X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Fparamodulation%2Findexing.ml;h=cf6a76cdca29835f60dd5a9691b98cfb62c5865f;hb=33a02e0b639217093eb63f30169aaa6ac8c78907;hp=5a8960101d21c2a513b4acc18223817c1aad27c7;hpb=bbe7741f3bbaacb93f2876c018dace82f5e929b8;p=helm.git

diff --git a/helm/ocaml/paramodulation/indexing.ml b/helm/ocaml/paramodulation/indexing.ml
index 5a8960101..cf6a76cdc 100644
--- a/helm/ocaml/paramodulation/indexing.ml
+++ b/helm/ocaml/paramodulation/indexing.ml
@@ -1,4 +1,7 @@
 
+let debug_print = Utils.debug_print;;
+
+
 type retrieval_mode = Matching | Unification;;
 
 
@@ -70,6 +73,31 @@ let apply_subst =
 
 
 (*
+(* NO INDEXING *)
+let empty_table () = []
+
+let index table equality =
+  let _, _, (_, l, r, ordering), _, _ = equality in
+  match ordering with
+  | Utils.Gt -> (Utils.Left, equality)::table
+  | Utils.Lt -> (Utils.Right, equality)::table
+  | _ -> (Utils.Left, equality)::(Utils.Right, equality)::table
+;;
+
+let remove_index table equality =
+  List.filter (fun (p, e) -> e != equality) table
+;;
+
+let in_index table equality =
+  List.exists (fun (p, e) -> e == equality) table
+;;
+
+let get_candidates mode table term = table
+*)
+
+
+(*
+(* PATH INDEXING *)
 let empty_table () =
   Path_indexing.PSTrie.empty
 ;;
@@ -97,6 +125,7 @@ let get_candidates mode trie term =
 *)
 
 
+(* DISCRIMINATION TREES *)
 let empty_table () =
   Discrimination_tree.DiscriminationTree.empty
 ;;
@@ -116,6 +145,8 @@ let get_candidates mode tree term =
     Discrimination_tree.PosEqSet.elements s
   in
 (*   print_candidates mode term res; *)
+(*   print_endline (Discrimination_tree.string_of_discrimination_tree tree); *)
+(*   print_newline (); *)
   let t2 = Unix.gettimeofday () in
   indexing_retrieval_time := !indexing_retrieval_time +. (t2 -. t1);
   res
@@ -132,123 +163,157 @@ let match_unif_time_ok = ref 0.;;
 let match_unif_time_no = ref 0.;;
 
 
-let rec find_matches metasenv context ugraph lift_amount term =
+let rec find_matches metasenv context ugraph lift_amount term termty =
   let module C = Cic in
   let module U = Utils in
   let module S = CicSubstitution in
   let module M = CicMetaSubst in
   let module HL = HelmLibraryObjects in
   let cmp = !Utils.compare_terms in
-  let names = Utils.names_of_context context in
+(*   let names = Utils.names_of_context context in *)
+(*   let termty, ugraph = *)
+(*     CicTypeChecker.type_of_aux' metasenv context term ugraph *)
+(*   in *)
   function
     | [] -> None
     | candidate::tl ->
-        let pos, (proof, (ty, left, right, o), metas, args) = candidate in
-        let do_match c other eq_URI =
-          let subst', metasenv', ugraph' =
-            let t1 = Unix.gettimeofday () in
-            try
-              let r = 
-                Inference.matching (metasenv @ metas) context
-                  term (S.lift lift_amount c) ugraph in
-              let t2 = Unix.gettimeofday () in
-              match_unif_time_ok := !match_unif_time_ok +. (t2 -. t1);
-              r
-            with e ->
-              let t2 = Unix.gettimeofday () in
-              match_unif_time_no := !match_unif_time_no +. (t2 -. t1);
-              raise e
-          in
+        let pos, (_, proof, (ty, left, right, o), metas, args) = candidate in
+(*         if not (fst (CicReduction.are_convertible *)
+(*                        ~metasenv context termty ty ugraph)) then ( *)
+(* (\*           debug_print ( *\) *)
+(* (\*             Printf.sprintf "CANDIDATE HAS WRONG TYPE: %s required, %s found" *\) *)
+(* (\*               (CicPp.pp termty names) (CicPp.pp ty names)); *\) *)
+(*           find_matches metasenv context ugraph lift_amount term termty tl *)
+(*         ) else *)
+          let do_match c other eq_URI =
+            let subst', metasenv', ugraph' =
+              let t1 = Unix.gettimeofday () in
+              try
+                let r =
+                  Inference.matching (metasenv @ metas) context
+                    term (S.lift lift_amount c) ugraph in
+                let t2 = Unix.gettimeofday () in
+                match_unif_time_ok := !match_unif_time_ok +. (t2 -. t1);
+                r
+              with Inference.MatchingFailure as e ->
+                let t2 = Unix.gettimeofday () in
+                match_unif_time_no := !match_unif_time_no +. (t2 -. t1);
+                raise e
+            in
             Some (C.Rel (1 + lift_amount), subst', metasenv', ugraph',
                   (candidate, eq_URI))
-        in
-        let c, other, eq_URI =
-          if pos = Utils.Left then left, right, HL.Logic.eq_ind_URI
-          else right, left, HL.Logic.eq_ind_r_URI
-        in
-        if o <> U.Incomparable then
-          try
-            do_match c other eq_URI
-          with e ->
-            find_matches metasenv context ugraph lift_amount term tl
-        else
-          let res = try do_match c other eq_URI with e -> None in
-          match res with
-          | Some (_, s, _, _, _) ->
-              let c' = (* M. *)apply_subst s c
-              and other' = (* M. *)apply_subst s other in
-              let order = cmp c' other' in
-              let names = U.names_of_context context in
-              if order = U.Gt then
-                res
-              else
-                find_matches metasenv context ugraph lift_amount term tl
-          | None ->
-              find_matches metasenv context ugraph lift_amount term tl
+          in
+          let c, other, eq_URI =
+            if pos = Utils.Left then left, right, HL.Logic.eq_ind_URI
+            else right, left, HL.Logic.eq_ind_r_URI
+          in
+          if o <> U.Incomparable then
+            try
+              do_match c other eq_URI
+            with Inference.MatchingFailure ->
+              find_matches metasenv context ugraph lift_amount term termty tl
+          else
+            let res =
+              try do_match c other eq_URI
+              with Inference.MatchingFailure -> None
+            in
+            match res with
+            | Some (_, s, _, _, _) ->
+                let c' = (* M. *)apply_subst s c
+                and other' = (* M. *)apply_subst s other in
+                let order = cmp c' other' in
+                let names = U.names_of_context context in
+                if order = U.Gt then
+                  res
+                else
+                  find_matches
+                    metasenv context ugraph lift_amount term termty tl
+            | None ->
+                find_matches metasenv context ugraph lift_amount term termty tl
 ;;
 
 
 let rec find_all_matches ?(unif_fun=Inference.unification)
-    metasenv context ugraph lift_amount term =
+    metasenv context ugraph lift_amount term termty =
   let module C = Cic in
   let module U = Utils in
   let module S = CicSubstitution in
   let module M = CicMetaSubst in
   let module HL = HelmLibraryObjects in
   let cmp = !Utils.compare_terms in
-  let names = Utils.names_of_context context in
+(*   let names = Utils.names_of_context context in *)
+(*   let termty, ugraph = *)
+(*     CicTypeChecker.type_of_aux' metasenv context term ugraph *)
+(*   in *)
   function
     | [] -> []
     | candidate::tl ->
-        let pos, (proof, (ty, left, right, o), metas, args) = candidate in
-        let do_match c other eq_URI =
-          let subst', metasenv', ugraph' =
-            let t1 = Unix.gettimeofday () in
-            try
-              let r = 
-                unif_fun (metasenv @ metas) context
-                  term (S.lift lift_amount c) ugraph in
-              let t2 = Unix.gettimeofday () in
-              match_unif_time_ok := !match_unif_time_ok +. (t2 -. t1);
-              r
-            with e ->
-              let t2 = Unix.gettimeofday () in
-              match_unif_time_no := !match_unif_time_no +. (t2 -. t1);
-              raise e
+        let pos, (_, _, (ty, left, right, o), metas, args) = candidate in
+(*         if not (fst (CicReduction.are_convertible *)
+(*                        ~metasenv context termty ty ugraph)) then ( *)
+(* (\*           debug_print ( *\) *)
+(* (\*             Printf.sprintf "CANDIDATE HAS WRONG TYPE: %s required, %s found" *\) *)
+(* (\*               (CicPp.pp termty names) (CicPp.pp ty names)); *\) *)
+(*           find_all_matches ~unif_fun metasenv context ugraph *)
+(*             lift_amount term termty tl *)
+(*         ) else *)
+          let do_match c other eq_URI =
+            let subst', metasenv', ugraph' =
+              let t1 = Unix.gettimeofday () in
+              try
+                let r = 
+                  unif_fun (metasenv @ metas) context
+                    term (S.lift lift_amount c) ugraph in
+                let t2 = Unix.gettimeofday () in
+                match_unif_time_ok := !match_unif_time_ok +. (t2 -. t1);
+                r
+              with
+              | Inference.MatchingFailure
+              | CicUnification.UnificationFailure _
+              | CicUnification.Uncertain _ as e ->
+                let t2 = Unix.gettimeofday () in
+                match_unif_time_no := !match_unif_time_no +. (t2 -. t1);
+                raise e
+            in
+            (C.Rel (1 + lift_amount), subst', metasenv', ugraph',
+             (candidate, eq_URI))
           in
-          (C.Rel (1 + lift_amount), subst', metasenv', ugraph',
-           (candidate, eq_URI))
-        in
-        let c, other, eq_URI =
-          if pos = Utils.Left then left, right, HL.Logic.eq_ind_URI
-          else right, left, HL.Logic.eq_ind_r_URI
-        in
-        if o <> U.Incomparable then
-          try
-            let res = do_match c other eq_URI in
-            res::(find_all_matches ~unif_fun metasenv context ugraph
-                    lift_amount term tl)
-          with e ->
-            find_all_matches ~unif_fun metasenv context ugraph
-              lift_amount term tl
-        else
-          try
-            let res = do_match c other eq_URI in
-            match res with
-            | _, s, _, _, _ ->
-                let c' = (* M. *)apply_subst s c
-                and other' = (* M. *)apply_subst s other in
-                let order = cmp c' other' in
-                let names = U.names_of_context context in
-                if order <> U.Lt && order <> U.Le then
-                  res::(find_all_matches ~unif_fun metasenv context ugraph
-                          lift_amount term tl)
-                else
-                  find_all_matches ~unif_fun metasenv context ugraph
-                    lift_amount term tl
-          with e ->
-            find_all_matches ~unif_fun metasenv context ugraph
-              lift_amount term tl
+          let c, other, eq_URI =
+            if pos = Utils.Left then left, right, HL.Logic.eq_ind_URI
+            else right, left, HL.Logic.eq_ind_r_URI
+          in
+          if o <> U.Incomparable then
+            try
+              let res = do_match c other eq_URI in
+              res::(find_all_matches ~unif_fun metasenv context ugraph
+                      lift_amount term termty tl)
+            with
+            | Inference.MatchingFailure
+            | CicUnification.UnificationFailure _
+            | CicUnification.Uncertain _ ->
+              find_all_matches ~unif_fun metasenv context ugraph
+                lift_amount term termty tl
+          else
+            try
+              let res = do_match c other eq_URI in
+              match res with
+              | _, s, _, _, _ ->
+                  let c' = (* M. *)apply_subst s c
+                  and other' = (* M. *)apply_subst s other in
+                  let order = cmp c' other' in
+                  let names = U.names_of_context context in
+                  if order <> U.Lt && order <> U.Le then
+                    res::(find_all_matches ~unif_fun metasenv context ugraph
+                            lift_amount term termty tl)
+                  else
+                    find_all_matches ~unif_fun metasenv context ugraph
+                      lift_amount term termty tl
+            with
+            | Inference.MatchingFailure
+            | CicUnification.UnificationFailure _
+            | CicUnification.Uncertain _ ->
+                find_all_matches ~unif_fun metasenv context ugraph
+                  lift_amount term termty tl
 ;;
 
 
@@ -275,9 +340,9 @@ let subsumption env table target =
     | _ ->
         let leftc = get_candidates Matching table left in
         find_all_matches ~unif_fun:Inference.matching
-          metasenv context ugraph 0 left leftc
+          metasenv context ugraph 0 left ty leftc
   in
-  let ok what (_, subst, menv, ug, ((pos, (_, (_, l, r, o), _, _)), _)) =
+  let ok what (_, subst, menv, ug, ((pos, (_, _, (_, l, r, o), _, _)), _)) =
     try
       let other = if pos = Utils.Left then r else l in
       let subst', menv', ug' =
@@ -288,13 +353,13 @@ let subsumption env table target =
           let t2 = Unix.gettimeofday () in
           match_unif_time_ok := !match_unif_time_ok +. (t2 -. t1);
           r
-        with e ->
+        with Inference.MatchingFailure as e ->
           let t2 = Unix.gettimeofday () in
           match_unif_time_no := !match_unif_time_no +. (t2 -. t1);
           raise e
       in
       samesubst subst subst'
-    with e ->
+    with Inference.MatchingFailure ->
       false
   in
   let r = List.exists (ok right) leftr in
@@ -307,7 +372,7 @@ let subsumption env table target =
       | _ ->
           let rightc = get_candidates Matching table right in
           find_all_matches ~unif_fun:Inference.matching
-            metasenv context ugraph 0 right rightc
+            metasenv context ugraph 0 right ty rightc
     in
     List.exists (ok left) rightr
 ;;
@@ -322,8 +387,12 @@ let rec demodulate_term metasenv context ugraph table lift_amount term =
   match term with
   | C.Meta _ -> None
   | term ->
+      let termty, ugraph =
+        C.Implicit None, ugraph
+(*         CicTypeChecker.type_of_aux' metasenv context term ugraph *)
+      in
       let res =
-        find_matches metasenv context ugraph lift_amount term candidates
+        find_matches metasenv context ugraph lift_amount term termty candidates
       in
       if res <> None then
         res
@@ -375,38 +444,101 @@ let rec demodulate_term metasenv context ugraph table lift_amount term =
 ;;
 
 
+let build_ens_for_sym_eq ty x y = 
+  [(UriManager.uri_of_string
+      "cic:/Coq/Init/Logic/Logic_lemmas/equality/A.var", ty);
+   (UriManager.uri_of_string
+      "cic:/Coq/Init/Logic/Logic_lemmas/equality/x.var", x);
+   (UriManager.uri_of_string
+      "cic:/Coq/Init/Logic/Logic_lemmas/equality/y.var", y)]
+;;
+
+
 let build_newtarget_time = ref 0.;;
 
-let rec demodulation newmeta env table target =
+
+let demod_counter = ref 1;;
+
+let rec demodulation newmeta env table sign target =
   let module C = Cic in
   let module S = CicSubstitution in
   let module M = CicMetaSubst in
   let module HL = HelmLibraryObjects in
   let metasenv, context, ugraph = env in
-  let proof, (eq_ty, left, right, order), metas, args = target in
+  let _, proof, (eq_ty, left, right, order), metas, args = target in
   let metasenv' = metasenv @ metas in
+
+  let maxmeta = ref newmeta in
+  
   let build_newtarget is_left (t, subst, menv, ug, (eq_found, eq_URI)) =
     let time1 = Unix.gettimeofday () in
     
-    let pos, (proof', (ty, what, other, _), menv', args') = eq_found in
+    let pos, (_, proof', (ty, what, other, _), menv', args') = eq_found in
     let what, other = if pos = Utils.Left then what, other else other, what in
     let newterm, newproof =
       let bo = (* M. *)apply_subst subst (S.subst other t) in
-      let bo'' =
-        C.Appl ([C.MutInd (HL.Logic.eq_URI, 0, []);
-                 S.lift 1 eq_ty] @
-                 if is_left then [bo; S.lift 1 right] else [S.lift 1 left; bo])
+      let t' =
+        let name = C.Name ("x_Demod_" ^ (string_of_int !demod_counter)) in
+        incr demod_counter;
+        let l, r =
+          if is_left then t, S.lift 1 right else S.lift 1 left, t in
+        (name, ty, S.lift 1 eq_ty, l, r)
       in
-      let t' = C.Lambda (C.Anonymous, ty, bo'') in
-      bo,
-      C.Implicit None
-(*       (\* M. *\)apply_subst subst (C.Appl [C.Const (eq_URI, []); ty; what; t'; *)
-(*                                    proof; other; proof']) *)
+      if sign = Utils.Positive then
+        (bo,
+         Inference.ProofBlock (subst, eq_URI, t', eq_found, proof))
+      else
+        let metaproof = 
+          incr maxmeta;
+          let irl =
+            CicMkImplicit.identity_relocation_list_for_metavariable context in
+          Printf.printf "\nADDING META: %d\n" !maxmeta;
+          print_newline ();
+          C.Meta (!maxmeta, irl)
+        in
+        let target' =
+          let eq_found =
+            let proof' =
+              let ens =
+                if pos = Utils.Left then
+                  build_ens_for_sym_eq ty what other
+                else
+                  build_ens_for_sym_eq ty other what
+              in
+              Inference.ProofSymBlock (ens, proof')
+            in
+            let what, other =
+              if pos = Utils.Left then what, other else other, what
+            in
+            pos, (0, proof', (ty, other, what, Utils.Incomparable),
+                  menv', args')
+          in
+          let target_proof =
+            let pb =
+              Inference.ProofBlock (subst, eq_URI, t', eq_found,
+                                    Inference.BasicProof metaproof)
+            in
+            match proof with
+            | Inference.BasicProof _ ->
+                print_endline "replacing a BasicProof";
+                pb
+            | Inference.ProofGoalBlock (_, parent_eq) ->
+                print_endline "replacing another ProofGoalBlock";
+                Inference.ProofGoalBlock (pb, parent_eq)
+            | _ -> assert false
+          in
+          (0, target_proof, (eq_ty, left, right, order), metas, args)
+        in
+        let refl =
+          C.Appl [C.MutConstruct (* reflexivity *)
+                    (HelmLibraryObjects.Logic.eq_URI, 0, 1, []);
+                  eq_ty; if is_left then right else left]          
+        in
+        (bo,
+         Inference.ProofGoalBlock (Inference.BasicProof refl, target'))
     in
     let left, right = if is_left then newterm, right else left, newterm in
-    let m =
-      (Inference.metas_of_term left) @ (Inference.metas_of_term right)
-    in
+    let m = (Inference.metas_of_term left) @ (Inference.metas_of_term right) in
     let newmetasenv = List.filter (fun (i, _, _) -> List.mem i m) metas
     and newargs =
       List.filter
@@ -417,19 +549,24 @@ let rec demodulation newmeta env table target =
 
     let time2 = Unix.gettimeofday () in
     build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
-    
-    newmeta, (newproof, (eq_ty, left, right, ordering), newmetasenv, newargs)
+
+    let res =
+      let w = Utils.compute_equality_weight eq_ty left right in
+      (w, newproof, (eq_ty, left, right, ordering), newmetasenv, newargs)
+    in
+(*     if sign = Utils.Positive then ( *)
+(*       let newm, res = Inference.fix_metas !maxmeta res in *)
+(*       maxmeta := newm; *)
+(*       !maxmeta, res *)
+(*     ) else *)
+    !maxmeta(* newmeta *), res
   in
-(*   let build_newtarget = *)
-(*     let profile = CicUtil.profile "Indexing.demodulation.build_newtarget" in *)
-(*     (fun a b -> profile (build_newtarget a) b) *)
-(*   in *)
   let res = demodulate_term metasenv' context ugraph table 0 left in
-  let build_identity (p, (t, l, r, o), m, a) =
-    match o with
-    | Utils.Gt -> (p, (t, r, r, Utils.Eq), m, a)
-    | _ -> (p, (t, l, l, Utils.Eq), m, a)
-  in
+(*   let build_identity (w, p, (t, l, r, o), m, a) = *)
+(*     match o with *)
+(*     | Utils.Gt -> (w, p, (t, r, r, Utils.Eq), m, a) *)
+(*     | _ -> (w, p, (t, l, l, Utils.Eq), m, a) *)
+(*   in *)
   match res with
   | Some t ->
       let newmeta, newtarget = build_newtarget true t in
@@ -440,7 +577,7 @@ let rec demodulation newmeta env table target =
 (*         if subsumption env table newtarget then *)
 (*           newmeta, build_identity newtarget *)
 (*         else *)
-          demodulation newmeta env table newtarget
+        demodulation newmeta env table sign newtarget
   | None ->
       let res = demodulate_term metasenv' context ugraph table 0 right in
       match res with
@@ -453,7 +590,7 @@ let rec demodulation newmeta env table target =
 (*             if subsumption env table newtarget then *)
 (*               newmeta, build_identity newtarget *)
 (*             else *)
-              demodulation newmeta env table newtarget
+              demodulation newmeta env table sign newtarget
       | None ->
           newmeta, target
 ;;
@@ -551,45 +688,107 @@ let rec betaexpand_term metasenv context ugraph table lift_amount term =
   match term with
   | C.Meta _ -> res, lifted_term
   | term ->
+      let termty, ugraph =
+        C.Implicit None, ugraph
+(*         CicTypeChecker.type_of_aux' metasenv context term ugraph *)
+      in
       let r = 
-        find_all_matches metasenv context ugraph lift_amount term candidates
+        find_all_matches
+          metasenv context ugraph lift_amount term termty candidates
       in
       r @ res, lifted_term
 ;;
 
 
-let superposition_left (metasenv, context, ugraph) table target =
+let sup_l_counter = ref 1;;
+
+let superposition_left newmeta (metasenv, context, ugraph) table target =
   let module C = Cic in
   let module S = CicSubstitution in
   let module M = CicMetaSubst in
   let module HL = HelmLibraryObjects in
   let module CR = CicReduction in
   let module U = Utils in
-  let proof, (eq_ty, left, right, ordering), _, _ = target in
+  let weight, proof, (eq_ty, left, right, ordering), _, _ = target in
   let expansions, _ =
     let term = if ordering = U.Gt then left else right in
     betaexpand_term metasenv context ugraph table 0 term
   in
+  let maxmeta = ref newmeta in
   let build_new (bo, s, m, ug, (eq_found, eq_URI)) =
+
+    print_endline "\nSUPERPOSITION LEFT\n";
+    
     let time1 = Unix.gettimeofday () in
     
-    let pos, (proof', (ty, what, other, _), menv', args') = eq_found in
+    let pos, (_, proof', (ty, what, other, _), menv', args') = eq_found in
     let what, other = if pos = Utils.Left then what, other else other, what in
     let newgoal, newproof =
       let bo' = (* M. *)apply_subst s (S.subst other bo) in
-      let bo'' =
-        C.Appl (
-          [C.MutInd (HL.Logic.eq_URI, 0, []);
-           S.lift 1 eq_ty] @
-            if ordering = U.Gt then [bo'; S.lift 1 right]
-            else [S.lift 1 left; bo'])
+      let t' =
+        let name = C.Name ("x_SupL_" ^ (string_of_int !sup_l_counter)) in
+        incr sup_l_counter;
+        let l, r =
+          if ordering = U.Gt then bo, S.lift 1 right else S.lift 1 left, bo in
+        (name, ty, S.lift 1 eq_ty, l, r)
       in
-      let t' = C.Lambda (C.Anonymous, ty, bo'') in
-      bo',
-      C.Implicit None
-(*       (\* M. *\)apply_subst s *)
-(*         (C.Appl [C.Const (eq_URI, []); ty; what; t'; *)
-(*                  proof; other; proof']) *)
+(*       let bo'' = *)
+(*         C.Appl ( *)
+(*           [C.MutInd (HL.Logic.eq_URI, 0, []); *)
+(*            S.lift 1 eq_ty] @ *)
+(*             if ordering = U.Gt then [S.lift 1 bo'; S.lift 1 right] *)
+(*             else [S.lift 1 left; S.lift 1 bo']) *)
+(*       in *)
+(*       let t' = *)
+(*         let name = C.Name ("x_SupL_" ^ (string_of_int !sup_l_counter)) in *)
+(*         incr sup_l_counter; *)
+(*         C.Lambda (name, ty, bo'') *)
+(*       in *)
+      incr maxmeta;
+      let metaproof =
+        let irl =
+          CicMkImplicit.identity_relocation_list_for_metavariable context in
+        C.Meta (!maxmeta, irl)
+      in
+      let target' =
+        let eq_found =
+          let proof' =
+            let ens =
+              if pos = Utils.Left then
+                build_ens_for_sym_eq ty what other
+              else
+                build_ens_for_sym_eq ty other what
+            in
+            Inference.ProofSymBlock (ens, proof')
+          in
+          let what, other =
+            if pos = Utils.Left then what, other else other, what
+          in
+          pos, (0, proof', (ty, other, what, Utils.Incomparable), menv', args')
+        in
+        let target_proof =
+          let pb =
+            Inference.ProofBlock (s, eq_URI, t', eq_found,
+                                  Inference.BasicProof metaproof)
+          in
+          match proof with
+          | Inference.BasicProof _ ->
+              print_endline "replacing a BasicProof";
+              pb
+          | Inference.ProofGoalBlock (_, parent_eq) ->
+              print_endline "replacing another ProofGoalBlock";
+              Inference.ProofGoalBlock (pb, parent_eq)
+          | _ -> assert false
+        in
+        (weight, target_proof, (eq_ty, left, right, ordering), [], [])
+      in
+      let refl =
+        C.Appl [C.MutConstruct (* reflexivity *)
+                  (HelmLibraryObjects.Logic.eq_URI, 0, 1, []);
+                eq_ty; if ordering = U.Gt then right else left]
+      in
+      (bo',
+       Inference.ProofGoalBlock (Inference.BasicProof refl, target'))
     in
     let left, right =
       if ordering = U.Gt then newgoal, right else left, newgoal in
@@ -597,17 +796,19 @@ let superposition_left (metasenv, context, ugraph) table target =
 
     let time2 = Unix.gettimeofday () in
     build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
-    
-    (newproof, (eq_ty, left, right, neworder), [], [])
+
+    let res =
+      let w = Utils.compute_equality_weight eq_ty left right in
+      (w, newproof, (eq_ty, left, right, neworder), [], [])
+    in
+    res
   in
-(*   let build_new = *)
-(*     let profile = CicUtil.profile "Inference.superposition_left.build_new" in *)
-(*     (fun e -> profile build_new e) *)
-(*   in *)
-  List.map build_new expansions
+  !maxmeta, List.map build_new expansions
 ;;
 
 
+let sup_r_counter = ref 1;;
+
 let superposition_right newmeta (metasenv, context, ugraph) table target =
   let module C = Cic in
   let module S = CicSubstitution in
@@ -615,7 +816,7 @@ let superposition_right newmeta (metasenv, context, ugraph) table target =
   let module HL = HelmLibraryObjects in
   let module CR = CicReduction in
   let module U = Utils in
-  let eqproof, (eq_ty, left, right, ordering), newmetas, args = target in
+  let _, eqproof, (eq_ty, left, right, ordering), newmetas, args = target in
   let metasenv' = metasenv @ newmetas in
   let maxmeta = ref newmeta in
   let res1, res2 =
@@ -637,19 +838,30 @@ let superposition_right newmeta (metasenv, context, ugraph) table target =
 
     let time1 = Unix.gettimeofday () in
     
-    let pos, (proof', (ty, what, other, _), menv', args') = eq_found in
+    let pos, (_, proof', (ty, what, other, _), menv', args') = eq_found in
     let what, other = if pos = Utils.Left then what, other else other, what in
     let newgoal, newproof =
       let bo' = (* M. *)apply_subst s (S.subst other bo) in
-      let bo'' =
-        C.Appl (
-          [C.MutInd (HL.Logic.eq_URI, 0, []); S.lift 1 eq_ty] @
-            if ordering = U.Gt then [bo'; S.lift 1 right]
-            else [S.lift 1 left; bo'])
+      let t' =
+        let name = C.Name ("x_SupR_" ^ (string_of_int !sup_r_counter)) in
+        incr sup_r_counter;
+        let l, r =
+          if ordering = U.Gt then bo, S.lift 1 right else S.lift 1 left, bo in
+        (name, ty, S.lift 1 eq_ty, l, r)
       in
-      let t' = C.Lambda (C.Anonymous, ty, bo'') in
+(*       let bo'' = *)
+(*         C.Appl ( *)
+(*           [C.MutInd (HL.Logic.eq_URI, 0, []); S.lift 1 eq_ty] @ *)
+(*             if ordering = U.Gt then [S.lift 1 bo'; S.lift 1 right] *)
+(*             else [S.lift 1 left; S.lift 1 bo']) *)
+(*       in *)
+(*       let t' = *)
+(*         let name = C.Name ("x_SupR_" ^ (string_of_int !sup_r_counter)) in *)
+(*         incr sup_r_counter; *)
+(*         C.Lambda (name, ty, bo'') *)
+(*       in *)
       bo',
-      C.Implicit None
+      Inference.ProofBlock (s, eq_URI, t', eq_found, eqproof(* target *))
 (*       (\* M. *\)apply_subst s *)
 (*         (C.Appl [C.Const (eq_URI, []); ty; what; t'; *)
 (*                  eqproof; other; proof']) *)
@@ -661,7 +873,9 @@ let superposition_right newmeta (metasenv, context, ugraph) table target =
       let neworder = !Utils.compare_terms left right 
       and newmenv = newmetas @ menv'
       and newargs = args @ args' in
-      let eq' = (newproof, (eq_ty, left, right, neworder), newmenv, newargs)
+      let eq' =
+        let w = Utils.compute_equality_weight eq_ty left right in
+        (w, newproof, (eq_ty, left, right, neworder), newmenv, newargs)
       and env = (metasenv, context, ugraph) in
       let newm, eq' = Inference.fix_metas !maxmeta eq' in
       newm, eq'
@@ -670,7 +884,7 @@ let superposition_right newmeta (metasenv, context, ugraph) table target =
 
     let time2 = Unix.gettimeofday () in
     build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
-    
+
     newequality
   in
 
@@ -682,7 +896,7 @@ let superposition_right newmeta (metasenv, context, ugraph) table target =
   let new1 = List.map (build_new U.Gt) res1
   and new2 = List.map (build_new U.Lt) res2 in
   let ok = function
-    | _, (_, left, right, _), _, _ ->
+    | _, _, (_, left, right, _), _, _ ->
         not (fst (CR.are_convertible context left right ugraph))
   in
   (!maxmeta,