,so,ta) ->
+       let metasenv,so = aux true metasenv so in
+       let metasenv,ta = aux test_eq_only metasenv ta in
+        metasenv,NCic.Prod (n,so,ta)
+    | NCic.Sort (NCic.Type [(`CProp|`Type),_]) as orig when test_eq_only ->
+       metasenv,orig
+    | NCic.Sort (NCic.Type _) when test_eq_only -> raise exc
+    | NCic.Sort (NCic.Type u) when is_sup ->
+       metasenv, NCic.Sort (NCic.Type (unopt exc (NCicEnvironment.sup u)))
+    | NCic.Sort (NCic.Type u) ->
+       metasenv, NCic.Sort (NCic.Type 
+         (unopt exc (NCicEnvironment.inf ~strict:false u)))
+    | NCic.Meta (n,_) as orig ->
+        (try 
+          let _,_,_,_ = NCicUtils.lookup_subst n subst in metasenv,orig
+         with NCicUtils.Subst_not_found _ -> 
+          let metasenv, _ = NCicMetaSubst.extend_meta metasenv n in
+           metasenv, orig)
+    | t ->
+      NCicUntrusted.map_term_fold_a (fun _ x -> x) test_eq_only aux metasenv t
   in
-  let tags, ctx, ty = NCicUtils.lookup_meta n metasenv in
-  (* instantiation *)
-  pp (lazy(string_of_int n ^ " := 111 = "^ 
-    NCicPp.ppterm ~metasenv ~subst ~context t));
-  let (metasenv, subst), t = 
-    try 
-      NCicMetaSubst.delift 
-       ~unify:(fun m s c t1 t2 -> 
-         let ind = !indent in
-         let res = 
-           try Some (unify test_eq_only m s c t1 t2 )
-           with UnificationFailure _ | Uncertain _ -> None
+   aux test_eq_only metasenv t
+ (*D*)  in outside None; rc with exn -> outside (Some exn); raise exn 
+;;
+
+let metasenv_to_subst n (kind,context,ty) metasenv subst =
+ let infos,metasenv = List.partition (fun (n',_) -> n = n') metasenv in
+ let attrs,octx,oty = match infos with [_,infos] -> infos | _ -> assert false in
+ if octx=context && oty=ty then
+  (n,(NCicUntrusted.set_kind kind attrs, octx, oty))::metasenv,subst
+ else 
+  let metasenv, _, bo, _ = 
+   NCicMetaSubst.mk_meta metasenv context ~attrs ~with_type:ty kind in
+  let subst = (n,(NCicUntrusted.set_kind kind attrs,octx,bo,oty))::subst in
+   metasenv,subst
+;;
+
+let rec sortfy exc metasenv subst context t =
+ let t = NCicReduction.whd ~subst context t in
+ let metasenv,subst =
+  match t with
+   | NCic.Sort _ -> metasenv, subst
+   | NCic.Meta (n,_) -> 
+      let attrs, context, ty = NCicUtils.lookup_meta n metasenv in
+      let kind = NCicUntrusted.kind_of_meta attrs in
+       if kind = `IsSort then
+        metasenv,subst
+       else
+        (match ty with
+          | NCic.Implicit (`Typeof _) ->
+              metasenv_to_subst n (`IsSort,[],ty) metasenv subst
+          | ty ->
+             let metasenv,subst,ty = sortfy exc metasenv subst context ty in
+              metasenv_to_subst n (`IsSort,[],ty) metasenv subst)
+   | NCic.Implicit _ -> assert false
+   | _ -> raise exc
+ in
+  metasenv,subst,t
+
+let tipify exc metasenv subst context t ty =
+ let is_type attrs =
+  match NCicUntrusted.kind_of_meta attrs with
+     `IsType | `IsSort -> true
+   | `IsTerm -> false
+ in
+ let rec optimize_meta metasenv subst =
+  function 
+     NCic.Meta (n,lc) ->
+      (try
+        let attrs,_,_ = NCicUtils.lookup_meta n metasenv in
+        if is_type attrs then
+         metasenv,subst,true
+        else
+         let _,cc,ty = NCicUtils.lookup_meta n metasenv in
+         let metasenv,subst,ty = sortfy exc metasenv subst cc ty in
+         let metasenv = 
+           NCicUntrusted.replace_in_metasenv n
+            (fun attrs,cc,_ -> NCicUntrusted.set_kind `IsType attrs, cc, ty)
+            metasenv 
          in
-         indent := ind; res) 
-       metasenv subst context n lc t
-    with NCicMetaSubst.Uncertain msg -> 
-         pp (lazy ("delift fails: " ^ Lazy.force msg));
-         raise (Uncertain msg)
-    | NCicMetaSubst.MetaSubstFailure msg -> 
-         pp (lazy ("delift fails: " ^ Lazy.force msg));
-         raise (UnificationFailure msg)
+          metasenv,subst,false
+       with
+        NCicUtils.Meta_not_found _ ->
+         let attrs, _,bo,_ = NCicUtils.lookup_subst n subst in
+         if is_type attrs then
+          metasenv,subst,true
+         else
+          let _,cc,_,ty = NCicUtils.lookup_subst n subst in
+          let metasenv,subst,ty = sortfy exc metasenv subst cc ty in
+          let subst = 
+            NCicUntrusted.replace_in_subst n
+              (fun attrs,cc,bo,_->NCicUntrusted.set_kind `IsType attrs,cc,bo,ty)
+             subst 
+          in
+           optimize_meta metasenv subst (NCicSubstitution.subst_meta lc bo))
+   | _ -> metasenv,subst,false
+ in
+  let metasenv,subst,b = optimize_meta metasenv subst t in
+   if b then
+    metasenv,subst,t
+   else
+    let metasenv,subst,_ = sortfy exc metasenv subst context ty in
+     metasenv,subst,t
+;;
+
+let rec instantiate rdb test_eq_only metasenv subst context n lc t swap =
+ (*D*)  inside 'I'; try let rc =  
+  pp (lazy(string_of_int n^" :=?= "^ppterm ~metasenv ~subst ~context t));
+  let exc = 
+    UnificationFailure (mk_msg metasenv subst context (NCic.Meta (n,lc)) t) in
+  let move_to_subst i ((_,cc,t,_) as infos) metasenv subst =
+    let metasenv = List.remove_assoc i metasenv in
+    pp(lazy(string_of_int n ^ " :==> "^ ppterm ~metasenv ~subst ~context:cc t));
+    metasenv, (i,infos) :: subst
   in
-         pp (lazy(string_of_int n ^ " := 222 = "^
-           NCicPp.ppterm ~metasenv ~subst ~context:ctx t
-         ^ ppmetasenv ~subst metasenv));
-  (* Unifying the types may have already instantiated n. *)
-  try
-    let _, _,oldt,_ = NCicUtils.lookup_subst n subst in
-    let oldt = NCicSubstitution.subst_meta lc oldt in
-    let t = NCicSubstitution.subst_meta lc t in
-    (* conjecture: always fail --> occur check *)
-    unify test_eq_only metasenv subst context oldt t
-  with NCicUtils.Subst_not_found _ -> 
-    (* by cumulativity when unify(?,Type_i) 
-     * we could ? := Type_j with j <= i... *)
-    let subst = (n, (tags, ctx, t, ty)) :: subst in
-    pp (lazy ("?"^string_of_int n^" := "^NCicPp.ppterm
-      ~metasenv ~subst ~context (NCicSubstitution.subst_meta lc t)));
-    let metasenv = 
-      List.filter (fun (m,_) -> not (n = m)) metasenv 
+  let delift_to_subst test_eq_only n lc (attrs,cc,ty) t context metasenv subst =
+    pp (lazy(string_of_int n ^ " := 111 = "^ 
+      ppterm ~metasenv ~subst ~context t));
+    let (metasenv, subst), t = 
+      try 
+        NCicMetaSubst.delift 
+         ~unify:(fun m s c t1 t2 -> 
+           let ind = !indent in
+           let res = 
+             try Some (unify rdb test_eq_only m s c t1 t2 false)
+             with UnificationFailure _ | Uncertain _ -> None
+           in
+           indent := ind; res) 
+         metasenv subst context n lc t
+      with NCicMetaSubst.Uncertain msg -> 
+           pp (lazy ("delift is uncertain: " ^ Lazy.force msg));
+           raise (Uncertain msg)
+      | NCicMetaSubst.MetaSubstFailure msg -> 
+           pp (lazy ("delift fails: " ^ Lazy.force msg));
+           raise (UnificationFailure msg)
     in
-    metasenv, subst
- (*D*)  in outside true; rc with exn -> outside false; raise exn 
-
-and unify rdb test_eq_only metasenv subst context t1 t2 =
+    pp (lazy(string_of_int n ^ " := 222 = "^
+      ppterm ~metasenv ~subst ~context:cc t^ppmetasenv ~subst metasenv));
+    (* Unifying the types may have already instantiated n. *)
+    try
+      let _, _,oldt,_ = NCicUtils.lookup_subst n subst in
+      let oldt = NCicSubstitution.subst_meta lc oldt in
+      let t = NCicSubstitution.subst_meta lc t in
+      (* conjecture: always fail --> occur check *)
+      unify rdb test_eq_only metasenv subst context t oldt false
+    with NCicUtils.Subst_not_found _ -> 
+      move_to_subst n (attrs,cc,t,ty) metasenv subst
+  in
+  let attrs,cc,ty = NCicUtils.lookup_meta n metasenv in
+  let kind = NCicUntrusted.kind_of_meta attrs in
+  let metasenv,t = fix metasenv subst swap test_eq_only exc t in
+  let ty_t = NCicTypeChecker.typeof ~metasenv ~subst context t in
+  let metasenv,subst,t =
+   match kind with
+      `IsSort -> sortfy exc metasenv subst context t
+    | `IsType -> tipify exc metasenv subst context t ty_t
+    | `IsTerm -> metasenv,subst,t in
+  match kind with
+  | `IsSort ->
+     (match ty,t with
+         NCic.Implicit (`Typeof _), NCic.Sort _ ->
+           move_to_subst n (attrs,cc,t,ty_t) metasenv subst  
+       | NCic.Sort (NCic.Type u1), NCic.Sort s ->
+          let s =
+           match s,swap with
+              NCic.Type u2, false ->
+               NCic.Sort (NCic.Type
+                (unopt exc (NCicEnvironment.inf ~strict:false
+                 (unopt exc (NCicEnvironment.inf ~strict:true u1) @ u2))))
+            | NCic.Type u2, true ->
+               if NCicEnvironment.universe_lt u2 u1 then
+                NCic.Sort (NCic.Type u2)
+               else (raise exc)
+            | NCic.Prop,_ -> NCic.Sort NCic.Prop
+          in
+           move_to_subst n (attrs,cc,s,ty) metasenv subst  
+       | NCic.Implicit (`Typeof _), NCic.Meta _ ->
+          move_to_subst n (attrs,cc,t,ty_t) metasenv subst  
+       | _, NCic.Meta _
+       | NCic.Meta _, NCic.Sort _ ->
+          pp (lazy ("On the types: " ^
+            ppterm ~metasenv ~subst ~context ty ^ "=<=" ^
+            ppterm ~metasenv ~subst ~context ty_t)); 
+          let metasenv, subst = 
+            unify rdb false metasenv subst context ty_t ty false in
+          delift_to_subst test_eq_only n lc (attrs,cc,ty) t
+           context metasenv subst
+       | _ -> assert false)
+  | `IsType
+  | `IsTerm ->
+     (match ty with
+         NCic.Implicit (`Typeof _) ->
+          let (metasenv, subst), ty_t = 
+            try 
+              NCicMetaSubst.delift 
+               ~unify:(fun m s c t1 t2 -> 
+                 let ind = !indent in
+                 let res = try Some (unify rdb test_eq_only m s c t1 t2 false )
+                   with UnificationFailure _ | Uncertain _ -> None
+                 in
+                 indent := ind; res)
+               metasenv subst context n lc ty_t
+            with NCicMetaSubst.Uncertain msg -> 
+                 pp (lazy ("delift is uncertain: " ^ Lazy.force msg));
+                 raise (Uncertain msg)
+            | NCicMetaSubst.MetaSubstFailure msg -> 
+                 pp (lazy ("delift fails: " ^ Lazy.force msg));
+                 raise (UnificationFailure msg)
+          in
+           delift_to_subst test_eq_only n lc (attrs,cc,ty_t) t context metasenv
+            subst 
+       | _ ->
+        let lty = NCicSubstitution.subst_meta lc ty in
+        pp (lazy ("On the types: " ^
+          ppterm ~metasenv ~subst ~context lty ^ "=<=" ^
+          ppterm ~metasenv ~subst ~context ty_t)); 
+        let metasenv, subst = 
+          unify rdb false metasenv subst context ty_t lty false
+        in
+        delift_to_subst test_eq_only n lc (attrs,cc,ty) t context metasenv
+         subst)
+ (*D*)  in outside None; rc with exn -> outside (Some exn); raise exn 
+
+and unify rdb test_eq_only metasenv subst context t1 t2 swap =
  (*D*) inside 'U'; try let rc =
-   let fo_unif test_eq_only metasenv subst t1 t2 =
+   let fo_unif test_eq_only metasenv subst (norm1,t1) (norm2,t2) =
     (*D*) inside 'F'; try let rc =  
-     pp (lazy("  " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " ==?== " ^ 
-         NCicPp.ppterm ~metasenv ~subst ~context t2 ^ ppmetasenv
+     pp (lazy("  " ^ ppterm ~metasenv ~subst ~context t1 ^ 
+          (if swap then " ==>?== " 
+           else " ==<?==" ) ^ 
+         ppterm ~metasenv ~subst ~context t2 ^ ppmetasenv
+         ~subst metasenv));
+     pp (lazy("  " ^ ppterm ~metasenv ~subst:[] ~context t1 ^
+          (if swap then " ==>??== " 
+           else " ==<??==" ) ^ 
+         ppterm ~metasenv ~subst:[] ~context t2 ^ ppmetasenv
          ~subst metasenv));
      if t1 === t2 then
        metasenv, subst
+(* CSC: To speed up Oliboni's stuff. Why is it necessary, anyway?
+     else if
+      NCicUntrusted.metas_of_term subst context t1 = [] &&
+      NCicUntrusted.metas_of_term subst context t2 = []
+     then
+      if NCicReduction.are_convertible ~metasenv ~subst context t1 t2 then
+       metasenv,subst
+      else
+       raise (UnificationFailure (lazy "Closed terms not convertible"))
+*)
      else
        match (t1,t2) with
        | C.Appl [_], _ | _, C.Appl [_] | C.Appl [], _ | _, C.Appl [] 
        | C.Appl (C.Appl _::_), _ | _, C.Appl (C.Appl _::_) -> 
            prerr_endline "Appl [Appl _;_] or Appl [] or Appl [_] invariant";
            assert false 
-       | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only -> 
+       | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only ->
+           let a, b = if swap then b,a else a,b in
            if NCicEnvironment.universe_leq a b then metasenv, subst
-           else raise (fail_exc metasenv subst context t1 t2)
+           else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
        | (C.Sort (C.Type a), C.Sort (C.Type b)) -> 
            if NCicEnvironment.universe_eq a b then metasenv, subst
-           else raise (fail_exc metasenv subst context t1 t2)
-       | (C.Sort C.Prop,C.Sort (C.Type _)) -> 
+           else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
+       | (C.Sort C.Prop,C.Sort (C.Type _)) when not swap -> 
            if (not test_eq_only) then metasenv, subst
-           else raise (fail_exc metasenv subst context t1 t2)
+           else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
+       | (C.Sort (C.Type _), C.Sort C.Prop) when swap -> 
+           if (not test_eq_only) then metasenv, subst
+           else raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
 
        | (C.Lambda (name1,s1,t1), C.Lambda(_,s2,t2)) 
        | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
-           let metasenv, subst = unify rdb true metasenv subst context s1 s2 in
-           unify rdb test_eq_only metasenv subst ((name1, C.Decl s1)::context) t1 t2
+           let metasenv, subst = unify rdb true metasenv subst context s1 s2 swap in
+           unify rdb test_eq_only metasenv subst ((name1, C.Decl s1)::context) t1 t2 swap
        | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
-           let metasenv,subst=unify rdb test_eq_only metasenv subst context ty1 ty2 in
-           let metasenv,subst=unify rdb test_eq_only metasenv subst context s1 s2 in
+           let metasenv,subst=unify rdb test_eq_only metasenv subst context ty1 ty2 swap in
+           let metasenv,subst=unify rdb test_eq_only metasenv subst context s1 s2 swap in
            let context = (name1, C.Def (s1,ty1))::context in
-           unify rdb test_eq_only metasenv subst context t1 t2
+           unify rdb test_eq_only metasenv subst context t1 t2 swap
 
        | (C.Meta (n1,(s1,l1 as lc1)),C.Meta (n2,(s2,l2 as lc2))) when n1 = n2 ->
           (try 
@@ -383,8 +456,9 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
              (fun t1 t2 (metasenv, subst, to_restrict, i) -> 
                 try 
                   let metasenv, subst = 
-                   unify rdb test_eq_only metasenv subst context 
+                   unify rdb (*test_eq_only*) true metasenv subst context
                     (NCicSubstitution.lift s1 t1) (NCicSubstitution.lift s2 t2)
+                     swap
                   in
                   metasenv, subst, to_restrict, i-1  
                 with UnificationFailure _ | Uncertain _ ->
@@ -392,7 +466,7 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
              l1 l2 (metasenv, subst, [], List.length l1)
            in
            if to_restrict <> [] then
-             let metasenv, subst, _ = 
+             let metasenv, subst, _, _ = 
                NCicMetaSubst.restrict metasenv subst n1 to_restrict
              in
                metasenv, subst
@@ -404,18 +478,30 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
                 let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
                 let term1 = NCicSubstitution.subst_meta lc1 term in
                 let term2 = NCicSubstitution.subst_meta lc2 term in
-                  unify rdb test_eq_only metasenv subst context term1 term2
+                  unify rdb test_eq_only metasenv subst context term1 term2 swap
               with NCicUtils.Subst_not_found _-> raise (UnificationFailure msg))
+
+       |  NCic.Appl (NCic.Meta (i,_)::_ as l1),
+          NCic.Appl (NCic.Meta (j,_)::_ as l2) when i=j ->
+            (try
+              List.fold_left2 
+                (fun (metasenv, subst) t1 t2 ->
+                  unify rdb (*test_eq_only*) true metasenv subst context t1 
+                    t2 swap)
+                (metasenv,subst) l1 l2
+            with Invalid_argument _ -> 
+              raise (UnificationFailure (mk_msg metasenv subst context t1 t2)))
        
-       | _, NCic.Meta (n, _) when is_locked n subst ->
+       | _, NCic.Meta (n, _) when is_locked n subst && not swap->
            (let (metasenv, subst), i = 
               match NCicReduction.whd ~subst context t1 with
-              | NCic.Appl (NCic.Meta (i,l)::args) ->
-                 let metasenv, subst, lambda_Mj =
-                   lambda_intros rdb metasenv subst context t1 args
+              | NCic.Appl (NCic.Meta (i,l) as meta :: args) ->
+                 let metasenv, lambda_Mj =
+                   lambda_intros rdb metasenv subst context (List.length args)
+                    (NCicTypeChecker.typeof ~metasenv ~subst context meta)
                  in
                    unify rdb test_eq_only metasenv subst context 
-                    (C.Meta (i,l)) lambda_Mj,
+                    (C.Meta (i,l)) lambda_Mj false,
                    i
               | NCic.Meta (i,_) -> (metasenv, subst), i
               | _ ->
@@ -446,57 +532,51 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
                 let subst = List.filter (fun (j,_) -> j <> i) subst in
                 metasenv, ((i, (name, ctx, term, ty)) :: subst)
               with Not_found -> assert false))
+       | NCic.Meta (n, _), _ when is_locked n subst && swap ->
+           unify rdb test_eq_only metasenv subst context t2 t1 false
 
-       | C.Meta (n,lc), t -> 
-           (try 
-             let _,_,term,_ = NCicUtils.lookup_subst n subst in
-             let term = NCicSubstitution.subst_meta lc term in
-               unify rdb test_eq_only metasenv subst context term t
-           with NCicUtils.Subst_not_found _-> 
-             instantiate rdb test_eq_only metasenv subst context n lc 
-               (NCicReduction.head_beta_reduce ~subst t) false)
-
-       | t, C.Meta (n,lc) -> 
-           (try 
-             let _,_,term,_ = NCicUtils.lookup_subst n subst in
-             let term = NCicSubstitution.subst_meta lc term in
-               unify rdb test_eq_only metasenv subst context t term
-           with NCicUtils.Subst_not_found _-> 
-             instantiate rdb test_eq_only metasenv subst context n lc 
-              (NCicReduction.head_beta_reduce ~subst t) true)
-
-       | NCic.Appl (NCic.Meta (i,l)::args), _ when List.mem_assoc i subst ->
-            let _,_,term,_ = NCicUtils.lookup_subst i subst in
-            let term = NCicSubstitution.subst_meta l term in
-              unify rdb test_eq_only metasenv subst context 
-                (mk_appl ~upto:(List.length args) term args) t2
+       | t, C.Meta (n,lc) when List.mem_assoc n subst -> 
+          let _,_,term,_ = NCicUtils.lookup_subst n subst in
+          let term = NCicSubstitution.subst_meta lc term in
+            unify rdb test_eq_only metasenv subst context t term swap
+       | C.Meta (n,_), _ when List.mem_assoc n subst -> 
+            unify rdb test_eq_only metasenv subst context t2 t1 (not swap)
 
        | _, NCic.Appl (NCic.Meta (i,l)::args) when List.mem_assoc i subst ->
             let _,_,term,_ = NCicUtils.lookup_subst i subst in
             let term = NCicSubstitution.subst_meta l term in
               unify rdb test_eq_only metasenv subst context t1 
-                (mk_appl ~upto:(List.length args) term args)
-
-       |  NCic.Appl (NCic.Meta (i,_)::_ as l1),
-          NCic.Appl (NCic.Meta (j,_)::_ as l2) when i=j ->
-            (try
-              List.fold_left2 
-                (fun (metasenv, subst) t1 t2 ->
-                  unify rdb test_eq_only metasenv subst context t1 t2)
-                (metasenv,subst) l1 l2
-            with Invalid_argument _ -> 
-              raise (fail_exc metasenv subst context t1 t2))
+                (mk_appl ~upto:(List.length args) term args) swap
+       | NCic.Appl (NCic.Meta (i,_)::_), _ when List.mem_assoc i subst ->
+            unify rdb test_eq_only metasenv subst context t2 t1 (not swap)
+
+       | C.Meta (n,_), C.Meta (m,lc') when 
+           let _,cc1,_ = NCicUtils.lookup_meta n metasenv in
+           let _,cc2,_ = NCicUtils.lookup_meta m metasenv in
+            (n < m && cc1 = cc2) ||
+             let len1 = List.length cc1 in
+             let len2 = List.length cc2 in
+              len2 < len1 && cc2 = fst (HExtlib.split_nth len2 cc1) ->
+          instantiate rdb test_eq_only metasenv subst context m lc'
+            (NCicReduction.head_beta_reduce ~subst t1) (not swap)
+       | C.Meta (n,lc), t -> 
+          instantiate rdb test_eq_only metasenv subst context n lc 
+            (NCicReduction.head_beta_reduce ~subst t) swap
+       | t, C.Meta (n,lc) -> 
+          instantiate rdb test_eq_only metasenv subst context n lc 
+           (NCicReduction.head_beta_reduce ~subst t) (not swap)
 
-       | NCic.Appl (NCic.Meta (i,l)::args), _ ->
-          let metasenv, subst, lambda_Mj =
-            lambda_intros rdb metasenv subst context t1 args
+       | NCic.Appl (NCic.Meta (i,l) as meta :: args), _ ->
+          let metasenv, lambda_Mj =
+            lambda_intros rdb metasenv subst context (List.length args)
+             (NCicTypeChecker.typeof ~metasenv ~subst context meta)
           in
           let metasenv, subst = 
-            unify rdb test_eq_only metasenv subst context 
-              (C.Meta (i,l)) lambda_Mj
+           unify rdb test_eq_only metasenv subst context 
+            (C.Meta (i,l)) lambda_Mj swap
           in
           let metasenv, subst = 
-            unify rdb test_eq_only metasenv subst context t1 t2 
+            unify rdb test_eq_only metasenv subst context t1 t2 swap
           in
           (try
             let name, ctx, term, ty = NCicUtils.lookup_subst i subst in
@@ -504,38 +584,13 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
             let subst = List.filter (fun (j,_) -> j <> i) subst in
             metasenv, ((i, (name, ctx, term, ty)) :: subst)
           with Not_found -> assert false)
-
-       | _, NCic.Appl (NCic.Meta (i,l)::args) ->
-         let metasenv, subst, lambda_Mj =
-           lambda_intros rdb metasenv subst context t2 args
-         in
-         let metasenv, subst =
-           unify rdb test_eq_only metasenv subst context 
-            lambda_Mj (C.Meta (i,l))
-         in
-         let metasenv, subst = 
-           unify rdb test_eq_only metasenv subst context t1 t2 
-         in
-         (try
-           let name, ctx, term, ty = NCicUtils.lookup_subst i subst in
-           let term = eta_reduce subst term in
-           let subst = List.filter (fun (j,_) -> j <> i) subst in
-           metasenv, ((i, (name, ctx, term, ty)) :: subst)
-         with Not_found -> assert false)
+       | _, NCic.Appl (NCic.Meta (_,_) :: _) ->
+           unify rdb test_eq_only metasenv subst context t2 t1 (not swap)
 
        (* processing this case here we avoid a useless small delta step *)
        | (C.Appl ((C.Const r1) as _hd1::tl1), C.Appl (C.Const r2::tl2)) 
          when Ref.eq r1 r2 ->
            let relevance = NCicEnvironment.get_relevance r1 in
-           let relevance = match r1 with
-             | Ref.Ref (_,Ref.Con (_,_,lno)) ->
-                 let relevance =
-                  try snd (HExtlib.split_nth lno relevance)
-                  with Failure _ -> []
-                 in
-                   HExtlib.mk_list false lno @ relevance
-             | _ -> relevance
-           in
            let metasenv, subst, _ = 
              try
                List.fold_left2 
@@ -544,18 +599,21 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
                       match relevance with b::tl -> b,tl | _ -> true, [] in
                     let metasenv, subst = 
                       try unify rdb test_eq_only metasenv subst context t1 t2
+                            swap
                       with UnificationFailure _ | Uncertain _ when not b ->
                         metasenv, subst
                     in
                       metasenv, subst, relevance)
                  (metasenv, subst, relevance) tl1 tl2
-             with Invalid_argument _ -> 
-               raise (uncert_exc metasenv subst context t1 t2)
+             with
+                Invalid_argument _ -> 
+                 raise (Uncertain (mk_msg metasenv subst context t1 t2))
+              | KeepReducing _ | KeepReducingThis _ -> assert false
            in 
              metasenv, subst
 
        | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
-          C.Match (ref2,outtype2,term2,pl2)) ->
+          C.Match (ref2,outtype2,term2,pl2)) when Ref.eq ref1 ref2 ->
            let _,_,itl,_,_ = NCicEnvironment.get_checked_indtys ref1 in
            let _,_,ty,_ = List.nth itl tyno in
            let rec remove_prods ~subst context ty = 
@@ -571,36 +629,46 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
              | C.Sort C.Prop -> true
              | _ -> false 
            in
-           if not (Ref.eq ref1 ref2) then 
-             raise (uncert_exc metasenv subst context t1 t2) 
-           else
+           (* if not (Ref.eq ref1 ref2) then 
+             raise (Uncertain (mk_msg metasenv subst context t1 t2))
+           else*)
              let metasenv, subst = 
-              unify rdb test_eq_only metasenv subst context outtype1 outtype2 in
+              unify rdb test_eq_only metasenv subst context outtype1 outtype2 swap in
              let metasenv, subst = 
-               try unify rdb test_eq_only metasenv subst context term1 term2 
+               try unify rdb test_eq_only metasenv subst context term1 term2 swap
                with UnificationFailure _ | Uncertain _ when is_prop -> 
                  metasenv, subst
              in
              (try
               List.fold_left2 
-               (fun (metasenv,subst) -> 
-                  unify rdb test_eq_only metasenv subst context)
+               (fun (metasenv,subst) t1 t2 -> 
+                  unify rdb test_eq_only metasenv subst context t1 t2 swap)
                (metasenv, subst) pl1 pl2
              with Invalid_argument _ -> assert false)
        | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
-       | _ when NCicUntrusted.metas_of_term subst context t1 = [] && 
-                NCicUntrusted.metas_of_term subst context t2 = [] -> 
-                  raise (fail_exc metasenv subst context t1 t2)
-       | _ -> raise (uncert_exc metasenv subst context t1 t2)
-     (*D*)  in outside true; rc with exn -> outside false; raise exn 
+       | _ when norm1 && norm2 ->
+           if (could_reduce t1 || could_reduce t2) then
+            raise (Uncertain (mk_msg metasenv subst context t1 t2))
+           else
+            raise (UnificationFailure (mk_msg metasenv subst context t1 t2))
+       | _ -> raise (KeepReducing (mk_msg metasenv subst context t1 t2))
+     (*D*)  in outside None; rc with exn -> outside (Some exn); raise exn 
     in
-    let try_hints metasenv subst t1 t2 (* exc*) =
+    let fo_unif test_eq_only metasenv subst (norm1,t1 as nt1) (norm2,t2 as nt2)=
+     try fo_unif test_eq_only metasenv subst nt1 nt2
+     with
+      UnificationFailure _ | Uncertain _ when not norm1 || not norm2 ->
+       raise (KeepReducing (mk_msg metasenv subst context t1 t2))
+    in
+    let try_hints metasenv subst (_,t1 as mt1) (_,t2 as mt2) (* exc*) =
+      if NCicUntrusted.metas_of_term subst context t1 = [] &&
+         NCicUntrusted.metas_of_term subst context t2 = [] 
+      then None 
+      else begin
     (*D*) inside 'H'; try let rc =  
-(*
-      prerr_endline ("\nProblema:\n" ^
-        NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " =?= " ^
-        NCicPp.ppterm ~metasenv ~subst ~context t2);
-*)
+     pp(lazy ("\nProblema:\n" ^
+        ppterm ~metasenv ~subst ~context t1 ^ " =?= " ^
+        ppterm ~metasenv ~subst ~context t2));
       let candidates = 
         NCicUnifHint.look_for_hint rdb metasenv subst context t1 t2
       in
@@ -611,31 +679,82 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
               String.concat "\n"
                 (List.map 
                   (fun (a,b) ->
-                   NCicPp.ppterm ~metasenv ~subst ~context a ^  " =?= " ^
-                   NCicPp.ppterm ~metasenv ~subst ~context b) premises) ^
+                   ppterm ~metasenv ~subst ~context a ^  " =?= " ^
+                   ppterm ~metasenv ~subst ~context b) premises) ^
               "\n-------------------------------------------\n"^
-              NCicPp.ppterm ~metasenv ~subst ~context c1 ^  " = " ^
-              NCicPp.ppterm ~metasenv ~subst ~context c2));
+              ppterm ~metasenv ~subst ~context c1 ^  " = " ^
+              ppterm ~metasenv ~subst ~context c2));
             try 
     (*D*) inside 'K'; try let rc =  
               let metasenv,subst = 
-                fo_unif test_eq_only metasenv subst t1 c1 in
+                fo_unif test_eq_only metasenv subst mt1 (false,c1) in
               let metasenv,subst = 
-                fo_unif test_eq_only metasenv subst c2 t2 in
+                fo_unif test_eq_only metasenv subst (false,c2) mt2 in
               let metasenv,subst = 
                 List.fold_left 
                   (fun (metasenv, subst) (x,y) ->
-                     unify rdb test_eq_only metasenv subst context x y)
-                  (metasenv, subst) premises
+                     unify rdb test_eq_only metasenv subst context x y false)
+                  (metasenv, subst) (List.rev premises)
               in
+              pp(lazy("FUNZIONA!"));
               Some (metasenv, subst)
-     (*D*)  in outside true; rc with exn -> outside false; raise exn 
+     (*D*)  in outside None; rc with exn -> outside (Some exn); raise exn 
             with
-              UnificationFailure _ | Uncertain _ ->
-                cand_iter tl
+             KeepReducing _ | UnificationFailure _ | Uncertain _ -> cand_iter tl
+           | KeepReducingThis _ -> assert false
       in
         cand_iter candidates
-     (*D*)  in outside true; rc with exn -> outside false; raise exn 
+     (*D*)  in outside None; rc with exn -> outside (Some exn); raise exn 
+      end
+    in
+    let put_in_whd m1 m2 =
+      NCicReduction.reduce_machine ~delta:max_int ~subst context m1,
+      NCicReduction.reduce_machine ~delta:max_int ~subst context m2
+    in
+    let fo_unif_w_hints test_eq_only metasenv subst (_,t1 as m1) (_,t2 as m2) =
+      try fo_unif test_eq_only metasenv subst m1 m2
+      with 
+      | UnificationFailure _ as exn -> raise exn
+      | KeepReducing _ | Uncertain _ as exn ->
+        let (t1,norm1 as tm1),(t2,norm2 as tm2) =
+         put_in_whd (0,[],t1,[]) (0,[],t2,[])
+        in
+         match 
+           try_hints metasenv subst 
+            (norm1,NCicReduction.unwind t1) (norm2,NCicReduction.unwind t2)
+         with
+          | Some x -> x
+          | None -> 
+              match exn with 
+              | KeepReducing msg -> raise (KeepReducingThis (msg,tm1,tm2))
+              | Uncertain _ as exn -> raise exn
+              | _ -> assert false
+    in
+    let fo_unif_heads_and_cont_or_unwind_and_hints 
+      test_eq_only metasenv subst m1 m2 cont hm1 hm2
+     =
+      let ms, continuation = 
+        (* calling the continuation inside the outermost try is an option
+           and makes unification stronger, but looks not frequent to me
+           that heads unify but not the arguments and that an hints can fix 
+           that *)
+        try fo_unif test_eq_only metasenv subst m1 m2, cont
+        with 
+        | UnificationFailure _ 
+        | KeepReducing _ | Uncertain _ as exn ->
+           let (t1,norm1),(t2,norm2) = hm1, hm2 in
+           match 
+             try_hints metasenv subst 
+              (norm1,NCicReduction.unwind t1) (norm2,NCicReduction.unwind t2)
+           with
+            | Some x -> x, fun x -> x
+            | None -> 
+                match exn with 
+                | KeepReducing msg -> raise (KeepReducingThis (msg,hm1,hm2))
+                | UnificationFailure _ | Uncertain _ as exn -> raise exn
+                | _ -> assert false
+      in
+        continuation ms
     in
     let height_of = function
      | NCic.Const (Ref.Ref (_,Ref.Def h)) 
@@ -644,18 +763,14 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
      | NCic.Appl(NCic.Const(Ref.Ref(_,Ref.Fix (_,_,h)))::_) -> h
      | _ -> 0
     in
-    let put_in_whd m1 m2 =
-      NCicReduction.reduce_machine ~delta:max_int ~subst context m1,
-      NCicReduction.reduce_machine ~delta:max_int ~subst context m2
-    in
     let small_delta_step ~subst  
       ((_,_,t1,_ as m1, norm1) as x1) ((_,_,t2,_ as m2, norm2) as x2)
     =
      assert (not (norm1 && norm2));
      if norm1 then
-      x1,NCicReduction.reduce_machine ~delta:(height_of t2 -1) ~subst context m2
+      x1,NCicReduction.reduce_machine ~delta:0 ~subst context m2
      else if norm2 then
-      NCicReduction.reduce_machine ~delta:(height_of t1 -1) ~subst context m1,x2
+      NCicReduction.reduce_machine ~delta:0 ~subst context m1,x2
      else 
       let h1 = height_of t1 in 
       let h2 = height_of t2 in
@@ -668,17 +783,17 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
       | ((k1,e1,t1,s1),norm1 as m1),((k2,e2,t2,s2),norm2 as m2) ->
      (*D*) inside 'M'; try let rc = 
          pp (lazy("UM: " ^
-           NCicPp.ppterm ~metasenv ~subst ~context 
+           ppterm ~metasenv ~subst ~context 
              (NCicReduction.unwind (k1,e1,t1,s1)) ^
            " === " ^ 
-           NCicPp.ppterm ~metasenv ~subst ~context 
+           ppterm ~metasenv ~subst ~context 
              (NCicReduction.unwind (k2,e2,t2,s2))));
-pp (lazy (string_of_bool norm1 ^ " ?? " ^ string_of_bool norm2));
+         pp (lazy (string_of_bool norm1 ^ " ?? " ^ string_of_bool norm2));
           let relevance = [] (* TO BE UNDERSTOOD 
             match t1 with
             | C.Const r -> NCicEnvironment.get_relevance r
             | _ -> [] *) in
-          let unif_from_stack t1 t2 b metasenv subst =
+          let unif_from_stack (metasenv, subst) (t1, t2, b) =
               try
                 let t1 = NCicReduction.from_stack ~delta:max_int t1 in
                 let t2 = NCicReduction.from_stack ~delta:max_int t2 in
@@ -695,59 +810,70 @@ pp (lazy (string_of_bool norm1 ^ " ?? " ^ string_of_bool norm2));
                 NCicReduction.unwind (k2,e2,t2,List.rev l2),
                 todo
           in
-        let hh1,hh2,todo=check_stack (List.rev s1) (List.rev s2) relevance [] in
+          let check_stack l1 l2 r =
+            match t1, t2 with
+            | NCic.Meta _, _ | _, NCic.Meta _ ->
+                (NCicReduction.unwind (k1,e1,t1,s1)),
+                (NCicReduction.unwind (k2,e2,t2,s2)),[]     
+            | _ -> check_stack l1 l2 r []
+          in
+        let hh1,hh2,todo = check_stack (List.rev s1) (List.rev s2) relevance in
         try
-         let metasenv,subst = fo_unif test_eq_only metasenv subst hh1 hh2 in
-         List.fold_left
-          (fun (metasenv,subst) (x1,x2,r) ->
-            unif_from_stack x1 x2 r metasenv subst
-          ) (metasenv,subst) todo
-        with UnificationFailure _ | Uncertain _ when not (norm1 && norm2) ->
+          fo_unif_heads_and_cont_or_unwind_and_hints
+            test_eq_only metasenv subst (norm1,hh1) (norm2,hh2) 
+            (fun ms -> List.fold_left unif_from_stack ms todo)
+            m1 m2
+        with
+         | KeepReducing _ -> assert false
+         | KeepReducingThis _ ->
+            assert (not (norm1 && norm2));
 	    unif_machines metasenv subst (small_delta_step ~subst m1 m2)
-      (*D*)  in outside true; rc with exn -> outside false; raise exn 
+         | UnificationFailure _ | Uncertain _ when (not (norm1 && norm2))
+           -> unif_machines metasenv subst (small_delta_step ~subst m1 m2)
+         | UnificationFailure msg
+           when could_reduce (NCicReduction.unwind (fst m1))
+             || could_reduce (NCicReduction.unwind (fst m2))
+           -> raise (Uncertain msg)
+      (*D*)  in outside None; rc with exn -> outside (Some exn); raise exn 
      in
-     try fo_unif test_eq_only metasenv subst t1 t2
-     with 
-     | UnificationFailure msg as exn ->
-          (try 
-            unif_machines metasenv subst 
-             (put_in_whd (0,[],t1,[]) (0,[],t2,[]))
-          with 
-          | UnificationFailure _ -> raise (UnificationFailure msg)
-          | Uncertain _ -> raise exn)
-     | Uncertain msg as exn -> 
-       match try_hints metasenv subst t1 t2 with
-       | Some x -> x
-       | None -> 
-          try 
-            unif_machines metasenv subst 
-             (put_in_whd (0,[],t1,[]) (0,[],t2,[]))
+     try fo_unif_w_hints test_eq_only metasenv subst (false,t1) (false,t2)
+     with
+      | KeepReducingThis (msg,tm1,tm2) ->
+         (try 
+           unif_machines metasenv subst (tm1,tm2)
           with 
           | UnificationFailure _ -> raise (UnificationFailure msg)
-          | Uncertain _ -> raise exn
- (*D*)  in outside true; rc with exn -> outside false; raise exn 
+          | Uncertain _ -> raise (Uncertain msg)
+          | KeepReducing _ -> assert false)
+      | KeepReducing _ -> assert false
+
+ (*D*)  in outside None; rc with KeepReducing _ -> assert false | exn -> outside (Some exn); raise exn 
 
 and delift_type_wrt_terms rdb metasenv subst context t args =
+  let lc = List.rev args @ mk_irl (List.length context) (List.length args+1) in
   let (metasenv, subst), t =
    try
     NCicMetaSubst.delift 
       ~unify:(fun m s c t1 t2 -> 
          let ind = !indent in
          let res = 
-           try Some (unify rdb false m s c t1 t2 )
+           try Some (unify rdb false m s c t1 t2 false)
            with UnificationFailure _ | Uncertain _ -> None
          in
          indent := ind; res)
-      metasenv subst context 0 (0,NCic.Ctx (args @ 
-        List.rev (mk_irl (List.length context)))) t
-   with NCicMetaSubst.MetaSubstFailure _ -> (metasenv, subst), t
+      metasenv subst context 0 (0,NCic.Ctx lc) t
+   with
+      NCicMetaSubst.MetaSubstFailure _
+    | NCicMetaSubst.Uncertain _ -> (metasenv, subst), t
   in
    metasenv, subst, t
 ;;
 
 
-let unify rdb ?(test_eq_only=false) = 
+let unify rdb ?(test_eq_only=false) ?(swap=false) metasenv subst context t1 t2= 
   indent := "";      
-  unify rdb test_eq_only;;
+  unify rdb test_eq_only metasenv subst context t1 t2 swap;;
 
-let fix_sorts = fix_sorts true (UnificationFailure (lazy "no sup"));;
+let fix_sorts m s =
+  fix m s true false (UnificationFailure (lazy "no sup"))
+;;