X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Fparamodulation%2Findexing.ml;h=cf6a76cdca29835f60dd5a9691b98cfb62c5865f;hb=33a02e0b639217093eb63f30169aaa6ac8c78907;hp=8ed8f49a156adce5898b8ced5120178dbf3d31aa;hpb=5462948747cca234512fd998678cb9315785d68c;p=helm.git

diff --git a/helm/ocaml/paramodulation/indexing.ml b/helm/ocaml/paramodulation/indexing.ml
index 8ed8f49a1..cf6a76cdc 100644
--- a/helm/ocaml/paramodulation/indexing.ml
+++ b/helm/ocaml/paramodulation/indexing.ml
@@ -1,40 +1,904 @@
-(* type naif_indexing =
-    (Cic.term * ((bool * Inference.equality) list)) list 
-;; *)
-
-type pos = Left | Right 
-;;
-
-let head_of_term =
-  function 
-    | Cic.Appl hd::tl -> hd
-    | t -> t
-;;
-
-let index table eq =
-  let (_,(_,l,r,ordering),_,_) = eq in
-  let hl = head_of_term l in
-  let hr = head_of_term r in
-  let index x pos = 
-    let x_entry = 
-      try Hashtbl.find table x
-      with Not_found -> [] in
-      Hashtbl.replace table x (pos,eq)::x_entry in
-  (match ordering with
-    | Utils.Gt -> 
-	index hl Left
-    | Utils.Lt -> 
-	index hr Right
-    | _ -> index hl Left;
-	index hr Right);
-  table
-;;
-
-let demodulate_term env table cmp term =
-  let hd_term = head_of_term term in
-  let candidates = Hashtbl.find table hd_term in
+
+let debug_print = Utils.debug_print;;
+
+
+type retrieval_mode = Matching | Unification;;
+
+
+let print_candidates mode term res =
+  let _ =
+    match mode with
+    | Matching ->
+        Printf.printf "| candidates Matching %s\n" (CicPp.ppterm term)
+    | Unification ->
+        Printf.printf "| candidates Unification %s\n" (CicPp.ppterm term)
+  in
+  print_endline
+    (String.concat "\n"
+       (List.map
+          (fun (p, e) ->
+             Printf.sprintf "| (%s, %s)" (Utils.string_of_pos p)
+               (Inference.string_of_equality e))
+          res));
+  print_endline "|";
+;;
+
+
+let indexing_retrieval_time = ref 0.;;
+
+
+(* let my_apply_subst subst term = *)
+(*   let module C = Cic in *)
+(*   let lookup lift_amount meta = *)
+(*     match meta with *)
+(*     | C.Meta (i, _) -> ( *)
+(*         try *)
+(*           let _, (_, t, _) = List.find (fun (m, _) -> m = i) subst in *)
+(*           (\* CicSubstitution.lift lift_amount  *\)t *)
+(*         with Not_found -> meta *)
+(*       ) *)
+(*     | _ -> assert false *)
+(*   in *)
+(*   let rec apply_aux lift_amount =  function *)
+(*     | C.Meta (i, l) as t -> lookup lift_amount t *)
+(*     | C.Appl l -> C.Appl (List.map (apply_aux lift_amount) l) *)
+(*     | C.Prod (nn, s, t) -> *)
+(*         C.Prod (nn, apply_aux lift_amount s, apply_aux (lift_amount+1) t) *)
+(*     | C.Lambda (nn, s, t) -> *)
+(*         C.Lambda (nn, apply_aux lift_amount s, apply_aux (lift_amount+1) t) *)
+(*     | t -> t *)
+(*   in *)
+(*   apply_aux 0 term *)
+(* ;; *)
+
+
+(* let apply_subst subst term = *)
+(*   Printf.printf "| apply_subst:\n| subst: %s\n| term: %s\n" *)
+(*     (Utils.print_subst ~prefix:" ; " subst) (CicPp.ppterm term); *)
+(*   let res = my_apply_subst subst term in *)
+(* (\*   let res = CicMetaSubst.apply_subst subst term in *\) *)
+(*   Printf.printf "| res: %s\n" (CicPp.ppterm res); *)
+(*   print_endline "|"; *)
+(*   res *)
+(* ;; *)
+
+(* let apply_subst = my_apply_subst *)
+let apply_subst = CicMetaSubst.apply_subst
+
+
+let apply_subst =
+  let profile = CicUtil.profile "apply_subst" in
+  (fun s a -> profile (apply_subst s) a)
+;;
+
+
+(*
+(* 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
+;;
+
+let index = Path_indexing.index
+and remove_index = Path_indexing.remove_index
+and in_index = Path_indexing.in_index;;
+  
+let get_candidates mode trie term =
+  let t1 = Unix.gettimeofday () in
+  let res = 
+    let s = 
+      match mode with
+      | Matching -> Path_indexing.retrieve_generalizations trie term
+      | Unification -> Path_indexing.retrieve_unifiables trie term
+(*       Path_indexing.retrieve_all trie term *)
+    in
+    Path_indexing.PosEqSet.elements s
+  in
+(*   print_candidates mode term res; *)
+  let t2 = Unix.gettimeofday () in
+  indexing_retrieval_time := !indexing_retrieval_time +. (t2 -. t1);
+  res
+;;
+*)
+
+
+(* DISCRIMINATION TREES *)
+let empty_table () =
+  Discrimination_tree.DiscriminationTree.empty
+;;
+
+let index = Discrimination_tree.index
+and remove_index = Discrimination_tree.remove_index
+and in_index = Discrimination_tree.in_index;;
+
+let get_candidates mode tree term =
+  let t1 = Unix.gettimeofday () in
+  let res =
+    let s = 
+      match mode with
+      | Matching -> Discrimination_tree.retrieve_generalizations tree term
+      | Unification -> Discrimination_tree.retrieve_unifiables tree term
+    in
+    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
+;;
+
+
+(* let get_candidates = *)
+(*   let profile = CicUtil.profile "Indexing.get_candidates" in *)
+(*   (fun mode tree term -> profile (get_candidates mode tree) term) *)
+(* ;; *)
+
+
+let match_unif_time_ok = ref 0.;;
+let match_unif_time_no = ref 0.;;
+
+
+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 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
+(*         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 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 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 termty, ugraph = *)
+(*     CicTypeChecker.type_of_aux' metasenv context term ugraph *)
+(*   in *)
+  function
+    | [] -> []
+    | candidate::tl ->
+        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
+          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
+;;
+
+
+let subsumption env table target =
+  let _, (ty, left, right, _), tmetas, _ = target in
+  let metasenv, context, ugraph = env in
+  let metasenv = metasenv @ tmetas in
+  let samesubst subst subst' =
+    let tbl = Hashtbl.create (List.length subst) in
+    List.iter (fun (m, (c, t1, t2)) -> Hashtbl.add tbl m (c, t1, t2)) subst;
+    List.for_all
+      (fun (m, (c, t1, t2)) ->
+         try
+           let c', t1', t2' = Hashtbl.find tbl m in
+           if (c = c') && (t1 = t1') && (t2 = t2') then true
+           else false
+         with Not_found ->
+           true)
+      subst'
+  in
+  let leftr =
+    match left with
+    | Cic.Meta _ -> []
+    | _ ->
+        let leftc = get_candidates Matching table left in
+        find_all_matches ~unif_fun:Inference.matching
+          metasenv context ugraph 0 left ty leftc
+  in
+  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' =
+        let t1 = Unix.gettimeofday () in
+        try
+          let r = 
+            Inference.matching metasenv context what other 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
+      samesubst subst subst'
+    with Inference.MatchingFailure ->
+      false
+  in
+  let r = List.exists (ok right) leftr in
+  if r then
+    true
+  else
+    let rightr =
+      match right with
+      | Cic.Meta _ -> []
+      | _ ->
+          let rightc = get_candidates Matching table right in
+          find_all_matches ~unif_fun:Inference.matching
+            metasenv context ugraph 0 right ty rightc
+    in
+    List.exists (ok left) rightr
+;;
+
+
+let rec demodulate_term metasenv context ugraph table lift_amount term =
+  let module C = Cic in
+  let module S = CicSubstitution in
+  let module M = CicMetaSubst in
+  let module HL = HelmLibraryObjects in
+  let candidates = get_candidates Matching table term in
+  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 termty candidates
+      in
+      if res <> None then
+        res
+      else
+        match term with
+        | C.Appl l ->
+            let res, ll = 
+              List.fold_left
+                (fun (res, tl) t ->
+                   if res <> None then
+                     (res, tl @ [S.lift 1 t])
+                   else 
+                     let r =
+                       demodulate_term metasenv context ugraph table
+                         lift_amount t
+                     in
+                     match r with
+                     | None -> (None, tl @ [S.lift 1 t])
+                     | Some (rel, _, _, _, _) -> (r, tl @ [rel]))
+                (None, []) l
+            in (
+              match res with
+              | None -> None
+              | Some (_, subst, menv, ug, eq_found) ->
+                  Some (C.Appl ll, subst, menv, ug, eq_found)
+            )
+        | C.Prod (nn, s, t) ->
+            let r1 =
+              demodulate_term metasenv context ugraph table lift_amount s in (
+              match r1 with
+              | None ->
+                  let r2 =
+                    demodulate_term metasenv
+                      ((Some (nn, C.Decl s))::context) ugraph
+                      table (lift_amount+1) t
+                  in (
+                    match r2 with
+                    | None -> None
+                    | Some (t', subst, menv, ug, eq_found) ->
+                        Some (C.Prod (nn, (S.lift 1 s), t'),
+                              subst, menv, ug, eq_found)
+                  )
+              | Some (s', subst, menv, ug, eq_found) ->
+                  Some (C.Prod (nn, s', (S.lift 1 t)),
+                        subst, menv, ug, eq_found)
+            )
+        | t ->
+            None
+;;
+
+
+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 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 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 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 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
+      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 newmetasenv = List.filter (fun (i, _, _) -> List.mem i m) metas
+    and newargs =
+      List.filter
+        (function C.Meta (i, _) -> List.mem i m | _ -> assert false)
+        args
+    in
+    let ordering = !Utils.compare_terms left right in
+
+    let time2 = Unix.gettimeofday () in
+    build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
+
+    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 res = demodulate_term metasenv' context ugraph table 0 left 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
+      if (Inference.is_identity (metasenv', context, ugraph) newtarget) ||
+        (Inference.meta_convertibility_eq target newtarget) then
+          newmeta, newtarget
+      else
+(*         if subsumption env table newtarget then *)
+(*           newmeta, build_identity newtarget *)
+(*         else *)
+        demodulation newmeta env table sign newtarget
+  | None ->
+      let res = demodulate_term metasenv' context ugraph table 0 right in
+      match res with
+      | Some t ->
+          let newmeta, newtarget = build_newtarget false t in
+          if (Inference.is_identity (metasenv', context, ugraph) newtarget) ||
+            (Inference.meta_convertibility_eq target newtarget) then
+              newmeta, newtarget
+          else
+(*             if subsumption env table newtarget then *)
+(*               newmeta, build_identity newtarget *)
+(*             else *)
+              demodulation newmeta env table sign newtarget
+      | None ->
+          newmeta, target
+;;
+
+
+let rec betaexpand_term metasenv context ugraph table lift_amount term =
+  let module C = Cic in
+  let module S = CicSubstitution in
+  let module M = CicMetaSubst in
+  let module HL = HelmLibraryObjects in
+  let candidates = get_candidates Unification table term in
+  let res, lifted_term = 
+    match term with
+    | C.Meta (i, l) ->
+        let l', lifted_l = 
+          List.fold_right
+            (fun arg (res, lifted_tl) ->
+               match arg with
+               | Some arg ->
+                   let arg_res, lifted_arg =
+                     betaexpand_term metasenv context ugraph table
+                       lift_amount arg in
+                   let l1 =
+                     List.map
+                       (fun (t, s, m, ug, eq_found) ->
+                          (Some t)::lifted_tl, s, m, ug, eq_found)
+                       arg_res
+                   in
+                   (l1 @
+                      (List.map
+                         (fun (l, s, m, ug, eq_found) ->
+                            (Some lifted_arg)::l, s, m, ug, eq_found)
+                         res),
+                    (Some lifted_arg)::lifted_tl)
+               | None ->
+                   (List.map
+                      (fun (r, s, m, ug, eq_found) ->
+                         None::r, s, m, ug, eq_found) res, 
+                    None::lifted_tl)
+            ) l ([], [])
+        in
+        let e = 
+          List.map
+            (fun (l, s, m, ug, eq_found) ->
+               (C.Meta (i, l), s, m, ug, eq_found)) l'
+        in
+        e, C.Meta (i, lifted_l)
+          
+    | C.Rel m ->
+        [], if m <= lift_amount then C.Rel m else C.Rel (m+1)
+          
+    | C.Prod (nn, s, t) ->
+        let l1, lifted_s =
+          betaexpand_term metasenv context ugraph table lift_amount s in
+        let l2, lifted_t =
+          betaexpand_term metasenv ((Some (nn, C.Decl s))::context) ugraph
+            table (lift_amount+1) t in
+        let l1' =
+          List.map
+            (fun (t, s, m, ug, eq_found) ->
+               C.Prod (nn, t, lifted_t), s, m, ug, eq_found) l1
+        and l2' =
+          List.map
+            (fun (t, s, m, ug, eq_found) ->
+               C.Prod (nn, lifted_s, t), s, m, ug, eq_found) l2 in
+        l1' @ l2', C.Prod (nn, lifted_s, lifted_t)
+          
+    | C.Appl l ->
+        let l', lifted_l =
+          List.fold_right
+            (fun arg (res, lifted_tl) ->
+               let arg_res, lifted_arg =
+                 betaexpand_term metasenv context ugraph table lift_amount arg
+               in
+               let l1 =
+                 List.map
+                   (fun (a, s, m, ug, eq_found) ->
+                      a::lifted_tl, s, m, ug, eq_found)
+                   arg_res
+               in
+               (l1 @
+                  (List.map
+                     (fun (r, s, m, ug, eq_found) ->
+                        lifted_arg::r, s, m, ug, eq_found)
+                     res),
+                lifted_arg::lifted_tl)
+            ) l ([], [])
+        in
+        (List.map
+           (fun (l, s, m, ug, eq_found) -> (C.Appl l, s, m, ug, eq_found)) l',
+         C.Appl lifted_l)
+
+    | t -> [], (S.lift lift_amount t)
+  in
+  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 termty candidates
+      in
+      r @ res, lifted_term
+;;
+
+
+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 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 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 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 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
+    let neworder = !Utils.compare_terms left right in
+
+    let time2 = Unix.gettimeofday () in
+    build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
+
+    let res =
+      let w = Utils.compute_equality_weight eq_ty left right in
+      (w, newproof, (eq_ty, left, right, neworder), [], [])
+    in
+    res
+  in
+  !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
+  let module M = CicMetaSubst in
+  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 metasenv' = metasenv @ newmetas in
+  let maxmeta = ref newmeta in
+  let res1, res2 =
+    match ordering with
+    | U.Gt -> fst (betaexpand_term metasenv' context ugraph table 0 left), []
+    | U.Lt -> [], fst (betaexpand_term metasenv' context ugraph table 0 right)
+    | _ ->
+        let res l r =
+          List.filter
+            (fun (_, subst, _, _, _) ->
+               let subst = (* M. *)apply_subst subst in
+               let o = !Utils.compare_terms (subst l) (subst r) in
+               o <> U.Lt && o <> U.Le)
+            (fst (betaexpand_term metasenv' context ugraph table 0 l))
+        in
+        (res left right), (res right left)
+  in
+  let build_new ordering (bo, s, m, ug, (eq_found, eq_URI)) =
+
+    let time1 = Unix.gettimeofday () 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 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 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',
+      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']) *)
+    in
+    let newmeta, newequality = 
+      let left, right =
+        if ordering = U.Gt then newgoal, (* M. *)apply_subst s right
+        else (* M. *)apply_subst s left, newgoal in
+      let neworder = !Utils.compare_terms left right 
+      and newmenv = newmetas @ menv'
+      and newargs = args @ args' in
+      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'
+    in
+    maxmeta := newmeta;
+
+    let time2 = Unix.gettimeofday () in
+    build_newtarget_time := !build_newtarget_time +. (time2 -. time1);
+
+    newequality
+  in
+
+(*   let build_new = *)
+(*     let profile = CicUtil.profile "Indexing.superposition_right.build_new" in *)
+(*     (fun o e -> profile (build_new o) e) *)
+(*   in *)
   
+  let new1 = List.map (build_new U.Gt) res1
+  and new2 = List.map (build_new U.Lt) res2 in
+  let ok = function
+    | _, _, (_, left, right, _), _, _ ->
+        not (fst (CR.are_convertible context left right ugraph))
+  in
+  (!maxmeta,
+   (List.filter ok (new1 @ new2)))
+;;