]> matita.cs.unibo.it Git - helm.git/blobdiff - components/tactics/paramodulation/saturation.ml
Build_proof_goal does not return the metasenv any more.
[helm.git] / components / tactics / paramodulation / saturation.ml
index 5b5121e8677ea61a45642b6fd236302e9e4d6540..4423661b00b118073a45e4d0d071bfec56c8921a 100644 (file)
@@ -70,16 +70,20 @@ let maxmeta = ref 0;;
 let maxdepth = ref 3;;
 let maxwidth = ref 3;;
 
+type new_proof = 
+  Equality.goal_proof * Equality.new_proof * Equality.substitution * Cic.metasenv
+type old_proof = Equality.old_proof * Cic.metasenv
 type result =
   | ParamodulationFailure
-  | ParamodulationSuccess of (Inference.proof * Cic.metasenv) option
+  | ParamodulationSuccess of (new_proof * old_proof) option
 ;;
 
-type goal = proof * Cic.metasenv * Cic.term;;
+type goal = (Equality.goal_proof * Equality.old_proof) * Cic.metasenv * Cic.term;;
 
 type theorem = Cic.term * Cic.term * Cic.metasenv;;
 
-let symbols_of_equality (_, _, (_, left, right, _), _) =
+let symbols_of_equality equality = 
+  let (_, _, (_, left, right, _), _,_) = Equality.open_equality equality in
   let m1 = symbols_of_term left in
   let m = 
     TermMap.fold
@@ -96,18 +100,19 @@ let symbols_of_equality (_, _, (_, left, right, _), _) =
 
 (* griggio *)
 module OrderedEquality = struct 
-  type t = Inference.equality
+  type t = Equality.equality
 
   let compare eq1 eq2 =
-    match meta_convertibility_eq eq1 eq2 with
+    match Equality.meta_convertibility_eq eq1 eq2 with
     | true -> 0
     | false ->
-        let w1, _, (ty, left, right, _), m1 = eq1
-        and w2, _, (ty', left', right', _), m2 = eq2 in
+        let w1, _, (ty,left, right, _), m1,_ = Equality.open_equality eq1 in
+        let w2, _, (ty',left', right', _), m2,_ = Equality.open_equality eq2 in
         match Pervasives.compare w1 w2 with
         | 0 -> 
             let res = (List.length m1) - (List.length m2) in 
-            if res <> 0 then res else Pervasives.compare eq1 eq2
+            if res <> 0 then res else 
+              Equality.compare eq1 eq2
         | res -> res 
 end 
 
@@ -142,7 +147,7 @@ let rec select env goals passive =
     match (List.rev goals) with (_, goal::_)::_ -> goal | _ -> assert false
   in
   let (pos_list, pos_set), passive_table = passive in
-  let remove eq l = List.filter (fun e -> e <> eq) l in
+  let remove eq l = List.filter (fun e -> Equality.compare e eq <> 0) l in
   if !weight_age_ratio > 0 then
     weight_age_counter := !weight_age_counter - 1;
   match !weight_age_counter with
@@ -192,7 +197,7 @@ let rec select env goals passive =
       let passive_table =
         Indexing.remove_index passive_table current
       in
-       current,
+        current,
       ((remove current pos_list, EqualitySet.remove current pos_set),
        passive_table))
   | _ ->
@@ -255,8 +260,6 @@ let prune_passive howmany (active, _) passive =
   and in_age = round (howmany /. (ratio +. 1.)) in 
   debug_print
     (lazy (Printf.sprintf "in_weight: %d, in_age: %d\n" in_weight in_age));
-  let symbols, card = None, 0
-  in
   let counter = ref !symbols_ratio in
   let rec pickw w ps =
     if w > 0 then
@@ -264,7 +267,7 @@ let prune_passive howmany (active, _) passive =
         let _ =
           counter := !counter - 1;
           if !counter = 0 then counter := !symbols_ratio in
-       let e = EqualitySet.min_elt ps in
+        let e = EqualitySet.min_elt ps in
         let ps' = pickw (w-1) (EqualitySet.remove e ps) in
           EqualitySet.add e ps'
       else
@@ -300,7 +303,7 @@ let prune_passive howmany (active, _) passive =
 
 
 (** inference of new equalities between current and some in active *)
-let infer env current ((active_list:Inference.equality list), active_table) =
+let infer env current (active_list, active_table) =
   let (_,c,_) = env in 
   if Utils.debug_metas then
     (ignore(Indexing.check_target c current "infer1");
@@ -325,9 +328,9 @@ let infer env current ((active_list:Inference.equality list), active_table) =
                      (function current -> 
                         Indexing.check_target c current "sup2") res);
               let pos = infer_positive table tl in
-             res @ pos
+              res @ pos
       in
-      let maxm, copy_of_current = Inference.fix_metas !maxmeta current in
+      let maxm, copy_of_current = Equality.fix_metas !maxmeta current in
         maxmeta := maxm;
       let curr_table = Indexing.index Indexing.empty current in
       let pos = infer_positive curr_table (copy_of_current::active_list) 
@@ -336,7 +339,7 @@ let infer env current ((active_list:Inference.equality list), active_table) =
         ignore(List.map 
                  (function current -> 
                     Indexing.check_target c current "sup3") pos);
-       res @ pos
+        res @ pos
   in
   derived_clauses := !derived_clauses + (List.length new_pos);
   match !maximal_retained_equality with
@@ -365,7 +368,7 @@ let forward_simplify env (sign,current) ?passive (active_list, active_table) =
     let newmeta, newcurrent =
       Indexing.demodulation_equality !maxmeta env table sign current in
     maxmeta := newmeta;
-    if is_identity env newcurrent then
+    if Equality.is_identity env newcurrent then
 (*         debug_print  *)
 (*           (lazy *)
 (*              (Printf.sprintf "\ncurrent was: %s\nnewcurrent is: %s\n" *)
@@ -396,7 +399,7 @@ let forward_simplify env (sign,current) ?passive (active_list, active_table) =
             match demodulate passive_table newcurrent with
               | None -> None
               | Some newnewcurrent -> 
-                  if newcurrent <> newnewcurrent then 
+                  if Equality.compare newcurrent newnewcurrent <> 0 then 
                     demod newnewcurrent
                   else Some newnewcurrent
   in 
@@ -404,6 +407,7 @@ let forward_simplify env (sign,current) ?passive (active_list, active_table) =
   match res with
   | None -> None
   | Some c ->
+      (* immagino non funzioni piu'... *)
       if Indexing.in_index active_table c then
         None
       else
@@ -471,7 +475,7 @@ let forward_simplify_new env new_pos ?passive active =
   let new_pos_set =
     List.fold_left
       (fun s e ->
-         if not (Inference.is_identity env e) then
+         if not (Equality.is_identity env e) then
            if EqualitySet.mem e s then s
            else EqualitySet.add e s
          else s)
@@ -510,12 +514,11 @@ let rec simplify_goal env goal ?passive (active_list, active_table) =
     | None -> None
     | Some ((_, _), pt) -> Some pt
   in
-
   let demodulate table goal = 
-    let newmeta, newgoal =
+    let changed, newmeta, newgoal =
       Indexing.demodulation_goal !maxmeta env table goal in
     maxmeta := newmeta;
-    goal <> newgoal, newgoal
+    changed, newgoal
   in
   let changed, goal =
     match passive_table with
@@ -565,28 +568,28 @@ let backward_simplify_active env new_pos new_table min_weight active =
   let active_list, newa = 
     List.fold_right
       (fun equality (res, newn) ->
-         let ew, _, _, _ = equality in
+         let ew, _, _, _,_ = Equality.open_equality equality in
          if ew < min_weight then
            equality::res, newn
          else
            match forward_simplify env (Utils.Positive, equality) (new_pos, new_table) with
            | None -> res, newn
            | Some e ->
-               if equality = e then
+               if Equality.compare equality e = 0 then
                  e::res, newn
                else 
                  res, e::newn)
       active_list ([], [])
   in
   let find eq1 where =
-    List.exists (meta_convertibility_eq eq1) where
+    List.exists (Equality.meta_convertibility_eq eq1) where
   in
   let active, newa =
     List.fold_right
       (fun eq (res, tbl) ->
          if List.mem eq res then
            res, tbl
-         else if (is_identity env eq) || (find eq res) then (
+         else if (Equality.is_identity env eq) || (find eq res) then (
            res, tbl
          ) 
          else
@@ -594,8 +597,8 @@ let backward_simplify_active env new_pos new_table min_weight active =
       active_list ([], Indexing.empty),
     List.fold_right
       (fun eq p ->
-         if (is_identity env eq) then p
-        else eq::p)
+         if (Equality.is_identity env eq) then p
+         else eq::p)
       newa []
   in
   match newa with
@@ -608,7 +611,7 @@ let backward_simplify_active env new_pos new_table min_weight active =
 let backward_simplify_passive env new_pos new_table min_weight passive =
   let (pl, ps), passive_table = passive in
   let f sign equality (resl, ress, newn) =
-    let ew, _, _, _ = equality in
+    let ew, _, _, _ , _ = Equality.open_equality equality in
     if ew < min_weight then
       equality::resl, ress, newn
     else
@@ -636,7 +639,7 @@ let backward_simplify env new' ?passive active =
   let new_pos, new_table, min_weight =
     List.fold_left
       (fun (l, t, w) e ->
-         let ew, _, _, _ = e in
+         let ew, _, _, _ , _ = Equality.open_equality e in
          e::l, Indexing.index t e, min ew w)
       ([], Indexing.empty, 1000000) new'
   in
@@ -658,7 +661,7 @@ let close env new' given =
   let new_pos, new_table, min_weight =
     List.fold_left
       (fun (l, t, w) e ->
-         let ew, _, _, _ = e in
+         let ew, _, _, _ , _ = Equality.open_equality e in
          e::l, Indexing.index t e, min ew w)
       ([], Indexing.empty, 1000000) (snd new')
   in
@@ -670,7 +673,9 @@ let close env new' given =
 ;;
 
 let is_commutative_law eq =
-  let w, proof, (eq_ty, left, right, order), metas = eq in
+  let w, proof, (eq_ty, left, right, order), metas , _ = 
+    Equality.open_equality eq 
+  in
     match left,right with
         Cic.Appl[f1;Cic.Meta _ as a1;Cic.Meta _ as b1], 
         Cic.Appl[f2;Cic.Meta _ as a2;Cic.Meta _ as b2] ->
@@ -686,7 +691,7 @@ let prova env new' active =
          (Printf.sprintf "symmetric:\n%s\n"
             (String.concat "\n"
                (List.map
-                  (fun e -> string_of_equality ~env e)
+                  (fun e -> Equality.string_of_equality ~env e)
                    given)))) in
     close env new' given
 ;;
@@ -794,7 +799,7 @@ let simplify_equalities env equalities =
     (lazy 
        (Printf.sprintf "equalities:\n%s\n"
           (String.concat "\n"
-             (List.map string_of_equality equalities))));
+             (List.map Equality.string_of_equality equalities))));
   debug_print (lazy "SIMPLYFYING EQUALITIES...");
   match equalities with
     | [] -> []
@@ -806,7 +811,7 @@ let simplify_equalities env equalities =
             (lazy
                (Printf.sprintf "equalities AFTER:\n%s\n"
                   (String.concat "\n"
-                     (List.map string_of_equality res))));
+                     (List.map Equality.string_of_equality res))));
           res
 ;;
 
@@ -822,28 +827,42 @@ let print_goals goals =
            Printf.sprintf "%d: %s" d (String.concat "; " gl')) goals))
 ;;
 
-let check_if_goal_is_subsumed env (proof,menv,ty) table =
+let check_if_goal_is_subsumed env ((cicproof,proof),menv,ty) table =
   match ty with
   | Cic.Appl[Cic.MutInd(uri,_,_);eq_ty;left;right] 
     when UriManager.eq uri (LibraryObjects.eq_URI ()) ->
-      (let goal_equation = 0,proof,(eq_ty,left,right,Eq),menv in
-      match Indexing.subsumption env table goal_equation with
-      | Some (subst, (_,p,_,m)) ->
-          let p = Inference.apply_subst subst (Inference.build_proof_term p) in
-          let newp =
-            let rec repl = function
-              | Inference.ProofGoalBlock (_, gp) ->
-                  Inference.ProofGoalBlock (Inference.BasicProof ([],p), gp)
-              | Inference.NoProof -> Inference.BasicProof ([],p)
-              | Inference.BasicProof _ -> Inference.BasicProof ([],p)
-              | Inference.SubProof (t, i, p2) ->
-                  Inference.SubProof (t, i, repl p2)
-              | _ -> assert false
-            in
-            repl proof
-          in
-          Some (newp,Inference.apply_subst_metasenv subst m @ menv)
-      | None -> None)
+      (let goal_equation = 
+         Equality.mk_equality
+           (0,(Equality.Exact (Cic.Rel (-1)),proof),(eq_ty,left,right,Eq),menv) 
+       in
+         match Indexing.subsumption env table goal_equation with
+           | Some (subst, equality ) ->
+               let (_,(np,p),(ty,l,r,_),m,id) = 
+                 Equality.open_equality equality in
+               let p = Equality.apply_subst subst 
+                 (Equality.build_proof_term_old p) in
+               let newp =
+                 let rec repl = function
+                   | Equality.ProofGoalBlock (_, gp) ->
+                       Equality.ProofGoalBlock 
+                         (Equality.BasicProof (Equality.empty_subst,p), gp)
+                   | Equality.NoProof -> 
+                       Equality.BasicProof (Equality.empty_subst,p)
+                   | Equality.BasicProof _ -> 
+                       Equality.BasicProof (Equality.empty_subst,p)
+                   | Equality.SubProof (t, i, p2) ->
+                       Equality.SubProof (t, i, repl p2)
+                   | _ -> assert false
+                 in
+                   repl proof
+               in
+               let newcicp,np,subst,cicmenv = 
+                 cicproof,np, subst, Equality.apply_subst_metasenv subst (m @ menv) 
+               in
+                 Some 
+                  ((newcicp,np,subst,cicmenv),
+                   (newp, Equality.apply_subst_metasenv subst m @ menv ))
+           | None -> None)
   | _ -> None
 ;;
 
@@ -883,22 +902,31 @@ let rec given_clause_fullred dbd env goals theorems ~passive active =
             in
             let newp =
               let rec repl = function
-                | Inference.ProofGoalBlock (_, gp) ->
-                    Inference.ProofGoalBlock (Inference.BasicProof ([],p), gp)
-                | Inference.NoProof -> Inference.BasicProof ([],p)
-                | Inference.BasicProof _ -> Inference.BasicProof ([],p)
-                | Inference.SubProof (t, i, p2) ->
-                    Inference.SubProof (t, i, repl p2)
+                | Equality.ProofGoalBlock (_, gp) ->
+                    Equality.ProofGoalBlock 
+                      (Equality.BasicProof (Equality.empty_subst,p), gp)
+                | Equality.NoProof -> 
+
+                    Equality.BasicProof (Equality.empty_subst,p)
+                | Equality.BasicProof _ -> 
+                    Equality.BasicProof (Equality.empty_subst,p)
+                | Equality.SubProof (t, i, p2) ->
+                    Equality.SubProof (t, i, repl p2)
                 | _ -> assert false
               in
-              repl proof
-            in true, Some (newp,m)
+              repl (snd proof)
+            in 
+                 let reflproof = Equality.refl_proof eq_ty left in
+            true, 
+              Some ((fst proof,Equality.Exact reflproof,
+                     Equality.empty_subst,m),
+                    (newp,m))
         | (_, [proof,m,ty])::_ ->
             (match check_if_goal_is_subsumed env (proof,m,ty) (snd active) with
             | None -> false,None
-            | Some (newproof,m) ->
+            | Some p ->
                 prerr_endline "Proof found by subsumption!";
-                true, Some (newproof,m))
+                true, Some p)
         | _ -> false, None
     in 
     if ok then
@@ -940,7 +968,6 @@ let rec given_clause_fullred dbd env goals theorems ~passive active =
 and given_clause_fullred_aux dbd env goals theorems passive active =
   prerr_endline (string_of_int !counter ^ 
                  " MAXMETA: " ^ string_of_int !maxmeta ^ 
-                 " LOCALMAX: " ^ string_of_int !Indexing.local_max ^
                  " #ACTIVES: " ^ string_of_int (size_of_active active) ^
                  " #PASSIVES: " ^ string_of_int (size_of_passive passive));
   incr counter;
@@ -1008,7 +1035,7 @@ and given_clause_fullred_aux dbd env goals theorems passive active =
   | false ->
       let current, passive = select env (fst goals) passive in
       prerr_endline 
-        ("Selected = " ^ string_of_equality ~env current);
+        ("Selected = " ^ Equality.string_of_equality ~env current);
 (* ^ 
            (let w,p,(t,l,r,o),m = current in
            " size w: " ^ string_of_int (HExtlib.estimate_size w)^
@@ -1029,8 +1056,8 @@ and given_clause_fullred_aux dbd env goals theorems passive active =
           (* weight_age_counter := !weight_age_counter + 1; *)
           given_clause_fullred dbd env goals theorems passive active
       | Some current ->
-          debug_print (lazy (Printf.sprintf "selected: %s"
-                               (string_of_equality ~env current)));
+          prerr_endline (Printf.sprintf "selected sipl: %s"
+                               (Equality.string_of_equality ~env current));
           let t1 = Unix.gettimeofday () in
           let new' = infer env current active in
           let _ =
@@ -1040,12 +1067,12 @@ and given_clause_fullred_aux dbd env goals theorems passive active =
                     (String.concat "\n"
                        (List.map
                           (fun e -> "Positive " ^
-                             (string_of_equality ~env e)) new'))))
+                             (Equality.string_of_equality ~env e)) new'))))
           in
           let t2 = Unix.gettimeofday () in
             infer_time := !infer_time +. (t2 -. t1);
             let active =
-              if is_identity env current then active
+              if Equality.is_identity env current then active
               else
                 let al, tbl = active in
                   al @ [current], Indexing.index tbl current
@@ -1065,14 +1092,13 @@ and given_clause_fullred_aux dbd env goals theorems passive active =
               | None, None -> active, passive, new'
               | Some p, None
               | None, Some p ->
-                  let np = new' in
-                    if Utils.debug_metas then
-                      begin
-                        List.iter 
-                          (fun x->Indexing.check_target context x "simplify1")
-                          p;
-                      end;
-                    simplify (new' @ p) active passive
+                  if Utils.debug_metas then
+                    begin
+                      List.iter 
+                        (fun x->Indexing.check_target context x "simplify1")
+                        p;
+                    end;
+                  simplify (new' @ p) active passive
               | Some p, Some rp ->
                   simplify (new' @ p @ rp) active passive
             in
@@ -1105,7 +1131,7 @@ end prova *)
                    (Printf.sprintf "active:\n%s\n"
                       (String.concat "\n"
                          ((List.map
-                             (fun e -> (string_of_equality ~env e))
+                             (fun e -> (Equality.string_of_equality ~env e))
                              (fst active))))))
             in
             let _ =
@@ -1115,7 +1141,7 @@ end prova *)
                       (String.concat "\n"
                          ((List.map
                              (fun e -> "Negative " ^
-                                (string_of_equality ~env e)) new')))))
+                                (Equality.string_of_equality ~env e)) new')))))
             in
             let passive = add_to_passive passive new' in
               given_clause_fullred dbd env goals theorems passive active
@@ -1142,10 +1168,10 @@ let rec saturate_equations env goal accept_fun passive active =
         saturate_equations env goal accept_fun passive active
     | Some current ->
         debug_print (lazy (Printf.sprintf "selected: %s"
-                             (string_of_equality ~env current)));
+                             (Equality.string_of_equality ~env current)));
         let new' = infer env current active in
         let active =
-          if is_identity env current then active
+          if Equality.is_identity env current then active
           else
             let al, tbl = active in
             al @ [current], Indexing.index tbl current
@@ -1167,24 +1193,25 @@ let rec saturate_equations env goal accept_fun passive active =
                (Printf.sprintf "active:\n%s\n"
                   (String.concat "\n"
                      (List.map
-                         (fun e -> string_of_equality ~env e)
+                         (fun e -> Equality.string_of_equality ~env e)
                          (fst active)))))
         in
-       let _ =
+        let _ =
           debug_print
             (lazy
                (Printf.sprintf "new':\n%s\n"
                   (String.concat "\n"
                      (List.map
                          (fun e -> "Negative " ^
-                            (string_of_equality ~env e)) new'))))
+                            (Equality.string_of_equality ~env e)) new'))))
         in
         let new' = List.filter accept_fun new' in
         let passive = add_to_passive passive new' in
         saturate_equations env goal accept_fun passive active
 ;;
   
-
+let main dbd full term metasenv ugraph = ()
+(*
 let main dbd full term metasenv ugraph =
   let module C = Cic in
   let module T = CicTypeChecker in
@@ -1246,7 +1273,9 @@ let main dbd full term metasenv ugraph =
                   (fst theorems)))))
   in
   (*try*)
-    let goal = Inference.BasicProof ([],new_meta_goal), [], goal in
+    let goal = 
+      ([],Equality.BasicProof (Equality.empty_subst ,new_meta_goal)), [], goal 
+    in
     let equalities = simplify_equalities env 
       (equalities@library_equalities) in 
     let active = make_active () in
@@ -1258,7 +1287,7 @@ let main dbd full term metasenv ugraph =
     Printf.printf "\nequalities:\n%s\n"
       (String.concat "\n"
          (List.map
-            (string_of_equality ~env) equalities));
+            (Equality.string_of_equality ~env) equalities));
 (*             (equalities @ library_equalities))); *)
       print_endline "--------------------------------------------------";
       let start = Unix.gettimeofday () in
@@ -1274,17 +1303,27 @@ let main dbd full term metasenv ugraph =
         match res with
         | ParamodulationFailure ->
             Printf.printf "NO proof found! :-(\n\n"
-        | ParamodulationSuccess (Some (proof, env)) ->
-            let proof = Inference.build_proof_term proof in
+        | ParamodulationSuccess (Some ((cicproof,cicmenv),(proof, env))) ->
             Printf.printf "OK, found a proof!\n";
+            let oldproof = Equation.build_proof_term proof in
+            let newproof,_,newenv,_ = 
+                CicRefine.type_of_aux' 
+                  cicmenv context cicproof CicUniv.empty_ugraph
+            in
             (* REMEMBER: we have to instantiate meta_proof, we should use
                apply  the "apply" tactic to proof and status 
             *)
             let names = names_of_context context in
+            prerr_endline "OLD PROOF";
             print_endline (PP.pp proof names);
+            prerr_endline "NEW PROOF";
+            print_endline (PP.pp newproof names);
             let newmetasenv =
               List.fold_left
-                (fun m (_, _, _, menv) -> m @ menv) metasenv equalities
+                (fun m eq -> 
+                  let (_, _, _, menv,_) = Equality.open_equality eq in 
+                  m @ menv) 
+              metasenv equalities
             in
             let _ =
               (*try*)
@@ -1316,8 +1355,6 @@ let main dbd full term metasenv ugraph =
                        "backward_simpl_time: %.9f\n")
               !infer_time !forward_simpl_time !forward_simpl_new_time
               !backward_simpl_time) ^
-              (Printf.sprintf "beta_expand_time: %.9f\n"
-                 !Indexing.beta_expand_time) ^
               (Printf.sprintf "passive_maintainance_time: %.9f\n"
                  !passive_maintainance_time) ^
               (Printf.sprintf "    successful unification/matching time: %.9f\n"
@@ -1337,14 +1374,13 @@ let main dbd full term metasenv ugraph =
     raise exc
 *)
 ;;
-
+*)
 
 let default_depth = !maxdepth
 and default_width = !maxwidth;;
 
 let reset_refs () =
   maxmeta := 0;
-  Indexing.local_max := 100;
   symbols_counter := 0;
   weight_age_counter := !weight_age_ratio;
   processed_clauses := 0;
@@ -1358,8 +1394,7 @@ let reset_refs () =
   passive_maintainance_time := 0.;
   derived_clauses := 0;
   kept_clauses := 0;
-  Indexing.beta_expand_time := 0.;
-  Inference.metas_of_proof_time := 0.;
+  Equality.reset ();
 ;;
 
 let saturate 
@@ -1375,7 +1410,6 @@ let saturate
   let goal' = goal in
   let uri, metasenv, meta_proof, term_to_prove = proof in
   let _, context, goal = CicUtil.lookup_meta goal' metasenv in
-  prerr_endline ("CTX: " ^ string_of_int (HExtlib.estimate_size context));
   let eq_indexes, equalities, maxm = find_equalities context proof in
   let new_meta_goal, metasenv, type_of_goal =
     let irl =
@@ -1389,7 +1423,9 @@ let saturate
   in
   let ugraph = CicUniv.empty_ugraph in
   let env = (metasenv, context, ugraph) in 
-  let goal = Inference.BasicProof ([],new_meta_goal), [], goal in
+  let goal = 
+    ([],Equality.BasicProof (Equality.empty_subst,new_meta_goal)), [], goal 
+  in
   let res, time =
     let t1 = Unix.gettimeofday () in
     let lib_eq_uris, library_equalities, maxm =
@@ -1445,20 +1481,35 @@ let saturate
     (res, finish -. start)
   in
   match res with
-  | ParamodulationSuccess (Some (proof, proof_menv)) ->
+  | ParamodulationSuccess 
+      (Some 
+        ((goalproof,newproof,subsumption_subst, newproof_menv), (* NEW *)
+         (proof, proof_menv))) (* OLD *)
+      ->
       prerr_endline "OK, found a proof!";
-      debug_print (lazy "OK, found a proof!");
-      let proof = Inference.build_proof_term proof in
+      
+      (* generation of the old proof *)
+      let cic_proof = Equality.build_proof_term_old proof in
+     
+      (* generation of the new proof *)
+      let cic_proof_new = 
+        Equality.build_goal_proof 
+          goalproof (Equality.build_proof_term_new newproof) 
+      in
+      let cic_proof_new = 
+        Equality.apply_subst subsumption_subst cic_proof_new 
+      in
+      
+      (* replacing fake mets with real ones *)
       let equality_for_replace i t1 =
         match t1 with
         | C.Meta (n, _) -> n = i
         | _ -> false
       in
-      prerr_endline "replacing metas";
+      let mkirl = CicMkImplicit.identity_relocation_list_for_metavariable in
+      prerr_endline "replacing metas (old)";
       let proof_menv, what, with_what = 
-        let irl = 
-          CicMkImplicit.identity_relocation_list_for_metavariable context
-        in
+        let irl = mkirl context in
         List.fold_left 
           (fun (acc1,acc2,acc3) (i,_,ty) -> 
             (i,context,ty)::acc1, 
@@ -1466,13 +1517,39 @@ let saturate
             (Cic.Meta(i,irl)) ::acc3) 
           ([],[],[]) proof_menv 
       in
-      let proof = ProofEngineReduction.replace_lifting
+      let cic_proof = ProofEngineReduction.replace_lifting
               ~equality:(=)
               ~what ~with_what
-              ~where:proof
+              ~where:cic_proof
       in
-      (* prerr_endline (CicPp.ppterm proof); *)
+      prerr_endline "replacing metas (new)";
+      let newproof_menv, what, with_what = 
+        let irl = mkirl context in
+        List.fold_left 
+          (fun (acc1,acc2,acc3) (i,_,ty) -> 
+            (i,context,ty)::acc1, 
+            (Cic.Meta(i,[]))::acc2, 
+            (Cic.Meta(i,irl)) ::acc3) 
+          ([],[],[]) newproof_menv 
+      in
+      let cic_proof_new = ProofEngineReduction.replace_lifting
+              ~equality:(=)
+              ~what ~with_what
+              ~where:cic_proof_new
+      in
+
+      (* pp new/old proof *)
       let names = names_of_context context in
+      prerr_endline "OLDPROOF";
+      prerr_endline (Equality.string_of_proof_old proof);
+      prerr_endline "OLDPROOFCIC";
+      prerr_endline (CicPp.pp cic_proof names); 
+      prerr_endline "NEWPROOF";
+      prerr_endline (Equality.string_of_proof_new ~names newproof goalproof); 
+      prerr_endline "NEWPROOFCIC";
+      prerr_endline (CicPp.pp cic_proof_new names); 
+
+      (* generation of proof metasenv *)
       let newmetasenv =
         let i1 =
           match new_meta_goal with
@@ -1481,67 +1558,108 @@ let saturate
         List.filter (fun (i, _, _) -> i <> i1 && i <> goal') metasenv
       in
       let newmetasenv = newmetasenv@proof_menv in
+      let newmetasenv_new = newmetasenv@newproof_menv in
+
+      (* check/refine/... build the new proof *)
       let newstatus =
-        try
-          let ty, ug =
-            prerr_endline "type checking ... ";
-            CicTypeChecker.type_of_aux' newmetasenv context proof ugraph
+        let cic_proof,newmetasenv,proof_menv,ty, ug =
+          prerr_endline "type checking ... (old) ";
+          let _old_ty, _oldug = 
+            try 
+              CicTypeChecker.type_of_aux' newmetasenv context cic_proof ugraph
+            with 
+              CicTypeChecker.TypeCheckerFailure s ->
+                prerr_endline "THE *OLD* PROOF DOESN'T TYPECHECK!!!";
+                prerr_endline (Lazy.force s);
+                Cic.Implicit None, CicUniv.empty_ugraph
           in
-          prerr_endline (CicPp.pp proof [](* names *));
-          debug_print
-            (lazy
-               (Printf.sprintf
-                  "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n"
-                  (CicPp.pp type_of_goal names) (CicPp.pp ty names)
-                  (string_of_bool
-                     (fst (CicReduction.are_convertible
-                             context type_of_goal ty ug)))));
-          let real_proof =
-            ProofEngineReduction.replace
-              ~equality:equality_for_replace
-              ~what:[goal'] ~with_what:[proof]
-              ~where:meta_proof
+          let cic_proof_new,new_ty,newmetasenv_new,newug = 
+            try
+              (*
+               prerr_endline "refining ... (new) ";
+               CicRefine.type_of_aux' 
+                newmetasenv_new context cic_proof_new ugraph
+              *)
+              let ty,ug = 
+                prerr_endline "typechecking ... (new) ";
+                CicTypeChecker.type_of_aux' 
+                  newmetasenv_new context cic_proof_new ugraph
+              in
+              cic_proof_new, ty, newmetasenv_new, ug
+            with
+            | CicTypeChecker.TypeCheckerFailure s ->
+                prerr_endline "THE PROOF DOESN'T TYPECHECK!!!";
+                prerr_endline (Lazy.force s);
+                assert false
+            | CicRefine.RefineFailure s 
+            | CicRefine.Uncertain s 
+            | CicRefine.AssertFailure s -> 
+                prerr_endline "FAILURE IN REFINE";
+                prerr_endline (Lazy.force s);
+                assert false
           in
-          debug_print
-            (lazy
-               (Printf.sprintf "status:\n%s\n%s\n%s\n%s\n"
-                  (match uri with Some uri -> UriManager.string_of_uri uri
-                   | None -> "")
-                  (print_metasenv newmetasenv)
-                  (CicPp.pp real_proof [](* names *))
-                  (CicPp.pp term_to_prove names)));
-          ((uri, newmetasenv, real_proof, term_to_prove), 
-            List.map (fun (i,_,_) -> i) proof_menv)
-        with CicTypeChecker.TypeCheckerFailure _ ->
-          debug_print (lazy "THE PROOF DOESN'T TYPECHECK!!!");
-          debug_print (lazy (CicPp.pp proof names));
-          raise (ProofEngineTypes.Fail
-                  (lazy "Found a proof, but it doesn't typecheck"))
+          if List.length newmetasenv_new <> 0 then
+            prerr_endline 
+              ("Some METAS are still open: " ^ CicMetaSubst.ppmetasenv
+               [] newmetasenv_new);
+          cic_proof_new, newmetasenv_new, newmetasenv_new,new_ty, newug
+          (* THE OLD PROOF: cic_proof,newmetasenv,proof_menv,oldty,oldug *)
+        in
+        prerr_endline "FINAL PROOF";
+        prerr_endline (CicPp.pp cic_proof names);
+        prerr_endline "ENDOFPROOFS";
+        (*  
+        debug_print
+          (lazy
+             (Printf.sprintf
+                "\nGOAL was: %s\nPROOF has type: %s\nconvertible?: %s\n"
+                (CicPp.pp type_of_goal names) (CicPp.pp ty names)
+                (string_of_bool
+                   (fst (CicReduction.are_convertible
+                           context type_of_goal ty ug)))));
+        *)
+        let real_proof =
+          ProofEngineReduction.replace
+            ~equality:equality_for_replace
+            ~what:[goal'] ~with_what:[cic_proof]
+            ~where:meta_proof
+        in
+        (*
+        debug_print
+          (lazy
+             (Printf.sprintf "status:\n%s\n%s\n%s\n%s\n"
+                (match uri with Some uri -> UriManager.string_of_uri uri
+                 | None -> "")
+                (print_metasenv newmetasenv)
+                (CicPp.pp real_proof [](* names *))
+                (CicPp.pp term_to_prove names)));
+        *)
+        let open_goals = List.map (fun (i,_,_) -> i) proof_menv in
+        (uri, newmetasenv, real_proof, term_to_prove), open_goals
       in
-      let tall = fs_time_info.build_all in
-      let tdemodulate = fs_time_info.demodulate in
-      let tsubsumption = fs_time_info.subsumption in
       if Utils.time then
         begin
+          let tall = fs_time_info.build_all in
+          let tdemodulate = fs_time_info.demodulate in
+          let tsubsumption = fs_time_info.subsumption in
           prerr_endline (
             (Printf.sprintf "\nTIME NEEDED: %.9f" time) ^
               (Printf.sprintf "\ntall: %.9f" tall) ^
               (Printf.sprintf "\ntdemod: %.9f" tdemodulate) ^
               (Printf.sprintf "\ntsubsumption: %.9f" tsubsumption) ^
               (Printf.sprintf "\ninfer_time: %.9f" !infer_time) ^
-              (Printf.sprintf "\nbeta_expand_time: %.9f\n"
-                 !Indexing.beta_expand_time) ^
-              (Printf.sprintf "\nmetas_of_proof: %.9f\n"
-                 !Inference.metas_of_proof_time) ^
-              (Printf.sprintf "\nforward_simpl_times: %.9f" !forward_simpl_time) ^
+              (Printf.sprintf "\nforward_simpl_times: %.9f" 
+                !forward_simpl_time) ^
               (Printf.sprintf "\nforward_simpl_new_times: %.9f" 
-                 !forward_simpl_new_time) ^
-              (Printf.sprintf "\nbackward_simpl_times: %.9f" !backward_simpl_time) ^
+                !forward_simpl_new_time) ^
+              (Printf.sprintf "\nbackward_simpl_times: %.9f" 
+                !backward_simpl_time) ^
               (Printf.sprintf "\npassive_maintainance_time: %.9f" 
                  !passive_maintainance_time))
         end;
-      newstatus          
-  | _ ->
+      newstatus 
+  | ParamodulationSuccess None -> assert false
+  | ParamodulationFailure ->
       raise (ProofEngineTypes.Fail (lazy "NO proof found"))
 ;;
 
@@ -1629,7 +1747,7 @@ let retrieve_and_print dbd term metasenv ugraph =
                           (fun (u, e) ->
                              Printf.sprintf "%s: %s"
                                (UriManager.string_of_uri u)
-                               (string_of_equality e)
+                               (Equality.string_of_equality e)
                           )
                           res))));
             res in
@@ -1669,7 +1787,9 @@ let main_demod_equalities dbd term metasenv ugraph =
   in
   let env = (metasenv, context, ugraph) in
   (*try*)
-    let goal = Inference.BasicProof ([],new_meta_goal), [], goal in
+    let goal = 
+      ([],Equality.BasicProof (Equality.empty_subst,new_meta_goal)), [], goal 
+    in
     let equalities = simplify_equalities env (equalities@library_equalities) in
     let active = make_active () in
     let passive = make_passive equalities in
@@ -1678,7 +1798,7 @@ let main_demod_equalities dbd term metasenv ugraph =
     Printf.printf "\nequalities:\n%s\n"
       (String.concat "\n"
          (List.map
-            (string_of_equality ~env) equalities));
+            (Equality.string_of_equality ~env) equalities));
     print_endline "--------------------------------------------------";
     print_endline "GO!";
     start_time := Unix.gettimeofday ();
@@ -1705,12 +1825,12 @@ let main_demod_equalities dbd term metasenv ugraph =
       EqualitySet.elements (List.fold_left addfun EqualitySet.empty l)
     in
     Printf.printf "\n\nRESULTS:\nActive:\n%s\n\nPassive:\n%s\n"
-       (String.concat "\n" (List.map (string_of_equality ~env) active)) 
+       (String.concat "\n" (List.map (Equality.string_of_equality ~env) active)) 
      (*  (String.concat "\n"
          (List.map (fun e -> CicPp.ppterm (term_of_equality e)) active)) *)
 (*       (String.concat "\n" (List.map (string_of_equality ~env) passive)); *)
       (String.concat "\n"
-         (List.map (fun e -> CicPp.ppterm (term_of_equality e)) passive));
+         (List.map (fun e -> CicPp.ppterm (Equality.term_of_equality e)) passive));
     print_newline ();
 (*
   with e ->
@@ -1729,7 +1849,9 @@ let demodulate_tac ~dbd ~pattern ((proof,goal) as initialstatus) =
   let irl = CicMkImplicit.identity_relocation_list_for_metavariable context in
   let library_equalities = List.map snd library_equalities in
   let goalterm = Cic.Meta (metano,irl) in
-  let initgoal = Inference.BasicProof ([],goalterm), [], ty in
+  let initgoal = 
+    ([],Equality.BasicProof (Equality.empty_subst,goalterm)), [], ty 
+  in
   let env = (metasenv, context, CicUniv.empty_ugraph) in
   let equalities = simplify_equalities env (equalities@library_equalities) in   
   let table = 
@@ -1737,14 +1859,15 @@ let demodulate_tac ~dbd ~pattern ((proof,goal) as initialstatus) =
       (fun tbl eq -> Indexing.index tbl eq) 
       Indexing.empty equalities 
   in
-  let newmeta,(newproof,newmetasenv, newty) = Indexing.demodulation_goal 
-    maxm (metasenv,context,CicUniv.empty_ugraph) table initgoal 
+  let _, newmeta,(newproof,newmetasenv, newty) = 
+    Indexing.demodulation_goal 
+      maxm (metasenv,context,CicUniv.empty_ugraph) table initgoal 
   in
   if newmeta != maxm then
     begin
       let opengoal = Cic.Meta(maxm,irl) in
       let proofterm = 
-        Inference.build_proof_term ~noproof:opengoal newproof in
+        Equality.build_proof_term_old ~noproof:opengoal (snd newproof) in
         let extended_metasenv = (maxm,context,newty)::metasenv in
         let extended_status = 
           (curi,extended_metasenv,pbo,pty),goal in