X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_refiner%2FnCicUnification.ml;h=09d9ede475cd12bc1a88e34fbf5be307527f1024;hb=2b837ca9e298eb44eee95d9ca0e331c577785dcb;hp=abbafc4583dc09b9d1553414cbc0de47bde2324a;hpb=f2e2d1f6cccad2cc1ce70ef7fa2841cf0a457953;p=helm.git

diff --git a/helm/software/components/ng_refiner/nCicUnification.ml b/helm/software/components/ng_refiner/nCicUnification.ml
index abbafc458..09d9ede47 100644
--- a/helm/software/components/ng_refiner/nCicUnification.ml
+++ b/helm/software/components/ng_refiner/nCicUnification.ml
@@ -29,42 +29,52 @@ let fail_exc metasenv subst context t1 t2 =
   " with " ^ NCicPp.ppterm ~metasenv ~subst ~context t2));
 ;;
 
-let mk_appl hd tl =
-  match hd with
-  | NCic.Appl l -> NCic.Appl (l@tl)
-  | _ -> NCic.Appl (hd :: tl)
-;;
-
-let flexible l = 
-  List.exists 
-    (function 
-       | NCic.Meta _  
-       | NCic.Appl (NCic.Meta _::_) -> true
-       | _ -> false) l
+let mk_appl ~upto hd tl =
+  NCicReduction.head_beta_reduce ~upto
+    (match hd with
+    | NCic.Appl l -> NCic.Appl (l@tl)
+    | _ -> NCic.Appl (hd :: tl))
 ;;
 
 exception WrongShape;;
 
-let eta_reduce = 
-  let delift_if_not_occur body orig =
+let eta_reduce subst t = 
+  let delift_if_not_occur body =
     try 
-        NCicSubstitution.psubst ~avoid_beta_redexes:true
-          (fun () -> raise WrongShape) [()] body
-    with WrongShape -> orig
+        Some (NCicSubstitution.psubst ~avoid_beta_redexes:true
+          (fun () -> raise WrongShape) [()] body)
+    with WrongShape -> None
+  in 
+  let rec eat_lambdas ctx = function
+    | NCic.Lambda (name, src, tgt) -> 
+        eat_lambdas ((name, src) :: ctx) tgt
+    | NCic.Meta (i,lc) as t->
+        (try 
+          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)
+    | t -> ctx, t
   in
-  function
-  | NCic.Lambda(_, _, NCic.Appl [hd; NCic.Rel 1]) as orig ->
-      delift_if_not_occur hd orig
-  | NCic.Lambda(_, _, NCic.Appl (hd :: l)) as orig
-    when HExtlib.list_last l = NCic.Rel 1 ->
-       let body = 
-         let args, _ = HExtlib.split_nth (List.length l - 1) l in
-         NCic.Appl (hd::args)
-       in
-       delift_if_not_occur body orig
-  | t -> t
+  let context_body = eat_lambdas [] t in
+  let rec aux = function
+    | [],body -> body
+    | (name, src)::ctx, (NCic.Appl (hd::[NCic.Rel 1]) as bo) -> 
+        (match delift_if_not_occur hd with
+        | None -> aux (ctx,NCic.Lambda(name,src, bo)) 
+        | Some bo -> aux (ctx,bo))
+    | (name, src)::ctx, (NCic.Appl args as bo) 
+      when HExtlib.list_last args = NCic.Rel 1 -> 
+        let args, _ = HExtlib.split_nth "NU 1" (List.length args - 1) args in
+        (match delift_if_not_occur (NCic.Appl args) with
+        | None -> aux (ctx,NCic.Lambda(name,src, bo)) 
+        | Some bo -> aux (ctx,bo))
+    | (name, src) :: ctx, t ->
+        aux (ctx,NCic.Lambda(name,src, t)) 
+  in
+    aux context_body
 ;;
- 
+
 module C = NCic;;
 module Ref = NReference;;
 
@@ -72,11 +82,9 @@ let indent = ref "";;
 let inside c = indent := !indent ^ String.make 1 c;;
 let outside () = indent := String.sub !indent 0 (String.length !indent -1);;
 
-(*
 let pp s = 
   prerr_endline (Printf.sprintf "%-20s" !indent ^ " " ^ Lazy.force s)
 ;;  
-*)
 
 let pp _ = ();;
 
@@ -99,66 +107,32 @@ let fix_sorts swap metasenv subst context meta t =
     aux () t
 ;;
 
-let rec beta_expand hdb num test_eq_only swap metasenv subst context t arg =
-  let rec aux (n,context,test_eq_only as k) (metasenv, subst as acc) t' =
+let is_locked n subst =
    try
-    let metasenv, subst =
-     if swap then
-      unify hdb test_eq_only metasenv subst context t' (NCicSubstitution.lift n arg)
-     else
-      unify hdb test_eq_only metasenv subst context (NCicSubstitution.lift n arg) t'
-    in
-     (metasenv, subst), NCic.Rel (1 + n)
-   with Uncertain _ | UnificationFailure _ ->
-       match t' with
-       | NCic.Rel m as orig -> 
-           (metasenv, subst), if m <= n then orig else NCic.Rel (m+1)
-       (* andrea: in general, beta_expand can create badly typed
-        terms. This happens quite seldom in practice, UNLESS we
-        iterate on the local context. For this reason, we renounce
-        to iterate and just lift *)
-       | NCic.Meta (i,(shift,lc)) ->
-           (metasenv,subst), NCic.Meta (i,(shift+1,lc))
-       | NCic.Prod (name, src, tgt) as orig ->
-           let (metasenv, subst), src1 = aux (n,context,true) acc src in 
-           let k = n+1, (name, NCic.Decl src) :: context, test_eq_only in
-           let ms, tgt1 = aux k (metasenv, subst) tgt in 
-           if src == src1 && tgt == tgt1 then ms, orig else
-           ms, NCic.Prod (name, src1, tgt1)
-       | t -> 
-           NCicUntrusted.map_term_fold_a 
-             (fun e (n,ctx,teq) -> n+1,e::ctx,teq) k aux acc t
+     match NCicUtils.lookup_subst n subst with
+     | Some tag, _,_,_ when NCicMetaSubst.is_out_scope_tag tag -> true
+     | _ -> false
+   with NCicUtils.Subst_not_found _ -> false
+;;
 
-  in
-  let argty = NCicTypeChecker.typeof ~metasenv ~subst context arg in
-  let fresh_name = "Hbeta" ^ string_of_int num in
-  let (metasenv,subst), t1 = 
-    aux (0, context, test_eq_only) (metasenv, subst) t in
-  let t2 = eta_reduce (NCic.Lambda (fresh_name,argty,t1)) in
-  try 
-    ignore(NCicTypeChecker.typeof ~metasenv ~subst context t2);
-    metasenv, subst, t2
-  with NCicTypeChecker.TypeCheckerFailure _ -> 
-    metasenv, subst, NCic.Lambda ("_", argty, NCicSubstitution.lift 1 arg)
 
-and beta_expand_many hdb test_equality_only swap metasenv subst context t args =
-(* (*D*)  inside 'B'; try let rc = *)
-  pp (lazy (String.concat ", "
-     (List.map (NCicPp.ppterm ~metasenv ~subst ~context)
-     args) ^ " ∈ " ^ NCicPp.ppterm ~metasenv ~subst ~context t));
-  let _, subst, metasenv, hd =
-    List.fold_right
-      (fun arg (num,subst,metasenv,t) ->
-         let metasenv, subst, t =
-           beta_expand hdb num test_equality_only swap metasenv subst context t arg
-         in
-           num+1,subst,metasenv,t)
-      args (1,subst,metasenv,t) 
-  in
-  pp (lazy ("Head syntesized by b-exp: " ^ 
-    NCicPp.ppterm ~metasenv ~subst ~context hd));
-    metasenv, subst, hd
-(* (*D*)  in outside (); rc with exn -> outside (); raise exn *)
+let rec lambda_intros metasenv subst context t args =
+ let tty = NCicTypeChecker.typeof ~metasenv ~subst context t in
+ let argsty = List.map (NCicTypeChecker.typeof ~metasenv ~subst context) args in
+ let rec mk_lambda context n = function
+   | [] -> 
+       let metasenv, _, bo, _ = 
+         NCicMetaSubst.mk_meta metasenv context 
+           (`WithType (NCicSubstitution.lift n tty))
+       in
+       metasenv, bo
+   | ty::tail -> 
+       let name = "HBeta"^string_of_int n in
+       let ty = NCicSubstitution.lift n ty in
+       let metasenv, bo = mk_lambda ((name,NCic.Decl ty)::context) (n+1) tail in
+       metasenv, NCic.Lambda (name, ty, bo)
+ in
+   mk_lambda context 0 argsty
 
 and instantiate hdb test_eq_only metasenv subst context n lc t swap =
  (*D*)  inside 'I'; try let rc =  
@@ -205,17 +179,32 @@ and instantiate hdb test_eq_only metasenv subst context n lc t swap =
               pp msg; assert false
        in
        let lty = NCicSubstitution.subst_meta lc ty in
-       pp (lazy ("On the types: " ^
-        NCicPp.ppterm ~metasenv ~subst ~context:ctx ty ^ " ~~~ " ^
-        NCicPp.ppterm ~metasenv ~subst ~context lty ^ " === "
-         ^ NCicPp.ppterm ~metasenv ~subst ~context ty_t)); 
-       let metasenv,subst= unify test_eq_only metasenv subst context lty ty_t in
-       metasenv, subst, t
+       match ty_t with
+       | NCic.Implicit _ -> 
+           raise (UnificationFailure 
+             (lazy "trying to unify a term with a type"))
+       | ty_t -> 
+          pp (lazy ("On the types: " ^
+           NCicPp.ppterm ~metasenv ~subst ~context:ctx ty ^ " ~~~ " ^
+           NCicPp.ppterm ~metasenv ~subst ~context lty ^ " === "
+            ^ NCicPp.ppterm ~metasenv ~subst ~context ty_t)); 
+          let metasenv,subst = 
+            unify test_eq_only metasenv subst context lty ty_t in
+          metasenv, subst, t
   in
          pp (lazy(string_of_int n ^ " := 111 = "^
            NCicPp.ppterm ~metasenv ~subst ~context t));
   let (metasenv, subst), t = 
-    try NCicMetaSubst.delift metasenv subst context n lc 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
+         in
+         indent := ind; res) 
+       metasenv subst context n lc t
     with NCicMetaSubst.Uncertain msg -> 
          pp (lazy ("delift fails: " ^ Lazy.force msg));
          raise (Uncertain msg)
@@ -247,223 +236,294 @@ and instantiate hdb test_eq_only metasenv subst context n lc t swap =
 
 and unify hdb test_eq_only metasenv subst context t1 t2 =
  (*D*) inside 'U'; try let rc =
-   let rec fo_unif test_eq_only metasenv subst t1 t2 =
-     let try_hints metasenv subst context t1 t2 (* exc*) =
-       let candidates = NCicUnifHint.look_for_hint hdb metasenv subst context t1 t2
-       in
-       let rec cand_iter = function
-         | [] -> None (* raise exc *)
-         | (metasenv,c1,c2)::tl -> 
-             try 
-               prerr_endline (NCicPp.ppterm ~metasenv ~subst ~context t1);
-               prerr_endline (NCicPp.ppterm ~metasenv ~subst ~context c1);
-               prerr_endline (NCicPp.ppterm ~metasenv ~subst ~context t2);
-               prerr_endline (NCicPp.ppterm ~metasenv ~subst ~context c2);
-               let metasenv,subst = fo_unif test_eq_only metasenv subst t1 c1 in
-               let metasenv,subst = fo_unif test_eq_only metasenv subst c2 t2 in
-               Some (fo_unif test_eq_only metasenv subst t1 t2)
-             with
-               UnificationFailure _ | Uncertain _ -> cand_iter tl
-       in
-         cand_iter candidates
-     in
-
+   let fo_unif test_eq_only metasenv subst t1 t2 =
     (*D*) inside 'F'; try let rc =  
-     pp (lazy("  " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " === " ^ 
-         NCicPp.ppterm ~metasenv ~subst ~context t2));
+     pp (lazy("  " ^ NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " ==?== " ^ 
+         NCicPp.ppterm ~metasenv ~subst ~context t2 ^ "\n" ^ NCicPp.ppmetasenv
+         ~subst metasenv));
      if t1 === t2 then
        metasenv, subst
      else
-       match (try_hints metasenv subst context t1 t2) with
-       | Some x -> x
-       | None ->
-         match (t1,t2) with
-         | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only -> 
-             if NCicEnvironment.universe_leq a b then metasenv, subst
-             else raise (fail_exc 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 _)) -> 
-             if (not test_eq_only) then metasenv, subst
-             else raise (fail_exc 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 hdb true metasenv subst context s1 s2 in
-             unify hdb test_eq_only metasenv subst ((name1, C.Decl s1)::context) t1 t2
-         | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
-             let metasenv,subst=unify hdb test_eq_only metasenv subst context ty1 ty2 in
-             let metasenv,subst=unify hdb test_eq_only metasenv subst context s1 s2 in
-             let context = (name1, C.Def (s1,ty1))::context in
-             unify hdb test_eq_only metasenv subst context t1 t2
-
-         | (C.Meta (n1,(s1,l1 as lc1)),C.Meta (n2,(s2,l2 as lc2))) when n1 = n2 ->
-            (try 
-             let l1 = NCicUtils.expand_local_context l1 in
-             let l2 = NCicUtils.expand_local_context l2 in
-             let metasenv, subst, to_restrict, _ =
-              List.fold_right2 
-               (fun t1 t2 (metasenv, subst, to_restrict, i) -> 
-                  try 
-                    let metasenv, subst = 
-                     unify hdb test_eq_only metasenv subst context 
-                      (NCicSubstitution.lift s1 t1) (NCicSubstitution.lift s2 t2)
-                    in
-                    metasenv, subst, to_restrict, i-1  
-                  with UnificationFailure _ | Uncertain _ ->
-                    metasenv, subst, i::to_restrict, i-1)
-               l1 l2 (metasenv, subst, [], List.length l1)
-             in
-             if to_restrict <> [] then
-               let metasenv, subst, _ = 
-                 NCicMetaSubst.restrict metasenv subst n1 to_restrict
-               in
-                 metasenv, subst
-             else metasenv, subst
-            with 
-             | Invalid_argument _ -> assert false
-             | NCicMetaSubst.MetaSubstFailure msg ->
+       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 -> 
+           if NCicEnvironment.universe_leq a b then metasenv, subst
+           else raise (fail_exc 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 _)) -> 
+           if (not test_eq_only) then metasenv, subst
+           else raise (fail_exc 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 hdb true metasenv subst context s1 s2 in
+           unify hdb test_eq_only metasenv subst ((name1, C.Decl s1)::context) t1 t2
+       | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
+           let metasenv,subst=unify hdb test_eq_only metasenv subst context ty1 ty2 in
+           let metasenv,subst=unify hdb test_eq_only metasenv subst context s1 s2 in
+           let context = (name1, C.Def (s1,ty1))::context in
+           unify hdb test_eq_only metasenv subst context t1 t2
+
+       | (C.Meta (n1,(s1,l1 as lc1)),C.Meta (n2,(s2,l2 as lc2))) when n1 = n2 ->
+          (try 
+           let l1 = NCicUtils.expand_local_context l1 in
+           let l2 = NCicUtils.expand_local_context l2 in
+           let metasenv, subst, to_restrict, _ =
+            List.fold_right2 
+             (fun t1 t2 (metasenv, subst, to_restrict, i) -> 
                 try 
-                  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 hdb test_eq_only metasenv subst context term1 term2
-                with NCicUtils.Subst_not_found _-> raise (UnificationFailure msg))
-
-         | C.Meta (n,lc), t -> 
-             (try 
-               let _,_,term,_ = NCicUtils.lookup_subst n subst in
-               let term = NCicSubstitution.subst_meta lc term in
-                 unify hdb test_eq_only metasenv subst context term t
-             with NCicUtils.Subst_not_found _-> 
-               instantiate hdb test_eq_only metasenv subst context n lc 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 hdb test_eq_only metasenv subst context t term
-             with NCicUtils.Subst_not_found _-> 
-               instantiate hdb test_eq_only metasenv subst context n lc 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 hdb test_eq_only metasenv subst context (mk_appl term args) t2
-
-         | _, 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 hdb test_eq_only metasenv subst context t1 (mk_appl 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 hdb test_eq_only metasenv subst context t1 t2)
-                  (metasenv,subst) l1 l2
-              with Invalid_argument _ -> 
-                raise (fail_exc metasenv subst context t1 t2))
-
-         | NCic.Appl (NCic.Meta (i,l)::args), _ when not (flexible args) ->
-             (* we verify that none of the args is a Meta, 
-                since beta expanding w.r.t a metavariable makes no sense  *)
-                let metasenv, subst, beta_expanded =
-                  beta_expand_many hdb 
-                    test_eq_only false 
-                    metasenv subst context t2 args
-                in
-                  unify hdb test_eq_only metasenv subst context 
-                    (C.Meta (i,l)) beta_expanded 
-
-         | _, NCic.Appl (NCic.Meta (i,l)::args) when not(flexible args) ->
-                let metasenv, subst, beta_expanded =
-                  beta_expand_many hdb 
-                    test_eq_only true 
-                    metasenv subst context t1 args
-                in
-                  unify hdb test_eq_only metasenv subst context 
-                    beta_expanded (C.Meta (i,l))
-
-         (* 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 = HExtlib.split_nth lno relevance in
-                     HExtlib.mk_list false lno @ relevance
-               | _ -> relevance
-             in
+                  let metasenv, subst = 
+                   unify hdb test_eq_only metasenv subst context 
+                    (NCicSubstitution.lift s1 t1) (NCicSubstitution.lift s2 t2)
+                  in
+                  metasenv, subst, to_restrict, i-1  
+                with UnificationFailure _ | Uncertain _ ->
+                  metasenv, subst, i::to_restrict, i-1)
+             l1 l2 (metasenv, subst, [], List.length l1)
+           in
+           if to_restrict <> [] then
              let metasenv, subst, _ = 
-               try
-                 List.fold_left2 
-                   (fun (metasenv, subst, relevance) t1 t2 ->
-                      let b, relevance = 
-                        match relevance with b::tl -> b,tl | _ -> true, [] in
-                      let metasenv, subst = 
-                        try unify hdb test_eq_only metasenv subst context t1 t2
-                        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)
-             in 
-               metasenv, subst
-
-         | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
-            C.Match (ref2,outtype2,term2,pl2)) ->
-             let _,_,itl,_,_ = NCicEnvironment.get_checked_indtys ref1 in
-             let _,_,ty,_ = List.nth itl tyno in
-             let rec remove_prods ~subst context ty = 
-               let ty = NCicReduction.whd ~subst context ty in
-               match ty with
-               | C.Sort _ -> ty
-               | C.Prod (name,so,ta) -> 
-                     remove_prods ~subst ((name,(C.Decl so))::context) ta
-               | _ -> assert false
+               NCicMetaSubst.restrict metasenv subst n1 to_restrict
              in
-             let is_prop = 
-               match remove_prods ~subst [] ty with
-               | C.Sort C.Prop -> true
-               | _ -> false 
+               metasenv, subst
+           else metasenv, subst
+          with 
+           | Invalid_argument _ -> assert false
+           | NCicMetaSubst.MetaSubstFailure msg ->
+              try 
+                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 hdb test_eq_only metasenv subst context term1 term2
+              with NCicUtils.Subst_not_found _-> raise (UnificationFailure msg))
+       
+       | _, NCic.Meta (n, _) when is_locked n subst ->
+           (let (metasenv, subst), i = 
+              match NCicReduction.whd ~subst context t1 with
+              | NCic.Appl (NCic.Meta (i,l)::args) when
+                  not (NCicMetaSubst.flexible subst args) 
+                ->
+                 let metasenv, lambda_Mj =
+                   lambda_intros metasenv subst context t1 args
+                 in
+                   unify hdb test_eq_only metasenv subst context 
+                    (C.Meta (i,l)) lambda_Mj,
+                   i
+              | NCic.Meta (i,_) -> (metasenv, subst), i
+              | _ -> assert false
              in
-             let rec remove_prods ~subst context ty = 
-               let ty = NCicReduction.whd ~subst context ty in
-               match ty with
-               | C.Sort _ -> ty
-               | C.Prod (name,so,ta) -> 
-                     remove_prods ~subst ((name,(C.Decl so))::context) ta
-               | _ -> assert false
+              let t1 = NCicReduction.whd ~subst context t1 in
+              let j, lj = 
+                match t1 with NCic.Meta (j,l) -> j, l | _ -> assert false
+              in
+              let metasenv, subst = 
+                instantiate hdb test_eq_only metasenv subst context j lj t2 true
+              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))
+
+       | C.Meta (n,lc), t -> 
+           (try 
+             let _,_,term,_ = NCicUtils.lookup_subst n subst in
+             let term = NCicSubstitution.subst_meta lc term in
+               unify hdb test_eq_only metasenv subst context term t
+           with NCicUtils.Subst_not_found _-> 
+             instantiate hdb 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 hdb test_eq_only metasenv subst context t term
+           with NCicUtils.Subst_not_found _-> 
+             instantiate hdb 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 hdb test_eq_only metasenv subst context 
+                (mk_appl ~upto:(List.length args) term args) t2
+
+       | _, 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 hdb 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 hdb test_eq_only metasenv subst context t1 t2)
+                (metasenv,subst) l1 l2
+            with Invalid_argument _ -> 
+              raise (fail_exc metasenv subst context t1 t2))
+
+       | NCic.Appl (NCic.Meta (i,l)::args), _ when 
+         not (NCicMetaSubst.flexible subst args) ->
+           (* we verify that none of the args is a Meta, 
+              since beta expanding w.r.t a metavariable makes no sense  *)
+              let metasenv, lambda_Mj =
+                lambda_intros metasenv subst context t1 args
+              in
+              let metasenv, subst = 
+                unify hdb test_eq_only metasenv subst context 
+                  (C.Meta (i,l)) lambda_Mj
+              in
+              let metasenv, subst = 
+                unify hdb 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)::args) when 
+         not(NCicMetaSubst.flexible subst args) ->
+              let metasenv, lambda_Mj =
+                lambda_intros metasenv subst context t2 args
+              in
+              let metasenv, subst =
+                unify hdb test_eq_only metasenv subst context 
+                 lambda_Mj (C.Meta (i,l))
+              in
+              let metasenv, subst = 
+                unify hdb 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)
+
+       (* 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 "NU 2" lno relevance)
+                  with Failure _ -> []
+                 in
+                   HExtlib.mk_list false lno @ relevance
+             | _ -> relevance
+           in
+           let metasenv, subst, _ = 
+             try
+               List.fold_left2 
+                 (fun (metasenv, subst, relevance) t1 t2 ->
+                    let b, relevance = 
+                      match relevance with b::tl -> b,tl | _ -> true, [] in
+                    let metasenv, subst = 
+                      try unify hdb test_eq_only metasenv subst context t1 t2
+                      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)
+           in 
+             metasenv, subst
+
+       | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
+          C.Match (ref2,outtype2,term2,pl2)) ->
+           let _,_,itl,_,_ = NCicEnvironment.get_checked_indtys ref1 in
+           let _,_,ty,_ = List.nth itl tyno in
+           let rec remove_prods ~subst context ty = 
+             let ty = NCicReduction.whd ~subst context ty in
+             match ty with
+             | C.Sort _ -> ty
+             | C.Prod (name,so,ta) -> 
+                   remove_prods ~subst ((name,(C.Decl so))::context) ta
+             | _ -> assert false
+           in
+           let is_prop = 
+             match remove_prods ~subst [] ty with
+             | C.Sort C.Prop -> true
+             | _ -> false 
+           in
+           if not (Ref.eq ref1 ref2) then 
+             raise (uncert_exc metasenv subst context t1 t2) 
+           else
+             let metasenv, subst = 
+              unify hdb test_eq_only metasenv subst context outtype1 outtype2 in
+             let metasenv, subst = 
+               try unify hdb test_eq_only metasenv subst context term1 term2 
+               with UnificationFailure _ | Uncertain _ when is_prop -> 
+                 metasenv, subst
              in
-             if not (Ref.eq ref1 ref2) then 
-               raise (uncert_exc metasenv subst context t1 t2) 
-             else
-               let metasenv, subst = 
-                 unify hdb test_eq_only metasenv subst context outtype1 outtype2 in
-               let metasenv, subst = 
-                 try unify hdb test_eq_only metasenv subst context term1 term2 
-                 with UnificationFailure _ | Uncertain _ when is_prop -> 
-                   metasenv, subst
-               in
-               (try
-                List.fold_left2 
-                 (fun (metasenv,subst) -> 
-                    unify hdb test_eq_only metasenv subst context)
-                 (metasenv, subst) pl1 pl2
-               with Invalid_argument _ -> 
-                 raise (uncert_exc metasenv subst context t1 t2))
-         | (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)
+             (try
+              List.fold_left2 
+               (fun (metasenv,subst) -> 
+                  unify hdb test_eq_only metasenv subst context)
+               (metasenv, subst) pl1 pl2
+             with Invalid_argument _ -> 
+               raise (uncert_exc metasenv subst context t1 t2))
+       | (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(); rc with exn -> outside (); raise exn 
     in
+    let try_hints metasenv subst t1 t2 (* exc*) =
+(*
+      prerr_endline ("\nProblema:\n" ^
+        NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " =?= " ^
+        NCicPp.ppterm ~metasenv ~subst ~context t2);
+*)
+      let candidates = 
+        NCicUnifHint.look_for_hint hdb metasenv subst context t1 t2
+      in
+      let rec cand_iter = function
+        | [] -> None (* raise exc *)
+        | (metasenv,(c1,c2),premises)::tl -> 
+(*
+            prerr_endline ("\nProvo il candidato:\n" ^ 
+              String.concat "\n"
+                (List.map 
+                  (fun (a,b) ->
+                   NCicPp.ppterm ~metasenv ~subst ~context a ^  " =?= " ^
+                   NCicPp.ppterm ~metasenv ~subst ~context b) premises) ^
+              "\n-------------------------------------------\n"^
+              NCicPp.ppterm ~metasenv ~subst ~context c1 ^  " = " ^
+              NCicPp.ppterm ~metasenv ~subst ~context c2);
+*)
+            try 
+              let metasenv,subst = 
+                fo_unif test_eq_only metasenv subst t1 c1 in
+              let metasenv,subst = 
+                fo_unif test_eq_only metasenv subst c2 t2 in
+              let metasenv,subst = 
+                List.fold_left 
+                  (fun (metasenv, subst) (x,y) ->
+                     unify hdb test_eq_only metasenv subst context x y)
+                  (metasenv, subst) premises
+              in
+              Some (metasenv, subst)
+            with
+              UnificationFailure _ | Uncertain _ ->
+                cand_iter tl
+      in
+        cand_iter candidates
+    in
     let height_of = function
      | NCic.Const (Ref.Ref (_,Ref.Def h)) 
      | NCic.Const (Ref.Ref (_,Ref.Fix (_,_,h))) 
@@ -475,7 +535,7 @@ and unify hdb test_eq_only metasenv subst context t1 t2 =
       NCicReduction.reduce_machine ~delta:max_int ~subst context m1,
       NCicReduction.reduce_machine ~delta:max_int ~subst context m2
     in
-    let small_delta_step 
+    let small_delta_step ~subst  
       ((_,_,t1,_ as m1, norm1) as x1) ((_,_,t2,_ as m2, norm2) as x2)
     =
      assert (not (norm1 && norm2));
@@ -494,12 +554,13 @@ and unify hdb test_eq_only metasenv subst context t1 t2 =
       function
       | ((k1,e1,t1,s1),norm1 as m1),((k2,e2,t2,s2),norm2 as m2) ->
      (*D*) inside 'M'; try let rc = 
-(*
-         pp (lazy((if are_normal then "*" else " ") ^ " " ^
-           NCicPp.ppterm ~metasenv ~subst ~context (NCicReduction.unwind m1) ^
+         pp (lazy("UM: " ^
+           NCicPp.ppterm ~metasenv ~subst ~context 
+             (NCicReduction.unwind (k1,e1,t1,s1)) ^
            " === " ^ 
-           NCicPp.ppterm ~metasenv ~subst ~context (NCicReduction.unwind m2)));
-*)
+           NCicPp.ppterm ~metasenv ~subst ~context 
+             (NCicReduction.unwind (k2,e2,t2,s2))));
+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
@@ -529,22 +590,31 @@ and unify hdb test_eq_only metasenv subst context t1 t2 =
             unif_from_stack x1 x2 r metasenv subst
           ) (metasenv,subst) todo
         with UnificationFailure _ | Uncertain _ when not (norm1 && norm2) ->
-	    unif_machines metasenv subst (small_delta_step m1 m2)
+	    unif_machines metasenv subst (small_delta_step ~subst m1 m2)
       (*D*)  in outside(); rc with exn -> outside (); raise exn 
      in
      try fo_unif test_eq_only metasenv subst t1 t2
-     with UnificationFailure msg | Uncertain msg as exn -> 
-       try 
-         unif_machines metasenv subst 
-          (put_in_whd (0,[],t1,[]) (0,[],t2,[]))
-       with 
-       | UnificationFailure _ -> raise (UnificationFailure msg)
-       | Uncertain _ -> raise exn
+     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,[]))
+          with 
+          | UnificationFailure _ -> raise (UnificationFailure msg)
+          | Uncertain _ -> raise exn
  (*D*)  in outside(); rc with exn -> outside (); raise exn 
 ;;
 
-let unify hdb = 
+let unify hdb ?(test_eq_only=false) = 
   indent := "";      
-  unify hdb false;;
-
-
+  unify hdb test_eq_only;;