X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_refiner%2FnCicUnification.ml;h=fcc76b0adc5bf72b38129bd36a3ddca7952d4676;hb=5c92c318030a05c766b3f6070dbd23589cbdee04;hp=71b790a26cf3c0e874963ec6ee7b530c57d9d393;hpb=08e552969f366bd18b5bb7515bbc514576a9b395;p=helm.git

diff --git a/helm/software/components/ng_refiner/nCicUnification.ml b/helm/software/components/ng_refiner/nCicUnification.ml
index 71b790a26..fcc76b0ad 100644
--- a/helm/software/components/ng_refiner/nCicUnification.ml
+++ b/helm/software/components/ng_refiner/nCicUnification.ml
@@ -50,7 +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
@@ -97,7 +97,7 @@ let outside exc_opt =
    let time2 = Unix.gettimeofday () in
    let time1 =
     match !times with time1::tl -> times := tl; time1 | [] -> assert false in
-   prerr_endline ("}}} " ^ string_of_float (time2 -. time1));
+   prerr_endline ("}}} " ^ !indent ^ " " ^ string_of_float (time2 -. time1));
    (match exc_opt with
    | Some e ->  prerr_endline ("exception raised: " ^ Printexc.to_string e)
    | None -> ());
@@ -165,6 +165,8 @@ let rec lambda_intros rdb metasenv subst context argsno ty =
 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
@@ -188,66 +190,100 @@ let fix metasenv subst is_sup test_eq_only exc t =
       NCicUntrusted.map_term_fold_a (fun _ x -> x) test_eq_only aux metasenv t
   in
    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 = function
-  | NCic.Sort _ as orig -> metasenv, orig
-  | NCic.Meta (n,lc) -> 
+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
-      kindfy exc metasenv subst context n lc ty kind `IsSort
-  | NCic.Implicit _ -> assert false
-  | _ -> raise exc
-
-and kindfy exc metasenv subst context n lc ty kind kind2 = 
-  match kind, ty, kind2 with
-  | `IsSort, _, _ -> assert(snd lc = NCic.Irl 0); metasenv, NCic.Meta(n,lc)
-  | k1, NCic.Implicit (`Typeof _), (`IsType|`IsTerm as k2) -> 
-     let k = NCicUntrusted.max_kind k1 k2 in
-     let metasenv = 
-       NCicUntrusted.replace_in_metasenv n
-         (fun attrs,cc,ty -> NCicUntrusted.set_kind k attrs, cc, ty) metasenv 
-     in
-     metasenv, NCic.Meta(n,lc)
-  | _, NCic.Implicit (`Typeof _), `IsSort ->
-     let metasenv = 
-       NCicUntrusted.replace_in_metasenv n
-        (fun attrs,_,ty-> NCicUntrusted.set_kind `IsSort attrs,[],ty) metasenv 
-     in
-     metasenv, NCic.Meta (n,(0,NCic.Irl 0))
-  | _, ty, `IsSort ->
-     let metasenv, ty = 
-       sortfy exc metasenv subst (NCicReduction.whd ~subst context ty) 
-     in
-     let metasenv = 
-       NCicUntrusted.replace_in_metasenv n
-        (fun attrs,_,_-> NCicUntrusted.set_kind `IsSort attrs,[],ty) metasenv 
-     in
-     metasenv, NCic.Meta (n,(0,NCic.Irl 0))
-  | k1, _, k2 when NCicUntrusted.max_kind k1 k2 = k1-> metasenv, NCic.Meta(n,lc)
-  | `IsTerm, ty, `IsType ->
-     let metasenv, ty = 
-       sortfy exc metasenv subst (NCicReduction.whd ~subst context ty) 
-     in
-     let metasenv = 
-       NCicUntrusted.replace_in_metasenv n
-        (fun attrs,cc,_-> NCicUntrusted.set_kind `IsType attrs,cc,ty) metasenv 
-     in
-     metasenv, NCic.Meta (n,lc)
-  | _ -> assert false (* XXX *)
+       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
+          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
+;;
 
-and instantiate rdb test_eq_only metasenv subst context n lc t swap =
+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 attrs cc t ty metasenv subst =
+  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,(attrs, cc, t, ty)) :: subst
+    pp(lazy(string_of_int n ^ " :==> "^ ppterm ~metasenv ~subst ~context:cc t));
+    metasenv, (i,infos) :: subst
   in
-  let delift_to_subst test_eq_only n lc attrs cc t ty context metasenv subst =
+  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 = 
@@ -256,7 +292,7 @@ and instantiate rdb test_eq_only metasenv subst context n lc t swap =
          ~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 )
+             try Some (unify rdb test_eq_only m s c t1 t2 false)
              with UnificationFailure _ | Uncertain _ -> None
            in
            indent := ind; res) 
@@ -276,124 +312,97 @@ and instantiate rdb test_eq_only metasenv subst context n lc t swap =
       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
+      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
+      move_to_subst n (attrs,cc,t,ty) metasenv subst
   in
-  let attrs, cc, ty = NCicUtils.lookup_meta n metasenv in
-  match NCicUntrusted.kind_of_meta attrs, ty, t, swap with
-  | `IsSort, (NCic.Implicit (`Typeof _) as bot), NCic.Sort (NCic.Type u),false->
-      pp(lazy("1"));
-      let u = NCicEnvironment.inf ~strict:false u in
-      let t = NCic.Sort (NCic.Type (unopt exc u)) in
-      move_to_subst n attrs cc t bot metasenv subst  
-  | `IsSort, (NCic.Implicit (`Typeof _) as bot), NCic.Sort (NCic.Type u),true ->
-      pp(lazy("2"));
-      let u = NCicEnvironment.sup u in
-      let t = NCic.Sort (NCic.Type (unopt exc u)) in
-      move_to_subst n attrs cc t bot metasenv subst  
-  | `IsSort, (NCic.Sort(NCic.Type u1) as ty), NCic.Sort (NCic.Type u2), false ->
-      pp(lazy("3"));
-      let u = 
-        NCicEnvironment.inf ~strict:false (u1 @
-          unopt exc (NCicEnvironment.inf ~strict:true u2)) 
-      in
-      let t = NCic.Sort (NCic.Type (unopt exc u)) in
-      move_to_subst n attrs cc t ty metasenv subst  
-  | `IsSort, (NCic.Sort(NCic.Type u1) as ty), NCic.Sort (NCic.Type u2), true ->
-      pp(lazy("4"));
-      let u = unopt exc (NCicEnvironment.sup u2) in
-      if NCicEnvironment.universe_lt u u1 then
-        let t = NCic.Sort (NCic.Type u) in
-        move_to_subst n attrs cc t ty metasenv subst  
-      else (raise exc)
-  | kind, ty, NCic.Meta(m,lcm), _ when List.mem_assoc m subst ->
-      let at,ccm,bo,tym = NCicUtils.lookup_subst m subst in
-       if NCicMetaSubst.is_out_scope_tag at then
-        begin
-         (* Case meta vs out-scope *)
-         pp(lazy("4.1"));
-         let ty_t, ccm, kindm = 
-           NCicSubstitution.subst_meta lcm tym, ccm,
-            NCicUntrusted.kind_of_meta at in
-         let lty = NCicSubstitution.subst_meta lc ty in
-         pp (lazy ("On the types: " ^
-           ppterm ~metasenv ~subst ~context lty ^
-           (if test_eq_only then " === " else "=<=") ^
-           ppterm ~metasenv ~subst ~context ty_t)); 
-         let metasenv, subst = 
-           unify rdb test_eq_only metasenv subst context ty_t lty in
-         (*CSC: here I should call kindfy, but it fails since the second
-           meta in in the susbt, not the metasenv! *)
-      (*  let metasenv,t = kindfy exc metasenv subst ccm m lcm ty_t kindm kind in *)
-         delift_to_subst test_eq_only n lc attrs cc t ty context metasenv subst 
-        end
-       else
-        let bo = NCicSubstitution.subst_meta lcm bo in
-        instantiate rdb test_eq_only metasenv subst context n lc bo swap
-  | kind, (NCic.Implicit (`Typeof _) as bot),  NCic.Meta(m,lcm), _ ->
-      pp(lazy("5"));
-      let attrsm, ccm, tym = NCicUtils.lookup_meta m metasenv in
-      let kindm = NCicUntrusted.kind_of_meta attrsm in
-      let metasenv, t = kindfy exc metasenv subst ccm m lcm tym kindm kind in
-      move_to_subst n attrs cc t bot metasenv subst  
-  | kind, ty,  (NCic.Meta(m,_) as t), _ when 
-    let _, _, tym = NCicUtils.lookup_meta m metasenv in
-    (match tym with NCic.Implicit (`Typeof _) -> true | _ -> false) ->
-      pp(lazy("6"));
-      let attrsm, _, _ = NCicUtils.lookup_meta m metasenv in
-      let kindm = NCicUntrusted.kind_of_meta attrsm in
-      let metasenv, _ = kindfy exc metasenv subst cc n lc ty kind kindm in
-      let attrs, cc, ty = NCicUtils.lookup_meta n metasenv in
-      let metasenv = NCicUntrusted.replace_in_metasenv m
-        (fun _,_,_ -> attrs,cc,ty) metasenv
-      in
-      (* XXX *)move_to_subst n attrs cc t ty metasenv subst  
-  | kind, ty,  NCic.Meta(m,lcm), _ ->
-      pp(lazy("7"));
-      let ty_t, ccm, kindm = 
-        let at, ccm, tym = NCicUtils.lookup_meta m metasenv in
-        NCicSubstitution.subst_meta lcm tym, ccm, NCicUntrusted.kind_of_meta at
-      in
-      let lty = NCicSubstitution.subst_meta lc ty in
-      pp (lazy ("On the types: " ^
-        ppterm ~metasenv ~subst ~context lty ^
-        (if test_eq_only then " === " else "=<=") ^
-        ppterm ~metasenv ~subst ~context ty_t)); 
-      let metasenv, subst = 
-        unify rdb test_eq_only metasenv subst context ty_t lty
-      in
-      let metasenv, t = kindfy exc metasenv subst ccm m lcm ty_t kindm kind in
-      delift_to_subst test_eq_only n lc attrs cc t ty context metasenv subst 
-  | _, (NCic.Implicit (`Typeof _) as bot), t, swap ->
-      pp(lazy("8"));
-      let metasenv, t = fix metasenv subst swap test_eq_only exc t in
-(*       let ty_t = NCicTypeChecker.typeof ~metasenv ~subst context t in *)
-      (* ty andrebbe deliftato *)
-      delift_to_subst test_eq_only n lc attrs cc t bot context metasenv subst 
-  | _, ty, t, swap ->
-      pp(lazy("9"));
-      let lty = NCicSubstitution.subst_meta lc ty in
-      let metasenv, t = fix metasenv subst swap test_eq_only exc t in
-      let ty_t = NCicTypeChecker.typeof ~metasenv ~subst context t in
-      pp (lazy ("On the types: " ^
-        ppterm ~metasenv ~subst ~context lty ^
-        (if test_eq_only then " === " else "=<=") ^
-        ppterm ~metasenv ~subst ~context ty_t)); 
-      let metasenv, subst = 
-        unify rdb test_eq_only metasenv subst context ty_t lty
-      in
-      delift_to_subst test_eq_only n lc attrs cc t ty context metasenv subst 
+  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 ty_t ^ "=<=" ^
+          ppterm ~metasenv ~subst ~context lty)); 
+        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 =
+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 (norm1,t1) (norm2,t2) =
     (*D*) inside 'F'; try let rc =  
-     pp (lazy("  " ^ ppterm ~metasenv ~subst ~context t1 ^ " ==?== " ^ 
+     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 ^ " ==??== " ^ 
+     pp (lazy("  " ^ ppterm ~metasenv ~subst:[] ~context t1 ^
+          (if swap then " ==>??== " 
+           else " ==<??==" ) ^ 
          ppterm ~metasenv ~subst:[] ~context t2 ^ ppmetasenv
          ~subst metasenv));
      if t1 === t2 then
@@ -414,25 +423,29 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
        | 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 (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 (UnificationFailure (mk_msg metasenv subst context t1 t2))
-       | (C.Sort C.Prop,C.Sort (C.Type _)) -> 
+       | (C.Sort C.Prop,C.Sort (C.Type _)) when not swap -> 
+           if (not test_eq_only) then metasenv, subst
+           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 
@@ -443,8 +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 _ ->
@@ -452,7 +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
@@ -464,7 +478,7 @@ 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),
@@ -472,12 +486,13 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
             (try
               List.fold_left2 
                 (fun (metasenv, subst) t1 t2 ->
-                  unify rdb test_eq_only metasenv subst context 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) as meta :: args) ->
@@ -486,7 +501,7 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
                     (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
               | _ ->
@@ -517,82 +532,109 @@ 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))
-
-       | C.Meta (n,lc), t 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 term t
+       | NCic.Meta (n, _), _ when is_locked n subst && swap ->
+           unify rdb test_eq_only metasenv subst context t2 t1 false
 
        | 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
-
-       | 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
+            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)
-
+                (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), C.Meta (m,lc') when
+          let _,_,tyn = NCicUtils.lookup_meta n metasenv in
+          let _,_,tym = NCicUtils.lookup_meta m metasenv in
+          let tyn = NCicSubstitution.subst_meta lc tyn in
+          let tym = NCicSubstitution.subst_meta lc tym in
+           match tyn,tym with
+              NCic.Sort NCic.Type u1, NCic.Sort NCic.Type u2 ->
+               NCicEnvironment.universe_lt u1 u2
+            | _,_ -> false ->
+          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) false
-
+            (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) true
+           (NCicReduction.head_beta_reduce ~subst t) (not swap)
 
+       (* higher order unification case *)
        | 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 = 
-           try
-            unify rdb test_eq_only metasenv subst context 
-              (C.Meta (i,l)) lambda_Mj
-           with UnificationFailure msg | Uncertain msg when not norm2->
-            (* failure: let's try again argument vs argument *)
-            raise (KeepReducing msg)
-          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 (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 =
-          try
-           unify rdb test_eq_only metasenv subst context 
-            lambda_Mj (C.Meta (i,l))
-          with UnificationFailure msg | Uncertain msg when not norm1 ->
-           (* failure: let's try again argument vs argument *)
-           raise (KeepReducing msg)
-         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)
+           (* this easy_case handles "(? ?) =?= (f a)", same number of 
+            * args, preferring the instantiation "f" over "\_.f a" for the
+            * metavariable in head position. Since the arguments of the meta
+            * are flexible, delift would ignore them generating a constant
+            * function even in the easy case above *)
+           let easy_case = 
+             match t2 with
+             | NCic.Appl (f :: f_args)
+               when 
+               List.exists (NCicMetaSubst.is_flexible context ~subst) args ->
+                let mlen = List.length args in
+                let flen = List.length f_args in
+                let min_len = min mlen flen in
+                let mhe,margs = HExtlib.split_nth (mlen - min_len) args in
+                let fhe,fargs = HExtlib.split_nth (flen - min_len) f_args in
+                 (try 
+                    Some (List.fold_left2 
+                      (fun (m, s) t1 t2 -> 
+                        unify rdb test_eq_only m s context t1 t2 swap
+                      ) (metasenv,subst)
+                        ((NCicUntrusted.mk_appl meta mhe)::margs)
+                        ((NCicUntrusted.mk_appl f fhe)::fargs))
+                  with UnificationFailure _ | Uncertain _ | KeepReducing _ ->
+                    None) 
+             | _ -> None
+           in
+           (match easy_case with
+           | Some ms -> ms
+           | None ->
+               (* This case handles "(?_f ..ti..) =?= t2", abstracting every
+                * non flexible ti (delift skips local context items that are
+                * flexible) from t2 in two steps:
+                *  1) ?_f := \..xi.. .?
+                *  2) ?_f ..ti..  =?= t2 --unif_machines-->
+                      ?_f[..ti..] =?= t2 --instantiate-->
+                      delift [..ti..] t2 *)
+               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 swap
+               in
+               let metasenv, subst = 
+                 unify rdb test_eq_only metasenv subst context t1 t2 swap
+               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)) 
@@ -606,6 +648,7 @@ 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
@@ -614,14 +657,12 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
              with
                 Invalid_argument _ -> 
                  raise (Uncertain (mk_msg metasenv subst context t1 t2))
-              | UnificationFailure _ | Uncertain _ when not (norm1 && norm2) ->
-                 raise (KeepReducing (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 = 
@@ -637,20 +678,20 @@ 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 
+           (* if not (Ref.eq ref1 ref2) then 
              raise (Uncertain (mk_msg metasenv subst context t1 t2))
-           else
+           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
@@ -662,7 +703,17 @@ and unify rdb test_eq_only 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 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 =  
      pp(lazy ("\nProblema:\n" ^
         ppterm ~metasenv ~subst ~context t1 ^ " =?= " ^
@@ -691,8 +742,8 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
               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)
@@ -703,6 +754,7 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
       in
         cand_iter candidates
      (*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,
@@ -727,6 +779,32 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
               | 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)) 
      | NCic.Const (Ref.Ref (_,Ref.Fix (_,_,h))) 
@@ -764,7 +842,7 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
             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
@@ -781,19 +859,24 @@ and unify rdb test_eq_only metasenv subst context t1 t2 =
                 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_w_hints test_eq_only metasenv subst (norm1,hh1) (norm2,hh2) in
-         List.fold_left
-          (fun (metasenv,subst) (x1,x2,r) ->
-            unif_from_stack x1 x2 r metasenv subst
-          ) (metasenv,subst) todo
+          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)
+            unif_machines metasenv subst (small_delta_step ~subst m1 m2)
          | UnificationFailure _ | Uncertain _ when (not (norm1 && norm2))
            -> unif_machines metasenv subst (small_delta_step ~subst m1 m2)
          | UnificationFailure msg
@@ -823,7 +906,7 @@ and delift_type_wrt_terms rdb metasenv subst context t args =
       ~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)
@@ -836,9 +919,9 @@ and delift_type_wrt_terms rdb metasenv subst context t args =
 ;;
 
 
-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 m s =
   fix m s true false (UnificationFailure (lazy "no sup"))