X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Ftactics%2Fparamodulation%2Fequality.ml;h=30138b378f9eac358305f3ffbcc4170e05de44c7;hb=b109559ac6795075508fd5c231a1bf2a3223031a;hp=57c440860a78dc3016ba1b3c11917861d9b13a5b;hpb=c90dd454864f9383d7b05cd060e656fbe69b52bd;p=helm.git

diff --git a/helm/software/components/tactics/paramodulation/equality.ml b/helm/software/components/tactics/paramodulation/equality.ml
index 57c440860..30138b378 100644
--- a/helm/software/components/tactics/paramodulation/equality.ml
+++ b/helm/software/components/tactics/paramodulation/equality.ml
@@ -23,10 +23,13 @@
  * http://cs.unibo.it/helm/.
  *)
 
+(* let _profiler = <:profiler<_profiler>>;; *)
+
 (* $Id: inference.ml 6245 2006-04-05 12:07:51Z tassi $ *)
 
 type rule = SuperpositionRight | SuperpositionLeft | Demodulation
 type uncomparable = int -> int 
+
 type equality =
     uncomparable *       (* trick to break structural equality *)
     int  *               (* weight *)
@@ -41,28 +44,32 @@ and proof =
   | Exact of Cic.term
   | Step of Subst.substitution * (rule * int*(Utils.pos*int)* Cic.term) 
             (* subst, (rule,eq1, eq2,predicate) *)  
-and goal_proof = (Utils.pos * int * Subst.substitution * Cic.term) list
+and goal_proof = (rule * Utils.pos * int * Subst.substitution * Cic.term) list
 ;;
+(* the hashtbl eq_id -> proof, max_eq_id *)
+type equality_bag = (int,equality) Hashtbl.t * int ref
+
+type goal = goal_proof * Cic.metasenv * Cic.term
 
 (* globals *)
-let maxid = ref 0;;
-let id_to_eq = Hashtbl.create 1024;;
+let mk_equality_bag () =
+  Hashtbl.create 1024, ref 0
+;;
 
-let freshid () =
-  incr maxid; !maxid
+let freshid (_,i) =
+  incr i; !i
 ;;
 
-let reset () = 
-  maxid := 0;
-  Hashtbl.clear  id_to_eq
+let add_to_bag (id_to_eq,_) id eq =
+  Hashtbl.add id_to_eq id eq
 ;;
 
 let uncomparable = fun _ -> 0
 
-let mk_equality (weight,p,(ty,l,r,o),m) =
-  let id = freshid () in
+let mk_equality bag (weight,p,(ty,l,r,o),m) =
+  let id = freshid bag in
   let eq = (uncomparable,weight,p,(ty,l,r,o),m,id) in
-  Hashtbl.add id_to_eq id eq;
+  add_to_bag bag id eq;
   eq
 ;;
 
@@ -75,28 +82,63 @@ let mk_tmp_equality (weight,(ty,l,r,o),m) =
 let open_equality (_,weight,proof,(ty,l,r,o),m,id) = 
   (weight,proof,(ty,l,r,o),m,id)
 
+let string_of_rule = function
+  | SuperpositionRight -> "SupR"
+  | SuperpositionLeft -> "SupL"
+  | Demodulation -> "Demod"
+;;
+
 let string_of_equality ?env eq =
   match env with
   | None ->
-      let w, _, (ty, left, right, o), _ , id = open_equality eq in
-      Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s" 
+      let w, _, (ty, left, right, o), m , id = open_equality eq in
+      Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]" 
               id w (CicPp.ppterm ty)
               (CicPp.ppterm left) 
               (Utils.string_of_comparison o) (CicPp.ppterm right)
+         (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m)) 
+(*          "..."  *)
   | Some (_, context, _) -> 
       let names = Utils.names_of_context context in
-      let w, _, (ty, left, right, o), _ , id = open_equality eq in
-      Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s" 
+      let w, _, (ty, left, right, o), m , id = open_equality eq in
+      Printf.sprintf "Id: %d, Weight: %d, {%s}: %s =(%s) %s [%s]" 
               id w (CicPp.pp ty names)
               (CicPp.pp left names) (Utils.string_of_comparison o)
               (CicPp.pp right names)
+         (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m)) 
+(*            "..." *)
 ;;
 
 let compare (_,_,_,s1,_,_) (_,_,_,s2,_,_) =
   Pervasives.compare s1 s2
 ;;
 
-let proof_of_id id =
+let rec max_weight_in_proof ((id_to_eq,_) as bag) current =
+  function
+   | Exact _ -> current
+   | Step (_, (_,id1,(_,id2),_)) ->
+       let eq1 = Hashtbl.find id_to_eq id1 in
+       let eq2 = Hashtbl.find id_to_eq id2 in  
+       let (w1,p1,(_,_,_,_),_,_) = open_equality eq1 in
+       let (w2,p2,(_,_,_,_),_,_) = open_equality eq2 in
+       let current = max current w1 in
+       let current = max_weight_in_proof bag current p1 in
+       let current = max current w2 in
+       max_weight_in_proof bag current p2
+
+let max_weight_in_goal_proof ((id_to_eq,_) as bag) =
+  List.fold_left 
+    (fun current (_,_,id,_,_) ->
+       let eq = Hashtbl.find id_to_eq id in
+       let (w,p,(_,_,_,_),_,_) = open_equality eq in
+       let current = max current w in
+       max_weight_in_proof bag current p)
+
+let max_weight bag goal_proof proof =
+  let current = max_weight_in_proof bag 0 proof in
+  max_weight_in_goal_proof bag current goal_proof
+
+let proof_of_id (id_to_eq,_) id =
   try
     let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
       p,l,r
@@ -104,12 +146,7 @@ let proof_of_id id =
       Not_found -> assert false
 
 
-let string_of_proof ?(names=[]) p gp = 
-  let str_of_rule = function
-    | SuperpositionRight -> "SupR"
-    | SuperpositionLeft -> "SupL"
-    | Demodulation -> "Demod"
-  in
+let string_of_proof ?(names=[]) bag p gp = 
   let str_of_pos = function
     | Utils.Left -> "left"
     | Utils.Right -> "right"
@@ -122,33 +159,42 @@ let string_of_proof ?(names=[]) p gp =
           prefix (CicPp.pp t names)
     | Step (subst,(rule,eq1,(pos,eq2),pred)) -> 
         Printf.sprintf "%s%s(%s|%d with %d dir %s pred %s))\n"
-          prefix (str_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos) 
+          prefix (string_of_rule rule) (Subst.ppsubst ~names subst) eq1 eq2 (str_of_pos pos) 
           (CicPp.pp pred names)^ 
-        aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id eq1)) ^ 
-        aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id eq2)) 
+        aux (margin+1) (Printf.sprintf "%d" eq1) (fst3 (proof_of_id bag eq1)) ^ 
+        aux (margin+1) (Printf.sprintf "%d" eq2) (fst3 (proof_of_id bag eq2)) 
   in
   aux 0 "" p ^ 
   String.concat "\n" 
     (List.map 
-      (fun (pos,i,s,t) -> 
+      (fun (r,pos,i,s,t) -> 
         (Printf.sprintf 
-          "GOAL: %s %d %s %s\n" 
+          "GOAL: %s %s %d %s %s\n" (string_of_rule r)
             (str_of_pos pos) i (Subst.ppsubst ~names s) (CicPp.pp t names)) ^ 
-        aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id i)))
+        aux 1 (Printf.sprintf "%d " i) (fst3 (proof_of_id bag i)))
       gp)
 ;;
 
-let rec depend eq id =
+let rec depend ((id_to_eq,_) as bag) eq id seen =
   let (_,p,(_,_,_,_),_,ideq) = open_equality eq in
-  if id = ideq then true else  
-  match p with
-      Exact _ -> false
-    | Step (_,(_,id1,(_,id2),_)) ->
-        let eq1 = Hashtbl.find id_to_eq id1 in
-        let eq2 = Hashtbl.find id_to_eq id2 in  
-        depend eq1 id || depend eq2 id
+  if List.mem ideq seen then 
+    false,seen
+  else
+    if id = ideq then 
+      true,seen
+    else  
+      match p with
+      | Exact _ -> false,seen
+      | Step (_,(_,id1,(_,id2),_)) ->
+          let seen = ideq::seen in
+          let eq1 = Hashtbl.find id_to_eq id1 in
+          let eq2 = Hashtbl.find id_to_eq id2 in  
+          let b1,seen = depend bag eq1 id seen in
+          if b1 then b1,seen else depend bag eq2 id seen
 ;;
 
+let depend bag eq id = fst (depend bag eq id []);;
+
 let ppsubst = Subst.ppsubst ~names:[];;
 
 (* returns an explicit named subst and a list of arguments for sym_eq_URI *)
@@ -156,7 +202,7 @@ let build_ens uri termlist =
   let obj, _ = CicEnvironment.get_obj CicUniv.empty_ugraph uri in
   match obj with
   | Cic.Constant (_, _, _, uris, _) ->
-      assert (List.length uris <= List.length termlist);
+      (* assert (List.length uris <= List.length termlist); *)
       let rec aux = function
         | [], tl -> [], tl
         | (uri::uris), (term::tl) ->
@@ -179,7 +225,8 @@ let mk_trans uri ty t1 t2 t3 p12 p23 =
 ;;
 
 let mk_eq_ind uri ty what pred p1 other p2 =
- Cic.Appl [Cic.Const (uri, []); ty; what; pred; p1; other; p2]
+  let ens, args = build_ens uri [ty; what; pred; p1; other; p2] in
+  Cic.Appl (Cic.Const (uri, ens) :: args)
 ;;
 
 let p_of_sym ens tl =
@@ -196,6 +243,13 @@ let open_trans ens tl =
     | _ -> assert false   
 ;;
 
+let open_sym ens tl =
+  let args = List.map snd ens @ tl in
+  match args with 
+    | [ty;l;r;p] -> ty,l,r,p
+    | _ -> assert false   
+;;
+
 let open_eq_ind args =
   match args with 
   | [ty;l;pred;pl;r;pleqr] -> ty,l,pred,pl,r,pleqr
@@ -204,9 +258,9 @@ let open_eq_ind args =
 
 let open_pred pred =
   match pred with 
-  | Cic.Lambda (_,ty,(Cic.Appl [Cic.MutInd (uri, 0,_);_;l;r])) 
+  | Cic.Lambda (_,_,(Cic.Appl [Cic.MutInd (uri, 0,_);ty;l;r])) 
      when LibraryObjects.is_eq_URI uri -> ty,uri,l,r
-  | _ -> prerr_endline (CicPp.ppterm pred); assert false   
+  | _ -> Utils.debug_print (lazy (CicPp.ppterm pred)); assert false   
 ;;
 
 let is_not_fixed t =
@@ -214,8 +268,49 @@ let is_not_fixed t =
    CicSubstitution.subst (Cic.Rel 1) t
 ;;
 
-
-let canonical t = 
+let canonical t context menv = 
+  let remove_cycles t =
+   let is_transitive =
+    function
+       Cic.Appl (Cic.Const (uri_trans,_)::_)
+        when LibraryObjects.is_trans_eq_URI uri_trans ->
+         true
+     | _ -> false in
+   let rec collect =
+    function
+       Cic.Appl (Cic.Const (uri_trans,ens)::tl)
+        when LibraryObjects.is_trans_eq_URI uri_trans ->
+         let ty,l,m,r,p1,p2 = open_trans ens tl in
+          (if is_transitive p1 then fst (collect p1) else [l,p1]) @
+           (if is_transitive p2 then fst (collect p2) else [m,p2]),
+          (r, uri_trans, ty)
+     | t -> assert false in
+   let rec cut_to_last_duplicate l acc =
+    function
+       [] -> List.rev acc
+     | (l',p)::tl when l=l' -> 
+if acc <> [] then
+Utils.debug_print (lazy ("!!! RISPARMIO " ^ string_of_int (List.length acc) ^ " PASSI"));
+         cut_to_last_duplicate l [l',p] tl
+     | (l',p)::tl ->
+         cut_to_last_duplicate l ((l',p)::acc) tl
+   in
+   let rec rebuild =
+    function
+       (l,_)::_::_ as steps, ((r,uri_trans,ty) as last) ->
+         (match cut_to_last_duplicate l [] steps with
+             (l,p1)::((m,_)::_::_ as tl) ->
+               mk_trans uri_trans ty l m r p1 (rebuild (tl,last))
+           | [l,p1 ; m,p2] -> mk_trans uri_trans ty l m r p1 p2
+           | [l,p1] -> p1
+           | [] -> assert false)
+     | _ -> assert false
+   in
+    if is_transitive t then
+     rebuild (collect t)
+    else
+     t
+  in
   let rec remove_refl t =
     match t with
     | Cic.Appl (((Cic.Const(uri_trans,ens))::tl) as args)
@@ -232,74 +327,66 @@ let canonical t =
         Cic.LetIn (name,remove_refl bo,remove_refl rest)
     | _ -> t
   in
-  let rec canonical t =
+  let rec canonical_trough_lambda context = function
+    | Cic.Lambda(name,ty,bo) -> 
+        let context' = (Some (name,Cic.Decl ty))::context in
+        Cic.Lambda(name,ty,canonical_trough_lambda context' bo)
+    | t -> canonical context t
+
+  and canonical context t =
     match t with
-      | Cic.LetIn(name,bo,rest) -> Cic.LetIn(name,canonical bo,canonical rest)
+      | Cic.LetIn(name,bo,rest) -> 
+          let bo = canonical_trough_lambda context bo in
+          let context' = (Some (name,Cic.Def (bo,None)))::context in
+          Cic.LetIn(name,bo,canonical context' rest)
       | Cic.Appl (((Cic.Const(uri_sym,ens))::tl) as args)
           when LibraryObjects.is_sym_eq_URI uri_sym ->
           (match p_of_sym ens tl with
              | Cic.Appl ((Cic.Const(uri,ens))::tl)
                  when LibraryObjects.is_sym_eq_URI uri -> 
-                   canonical (p_of_sym ens tl)
+                   canonical context (p_of_sym ens tl)
              | Cic.Appl ((Cic.Const(uri_trans,ens))::tl)
                  when LibraryObjects.is_trans_eq_URI uri_trans ->
                  let ty,l,m,r,p1,p2 = open_trans ens tl in
                    mk_trans uri_trans ty r m l 
-                     (canonical (mk_sym uri_sym ty m r p2)) 
-                     (canonical (mk_sym uri_sym ty l m p1))
-             | Cic.Appl (((Cic.Const(uri_ind,ens)) as he)::tl) 
-                 when LibraryObjects.is_eq_ind_URI uri_ind || 
-                      LibraryObjects.is_eq_ind_r_URI uri_ind ->
-                 let ty, what, pred, p1, other, p2 =
-                   match tl with
-                   | [ty;what;pred;p1;other;p2] -> ty, what, pred, p1, other, p2
-                   | _ -> assert false
+                     (canonical context (mk_sym uri_sym ty m r p2)) 
+                     (canonical context (mk_sym uri_sym ty l m p1))
+             | Cic.Appl (([Cic.Const(uri_feq,ens);ty1;ty2;f;x;y;p]))
+                 when LibraryObjects.is_eq_f_URI uri_feq ->
+                 let eq = LibraryObjects.eq_URI_of_eq_f_URI uri_feq in
+                 let eq_f_sym =
+                   Cic.Const (LibraryObjects.eq_f_sym_URI ~eq, [])
                  in
-                 let pred,l,r = 
-                   match pred with
-                   | Cic.Lambda (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;l;r])
-                       when LibraryObjects.is_eq_URI uri ->
-                         Cic.Lambda 
-                           (name,s,Cic.Appl [Cic.MutInd(uri,0,ens);ty;r;l]),l,r
-                   | _ -> 
-                       prerr_endline (CicPp.ppterm pred);
-                       assert false
-                 in
-                 let l = CicSubstitution.subst what l in
-                 let r = CicSubstitution.subst what r in
-                 Cic.Appl 
-                   [he;ty;what;pred;
-                    canonical (mk_sym uri_sym ty l r p1);other;canonical p2]
+                 let rc = Cic.Appl [eq_f_sym;ty1;ty2;f;x;y;p] in
+                 Utils.debug_print (lazy ("CANONICAL " ^ CicPp.ppterm rc));
+                 rc
              | Cic.Appl [Cic.MutConstruct (uri, 0, 1,_);_;_] as t
                  when LibraryObjects.is_eq_URI uri -> t
-             | _ -> Cic.Appl (List.map canonical args))
-      | Cic.Appl l -> Cic.Appl (List.map canonical l)
+             | _ -> Cic.Appl (List.map (canonical context) args))
+      | Cic.Appl l -> Cic.Appl (List.map (canonical context) l)
       | _ -> t
   in
-  remove_refl (canonical t)
+   remove_cycles (remove_refl (canonical context t))
 ;;
   
-let ty_of_lambda = function
-  | Cic.Lambda (_,ty,_) -> ty
-  | _ -> assert false 
-;;
-
 let compose_contexts ctx1 ctx2 = 
   ProofEngineReduction.replace_lifting 
-    ~equality:(=) ~what:[Cic.Rel 1] ~with_what:[ctx2] ~where:ctx1
+  ~equality:(fun _ ->(=)) ~context:[] ~what:[Cic.Implicit(Some `Hole)] ~with_what:[ctx2] ~where:ctx1
 ;;
 
 let put_in_ctx ctx t = 
   ProofEngineReduction.replace_lifting
-    ~equality:(=) ~what:[Cic.Rel 1] ~with_what:[t] ~where:ctx
+  ~equality:(fun _ -> (=)) ~context:[] ~what:[Cic.Implicit (Some `Hole)] ~with_what:[t] ~where:ctx
 ;;
 
 let mk_eq uri ty l r =
-  Cic.Appl [Cic.MutInd(uri,0,[]);ty;l;r]
+  let ens, args = build_ens uri [ty; l; r] in
+  Cic.Appl (Cic.MutInd(uri,0,ens) :: args)
 ;;
 
 let mk_refl uri ty t = 
-  Cic.Appl [Cic.MutConstruct(uri,0,1,[]);ty;t]
+  let ens, args = build_ens uri [ty; t] in
+  Cic.Appl (Cic.MutConstruct(uri,0,1,ens) :: args)
 ;;
 
 let open_eq = function 
@@ -308,19 +395,43 @@ let open_eq = function
   | _ -> assert false
 ;;
 
+let mk_feq uri_feq ty ty1 left pred right t = 
+  let ens, args = build_ens uri_feq [ty;ty1;pred;left;right;t] in
+  Cic.Appl (Cic.Const(uri_feq,ens) :: args)
+;;
+
+let rec look_ahead aux = function
+  | Cic.Appl ((Cic.Const(uri_ind,ens))::tl) as t
+        when LibraryObjects.is_eq_ind_URI uri_ind || 
+             LibraryObjects.is_eq_ind_r_URI uri_ind ->
+          let ty1,what,pred,p1,other,p2 = open_eq_ind tl in
+          let ty2,eq,lp,rp = open_pred pred in 
+          let hole = Cic.Implicit (Some `Hole) in
+          let ty2 = CicSubstitution.subst hole ty2 in
+          aux ty1 (CicSubstitution.subst other lp) (CicSubstitution.subst other rp) hole ty2 t
+  | Cic.Lambda (n,s,t) -> Cic.Lambda (n,s,look_ahead aux t)
+  | t -> t
+;;
+
 let contextualize uri ty left right t = 
-  (* aux [uri] [ty] [left] [right] [ctx] [t] 
+  let hole = Cic.Implicit (Some `Hole) in
+  (* aux [uri] [ty] [left] [right] [ctx] [ctx_ty] [t] 
    * 
    * the parameters validate this invariant  
    *   t: eq(uri) ty left right
    * that is used only by the base case
    *
-   * ctx is a term with an open (Rel 1). (Rel 1) is the empty context
+   * ctx is a term with an hole. Cic.Implicit(Some `Hole) is the empty context
+   * ctx_ty is the type of ctx
    *)
-    let rec aux uri ty left right ctx_d = function
+    let rec aux uri ty left right ctx_d ctx_ty t =
+      match t with 
+      | Cic.Appl ((Cic.Const(uri_sym,ens))::tl) 
+        when LibraryObjects.is_sym_eq_URI uri_sym  ->
+          let ty,l,r,p = open_sym ens tl in
+          mk_sym uri_sym ty l r (aux uri ty l r ctx_d ctx_ty p)
       | Cic.LetIn (name,body,rest) ->
-          (* we should go in body *)
-          Cic.LetIn (name,body,aux uri ty left right ctx_d rest)
+          Cic.LetIn (name,look_ahead (aux uri) body, aux uri ty left right ctx_d ctx_ty rest)
       | Cic.Appl ((Cic.Const(uri_ind,ens))::tl)
         when LibraryObjects.is_eq_ind_URI uri_ind || 
              LibraryObjects.is_eq_ind_r_URI uri_ind ->
@@ -331,12 +442,13 @@ let contextualize uri ty left right t =
           let is_not_fixed_lp = is_not_fixed lp in
           let avoid_eq_ind = LibraryObjects.is_eq_ind_URI uri_ind in
           (* extract the context and the fixed term from the predicate *)
-          let m, ctx_c = 
+          let m, ctx_c, ty2 = 
             let m, ctx_c = if is_not_fixed_lp then rp,lp else lp,rp in
             (* they were under a lambda *)
-            let m =  CicSubstitution.subst (Cic.Implicit None) m in
-            let ctx_c = CicSubstitution.subst (Cic.Rel 1) ctx_c in
-            m, ctx_c          
+            let m =  CicSubstitution.subst hole m in
+            let ctx_c = CicSubstitution.subst hole ctx_c in
+            let ty2 = CicSubstitution.subst hole ty2 in
+            m, ctx_c, ty2          
           in
           (* create the compound context and put the terms under it *)
           let ctx_dc = compose_contexts ctx_d ctx_c in
@@ -348,18 +460,18 @@ let contextualize uri ty left right t =
           let c_what = put_in_ctx ctx_c what in
           (* now put the proofs in the compound context *)
           let p1 = (* p1: dc_what = d_m *)
-            if is_not_fixed_lp then 
-              aux uri ty1 c_what m ctx_d p1 
+            if is_not_fixed_lp then
+              aux uri ty2 c_what m ctx_d ctx_ty p1
             else
-              mk_sym uri_sym ty d_m dc_what
-                (aux uri ty1 m c_what ctx_d p1)
+              mk_sym uri_sym ctx_ty d_m dc_what
+                (aux uri ty2 m c_what ctx_d ctx_ty p1)
           in
           let p2 = (* p2: dc_other = dc_what *)
             if avoid_eq_ind then
-              mk_sym uri_sym ty dc_what dc_other
-                (aux uri ty1 what other ctx_dc p2)
-            else
-              aux uri ty1 other what ctx_dc p2
+              mk_sym uri_sym ctx_ty dc_what dc_other
+                (aux uri ty1 what other ctx_dc ctx_ty p2)
+             else
+              aux uri ty1 other what ctx_dc ctx_ty p2
           in
           (* if pred = \x.C[x]=m --> t : C[other]=m --> trans other what m
              if pred = \x.m=C[x] --> t : m=C[other] --> trans m what other *)
@@ -368,37 +480,49 @@ let contextualize uri ty left right t =
               dc_other,dc_what,d_m,p2,p1
             else
               d_m,dc_what,dc_other,
-                (mk_sym uri_sym ty dc_what d_m p1),
-                (mk_sym uri_sym ty dc_other dc_what p2)
+                (mk_sym uri_sym ctx_ty dc_what d_m p1),
+                (mk_sym uri_sym ctx_ty dc_other dc_what p2)
           in
-          mk_trans uri_trans ty a b c paeqb pbeqc
+          mk_trans uri_trans ctx_ty a b c paeqb pbeqc
+    | t when ctx_d = hole -> t 
     | t -> 
-        let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in
-        let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in
+(*         let uri_sym = LibraryObjects.sym_eq_URI ~eq:uri in *)
+(*         let uri_ind = LibraryObjects.eq_ind_URI ~eq:uri in *)
+
+        let uri_feq = LibraryObjects.eq_f_URI ~eq:uri in
         let pred = 
-          (* ctx_d will go under a lambda, but put_in_ctx substitutes Rel 1 *)
-          let ctx_d = CicSubstitution.lift_from 2 1 ctx_d in (* bleah *)
-          let r = put_in_ctx ctx_d (CicSubstitution.lift 1 left) in
-          let l = ctx_d in
-          let lty = CicSubstitution.lift 1 ty in 
-          Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r))
+(*           let r = CicSubstitution.lift 1 (put_in_ctx ctx_d left) in *)
+          let l = 
+            let ctx_d = CicSubstitution.lift 1 ctx_d in
+            put_in_ctx ctx_d (Cic.Rel 1)
+          in
+(*           let lty = CicSubstitution.lift 1 ctx_ty in  *)
+(*           Cic.Lambda (Cic.Name "foo",ty,(mk_eq uri lty l r)) *)
+          Cic.Lambda (Cic.Name "foo",ty,l)
         in
-        let d_left = put_in_ctx ctx_d left in
-        let d_right = put_in_ctx ctx_d right in
-        let refl_eq = mk_refl uri ty d_left in
-        mk_sym uri_sym ty d_right d_left
-          (mk_eq_ind uri_ind ty left pred refl_eq right t)
+(*         let d_left = put_in_ctx ctx_d left in *)
+(*         let d_right = put_in_ctx ctx_d right in *)
+(*         let refl_eq = mk_refl uri ctx_ty d_left in *)
+(*         mk_sym uri_sym ctx_ty d_right d_left *)
+(*           (mk_eq_ind uri_ind ty left pred refl_eq right t) *)
+          (mk_feq uri_feq ty ctx_ty left pred right t)
   in
-  let empty_context = Cic.Rel 1 in
-  aux uri ty left right empty_context t
+  aux uri ty left right hole ty t
 ;;
 
 let contextualize_rewrites t ty = 
   let eq,ty,l,r = open_eq ty in
   contextualize eq ty l r t
 ;;
-  
-let build_proof_step lift subst p1 p2 pos l r pred =
+
+let add_subst subst =
+  function
+    | Exact t -> Exact (Subst.apply_subst subst t)
+    | Step (s,(rule, id1, (pos,id2), pred)) -> 
+        Step (Subst.concat subst s,(rule, id1, (pos,id2), pred))
+;;
+	
+let build_proof_step eq lift subst p1 p2 pos l r pred =
   let p1 = Subst.apply_subst_lift lift subst p1 in
   let p2 = Subst.apply_subst_lift lift subst p2 in
   let l  = CicSubstitution.lift lift l in
@@ -415,21 +539,41 @@ let build_proof_step lift subst p1 p2 pos l r pred =
   let what, other = 
     if pos = Utils.Left then l,r else r,l
   in
+  let p =
     match pos with
       | Utils.Left ->
-        mk_eq_ind (Utils.eq_ind_URI ()) ty what pred p1 other p2
+        mk_eq_ind (LibraryObjects.eq_ind_URI ~eq) ty what pred p1 other p2
       | Utils.Right ->
-        mk_eq_ind (Utils.eq_ind_r_URI ()) ty what pred p1 other p2
+        mk_eq_ind (LibraryObjects.eq_ind_r_URI ~eq) ty what pred p1 other p2
+  in
+    p
 ;;
 
-let parametrize_proof p l r ty = 
-  let parameters = CicUtil.metas_of_term p 
-@ CicUtil.metas_of_term l 
-@ CicUtil.metas_of_term r
-in (* ?if they are under a lambda? *)
+let parametrize_proof p l r = 
+  let uniq l = HExtlib.list_uniq (List.sort (fun (i,_) (j,_) -> Pervasives.compare i j) l) in
+  let mot = CicUtil.metas_of_term_set in
+  let parameters = uniq (mot p @ mot l @ mot r) in 
+  (* ?if they are under a lambda? *)
+(*
   let parameters = 
     HExtlib.list_uniq (List.sort Pervasives.compare parameters) 
   in
+*)
+  (* resorts l such that *hopefully* dependencies can be inferred *)
+  let guess_dependency p l =
+    match p with
+    | Cic.Appl ((Cic.Const(uri_ind,ens))::tl) 
+        when LibraryObjects.is_eq_ind_URI uri_ind || 
+             LibraryObjects.is_eq_ind_r_URI uri_ind ->
+        let ty,_,_,_,_,_ = open_eq_ind tl in
+        let metas = CicUtil.metas_of_term ty in
+        let nondep, dep = 
+          List.partition (fun (i,_) -> List.exists (fun (j,_) -> j=i) metas) l
+        in
+        nondep@dep
+    | _ -> l
+  in
+  let parameters = guess_dependency p parameters in
   let what = List.map (fun (i,l) -> Cic.Meta (i,l)) parameters in 
   let with_what, lift_no = 
     List.fold_right (fun _ (acc,n) -> ((Cic.Rel n)::acc),n+1) what ([],1) 
@@ -437,18 +581,18 @@ in (* ?if they are under a lambda? *)
   let p = CicSubstitution.lift (lift_no-1) p in
   let p = 
     ProofEngineReduction.replace_lifting
-    ~equality:(fun t1 t2 -> match t1,t2 with Cic.Meta (i,_),Cic.Meta(j,_) -> i=j | _ -> false) ~what ~with_what ~where:p
-  in
-  let ty_of_m _ = ty (*function 
-    | Cic.Meta (i,_) -> List.assoc i menv 
-    | _ -> assert false *)
+    ~equality:(fun _ t1 t2 -> 
+      match t1,t2 with Cic.Meta (i,_),Cic.Meta(j,_) -> i=j | _ -> false) 
+    ~context:[]
+    ~what ~with_what ~where:p
   in
+  let ty_of_m _ = Cic.Implicit (Some `Type) in
   let args, proof,_ = 
     List.fold_left 
       (fun (instance,p,n) m -> 
         (instance@[m],
         Cic.Lambda 
-          (Cic.Name ("x"^string_of_int n),
+          (Cic.Name ("X"^string_of_int n),
           CicSubstitution.lift (lift_no - n - 1) (ty_of_m m),
           p),
         n+1)) 
@@ -459,9 +603,9 @@ in (* ?if they are under a lambda? *)
   proof, instance
 ;;
 
-let wfo goalproof proof =
+let wfo bag goalproof proof id =
   let rec aux acc id =
-    let p,_,_ = proof_of_id id in
+    let p,_,_ = proof_of_id bag id in
     match p with
     | Exact _ -> if (List.mem id acc) then acc else id :: acc
     | Step (_,(_,id1, (_,id2), _)) -> 
@@ -471,98 +615,186 @@ let wfo goalproof proof =
   in
   let acc = 
     match proof with
-      | Exact _ -> []
-      | Step (_,(_,id1, (_,id2), _)) -> aux (aux [] id1) id2
+      | Exact _ -> [id]
+      | Step (_,(_,id1, (_,id2), _)) -> aux (aux [id] id1) id2
   in 
-  List.fold_left (fun acc (_,id,_,_) -> aux acc id) acc goalproof
+  List.fold_left (fun acc (_,_,id,_,_) -> aux acc id) acc goalproof
 ;;
 
-let string_of_id names id = 
+let string_of_id (id_to_eq,_) names id = 
+  if id = 0 then "" else 
   try
-    let (_,p,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
+    let (_,p,(t,l,r,_),m,_) = open_equality (Hashtbl.find id_to_eq id) in
     match p with
     | Exact t -> 
-        Printf.sprintf "%d = %s: %s = %s" id
+        Printf.sprintf "%d = %s: %s = %s [%s]" id
           (CicPp.pp t names) (CicPp.pp l names) (CicPp.pp r names)
-    | Step (_,(step,id1, (_,id2), _) ) ->
-        Printf.sprintf "%6d: %s %6d %6d   %s = %s" id
-          (if step = SuperpositionRight then "SupR" else "Demo") 
-          id1 id2 (CicPp.pp l names) (CicPp.pp r names)
+(*           "..." *)
+         (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m)) 
+    | Step (_,(step,id1, (dir,id2), p) ) ->
+        Printf.sprintf "%6d: %s %6d %6d   %s =(%s) %s [%s]" id
+          (string_of_rule step)
+          id1 id2 (CicPp.pp l names) (CicPp.pp t names) (CicPp.pp r names)
+         (String.concat ", " (List.map (fun (i,_,_) -> string_of_int i) m)) 
+          (*"..."*)
   with
       Not_found -> assert false
 
-let pp_proof names goalproof proof =
-  String.concat "\n" (List.map (string_of_id names) (wfo goalproof proof)) ^ 
-  "\ngoal is demodulated with " ^ 
-    (String.concat " " 
-      ((List.map (fun (_,i,_,_) -> string_of_int i) goalproof)))
+let pp_proof bag names goalproof proof subst id initial_goal =
+  String.concat "\n" (List.map (string_of_id bag names) (wfo bag goalproof proof id)) ^ 
+  "\ngoal:\n   " ^ 
+    (String.concat "\n   " 
+      (fst (List.fold_right
+        (fun (r,pos,i,s,pred) (acc,g) -> 
+          let _,_,left,right = open_eq g in
+          let ty = 
+            match pos with 
+            | Utils.Left -> CicReduction.head_beta_reduce (Cic.Appl[pred;right])
+            | Utils.Right -> CicReduction.head_beta_reduce (Cic.Appl[pred;left])
+          in
+          let ty = Subst.apply_subst s ty in
+          ("("^ string_of_rule r ^ " " ^ string_of_int i^") -> "
+          ^ CicPp.pp ty names) :: acc,ty) goalproof ([],initial_goal)))) ^
+  "\nand then subsumed by " ^ string_of_int id ^ " when " ^ Subst.ppsubst subst
+;;
+
+module OT = 
+  struct
+    type t = int
+    let compare = Pervasives.compare
+  end
+
+module M = Map.Make(OT)
+
+let rec find_deps bag m i = 
+  if M.mem i m then m
+  else 
+    let p,_,_ = proof_of_id bag i in
+    match p with
+    | Exact _ -> M.add i [] m
+    | Step (_,(_,id1,(_,id2),_)) -> 
+        let m = find_deps bag m id1 in
+        let m = find_deps bag m id2 in
+        (* without the uniq there is a stack overflow doing concatenation *)
+        let xxx = [id1;id2] @ M.find id1 m @ M.find id2 m in 
+        let xxx = HExtlib.list_uniq (List.sort Pervasives.compare xxx) in
+        M.add i xxx m
+;;
+
+let topological_sort bag l = 
+  (* build the partial order relation *)
+  let m = List.fold_left (fun m i -> find_deps bag m i) M.empty l in
+  let m = (* keep only deps inside l *) 
+    List.fold_left 
+      (fun m' i ->
+        M.add i (List.filter (fun x -> List.mem x l) (M.find i m)) m') 
+      M.empty l 
+  in
+  let m = M.map (fun x -> Some x) m in
+  (* utils *)
+  let keys m = M.fold (fun i _ acc -> i::acc) m [] in
+  let split l m = List.filter (fun i -> M.find i m = Some []) l in
+  let purge l m = 
+    M.mapi 
+      (fun k v -> if List.mem k l then None else 
+         match v with
+         | None -> None
+         | Some ll -> Some (List.filter (fun i -> not (List.mem i l)) ll)) 
+      m
+  in
+  let rec aux m res = 
+      let keys = keys m in
+      let ok = split keys m in
+      let m = purge ok m in
+      let res = ok @ res in
+      if ok = [] then res else aux m res
+  in
+  let rc = List.rev (aux m []) in
+  rc
 ;;
+  
 
 (* returns the list of ids that should be factorized *)
-let get_duplicate_step_in_wfo l p =
+let get_duplicate_step_in_wfo bag l p =
   let ol = List.rev l in
   let h = Hashtbl.create 13 in
-  let add i n = 
-    let p,_,_ = proof_of_id i in 
+  (* NOTE: here the n parameter is an approximation of the dependency 
+     between equations. To do things seriously we should maintain a 
+     dependency graph. This approximation is not perfect. *)
+  let add i = 
+    let p,_,_ = proof_of_id bag i in 
     match p with 
     | Exact _ -> true
     | _ -> 
-        try let (pos,no) = Hashtbl.find h i in Hashtbl.replace h i (pos,no+1);false
-        with Not_found -> Hashtbl.add h i (n,1);true
+        try 
+          let no = Hashtbl.find h i in
+          Hashtbl.replace h i (no+1);
+          false
+        with Not_found -> Hashtbl.add h i 1;true
   in
-  let rec aux n = function
-    | Exact _ -> n
+  let rec aux = function
+    | Exact _ -> ()
     | Step (_,(_,i1,(_,i2),_)) -> 
-	let go_on_1 = add i1 n in
-	let go_on_2 = add i2 n in
-        max 
-         (if go_on_1 then aux (n+1) (let p,_,_ = proof_of_id i1 in p) else n+1)
-         (if go_on_2 then aux (n+1) (let p,_,_ = proof_of_id i2 in p) else n+1)
-  in
-  let i = aux 0 p in 
-  let _ = 
-    List.fold_left 
-      (fun acc (_,id,_,_) -> aux acc (let p,_,_ = proof_of_id id in p))
-      i ol
+        let go_on_1 = add i1 in
+        let go_on_2 = add i2 in
+        if go_on_1 then aux (let p,_,_ = proof_of_id bag i1 in p);
+        if go_on_2 then aux (let p,_,_ = proof_of_id bag i2 in p)
   in
+  aux p;
+  List.iter
+    (fun (_,_,id,_,_) -> aux (let p,_,_ = proof_of_id bag id in p))
+    ol;
   (* now h is complete *)
-  let proofs = Hashtbl.fold (fun k (pos,count) acc->(k,pos,count)::acc) h [] in
-  let proofs = List.filter (fun (_,_,c) -> c > 1) proofs in
-  let proofs = 
-    List.sort (fun (_,c1,_) (_,c2,_) -> Pervasives.compare c2 c1) proofs 
-  in
-  List.map (fun (i,_,_) -> i) proofs
+  let proofs = Hashtbl.fold (fun k count acc-> (k,count)::acc) h [] in
+  let proofs = List.filter (fun (_,c) -> c > 1) proofs in
+  let res = topological_sort bag (List.map (fun (i,_) -> i) proofs) in
+  res
 ;;
 
-let build_proof_term h lift proof =
+let build_proof_term bag eq h lift proof =
   let proof_of_id aux id =
-    let p,l,r = proof_of_id id in
+    let p,l,r = proof_of_id bag id in
     try List.assoc id h,l,r with Not_found -> aux p, l, r
   in
   let rec aux = function
-     | Exact term -> CicSubstitution.lift lift term
-     | Step (subst,(_, id1, (pos,id2), pred)) ->
+     | Exact term -> 
+         CicSubstitution.lift lift term
+     | Step (subst,(rule, id1, (pos,id2), pred)) ->
          let p1,_,_ = proof_of_id aux id1 in
          let p2,l,r = proof_of_id aux id2 in
-           build_proof_step lift subst p1 p2 pos l r pred
+         let varname = 
+           match rule with
+           | SuperpositionRight -> Cic.Name ("SupR" ^ Utils.string_of_pos pos) 
+           | Demodulation -> Cic.Name ("DemEq"^ Utils.string_of_pos pos)
+           | _ -> assert false
+         in
+         let pred = 
+           match pred with
+           | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
+           | _ -> assert false
+         in
+         let p = build_proof_step eq lift subst p1 p2 pos l r pred in
+(*         let cond =  (not (List.mem 302 (Utils.metas_of_term p)) || id1 = 8 || id1 = 132) in
+           if not cond then
+             prerr_endline ("ERROR " ^ string_of_int id1 ^ " " ^ string_of_int id2);
+           assert cond;*)
+           p
   in
    aux proof
 ;;
 
-let build_goal_proof l initial ty se =
+let build_goal_proof bag eq l initial ty se context menv =
   let se = List.map (fun i -> Cic.Meta (i,[])) se in 
-  let lets = get_duplicate_step_in_wfo l initial in
+  let lets = get_duplicate_step_in_wfo bag l initial in
   let letsno = List.length lets in
-  let _,mty,_,_ = open_eq ty in
-  let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l 
-  in
+  let lift_list l = List.map (fun (i,t) -> i,CicSubstitution.lift 1 t) l in
   let lets,_,h = 
     List.fold_left
       (fun (acc,n,h) id -> 
-        let p,l,r = proof_of_id id in
-        let cic = build_proof_term h n p in
+        let p,l,r = proof_of_id bag id in
+        let cic = build_proof_term bag eq h n p in
         let real_cic,instance = 
-          parametrize_proof cic l r (CicSubstitution.lift n mty)
+          parametrize_proof cic l r 
         in
         let h = (id, instance)::lift_list h in
         acc@[id,real_cic],n+1,h) 
@@ -571,18 +803,29 @@ let build_goal_proof l initial ty se =
   let proof,se = 
     let rec aux se current_proof = function
       | [] -> current_proof,se
-      | (pos,id,subst,pred)::tl ->
-           let p,l,r = proof_of_id id in
-           let p = build_proof_term h letsno p in
+      | (rule,pos,id,subst,pred)::tl ->
+          let p,l,r = proof_of_id bag id in
+           let p = build_proof_term bag eq h letsno p in
            let pos = if pos = Utils.Left then Utils.Right else Utils.Left in
+         let varname = 
+           match rule with
+           | SuperpositionLeft -> Cic.Name ("SupL" ^ Utils.string_of_pos pos) 
+           | Demodulation -> Cic.Name ("DemG"^ Utils.string_of_pos pos)
+           | _ -> assert false
+         in
+         let pred = 
+           match pred with
+           | Cic.Lambda (_,a,b) -> Cic.Lambda (varname,a,b)
+           | _ -> assert false
+         in
            let proof = 
-             build_proof_step letsno subst current_proof p pos l r pred 
+             build_proof_step eq letsno subst current_proof p pos l r pred
            in
            let proof,se = aux se proof tl in
            Subst.apply_subst_lift letsno subst proof,
-           List.map (fun x -> Subst.apply_subst_lift letsno subst x) se
+           List.map (fun x -> Subst.apply_subst(*_lift letsno*) subst x) se
     in
-    aux se (build_proof_term h letsno initial) l
+    aux se (build_proof_term bag eq h letsno initial) l
   in
   let n,proof = 
     let initial = proof in
@@ -594,41 +837,77 @@ let build_goal_proof l initial ty se =
           cic, p))
     lets (letsno-1,initial)
   in
-  canonical (contextualize_rewrites proof (CicSubstitution.lift letsno ty)), se
+   canonical 
+     (contextualize_rewrites proof (CicSubstitution.lift letsno ty))
+     context menv,
+   se 
 ;;
 
-let refl_proof ty term = 
-  Cic.Appl 
-    [Cic.MutConstruct 
-       (LibraryObjects.eq_URI (), 0, 1, []);
-       ty; term]
+let refl_proof eq_uri ty term = 
+  Cic.Appl [Cic.MutConstruct (eq_uri, 0, 1, []); ty; term]
 ;;
 
-let metas_of_proof p =
-  let p = build_proof_term [] 0 p in
+let metas_of_proof bag p =
+  let eq = 
+    match LibraryObjects.eq_URI () with
+    | Some u -> u 
+    | None -> 
+        raise 
+          (ProofEngineTypes.Fail 
+            (lazy "No default equality defined when calling metas_of_proof"))
+  in
+  let p = build_proof_term bag eq [] 0 p in
   Utils.metas_of_term p
 ;;
 
-let relocate newmeta menv =
-  let subst, metasenv, newmeta = 
+let remove_local_context eq =
+   let w, p, (ty, left, right, o), menv,id = open_equality eq in
+   let p = Utils.remove_local_context p in
+   let ty = Utils.remove_local_context ty in
+   let left = Utils.remove_local_context left in
+   let right = Utils.remove_local_context right in
+   w, p, (ty, left, right, o), menv, id
+;;
+
+let relocate newmeta menv to_be_relocated =
+  let subst, newmetasenv, newmeta = 
     List.fold_right 
-      (fun (i, context, ty) (subst, menv, maxmeta) ->         
-        let irl = [] (*
-         CicMkImplicit.identity_relocation_list_for_metavariable context *)
-        in
-        let newsubst = Subst.buildsubst i context (Cic.Meta(maxmeta,irl)) ty subst in
-        let newmeta = maxmeta, context, ty in
-        newsubst, newmeta::menv, maxmeta+1) 
-      menv (Subst.empty_subst, [], newmeta+1)
+      (fun i (subst, metasenv, maxmeta) ->         
+        let _,context,ty = CicUtil.lookup_meta i menv in
+        let irl = [] in
+        let newmeta = Cic.Meta(maxmeta,irl) in
+        let newsubst = Subst.buildsubst i context newmeta ty subst in
+        newsubst, (maxmeta,context,ty)::metasenv, maxmeta+1) 
+      to_be_relocated (Subst.empty_subst, [], newmeta+1)
   in
-  let metasenv = Subst.apply_subst_metasenv subst metasenv in
-  let subst = Subst.flatten_subst subst in
-  subst, metasenv, newmeta
+  let menv = Subst.apply_subst_metasenv subst menv @ newmetasenv in
+  subst, menv, newmeta
 
+let fix_metas_goal newmeta goal =
+  let (proof, menv, ty) = goal in
+  let to_be_relocated = 
+    HExtlib.list_uniq (List.sort Pervasives.compare (Utils.metas_of_term ty))
+  in
+  let subst, menv, newmeta = relocate newmeta menv to_be_relocated in
+  let ty = Subst.apply_subst subst ty in
+  let proof = 
+    match proof with
+    | [] -> assert false (* is a nonsense to relocate the initial goal *)
+    | (r,pos,id,s,p) :: tl -> (r,pos,id,Subst.concat subst s,p) :: tl
+  in
+  newmeta+1,(proof, menv, ty)
+;;
 
-let fix_metas newmeta eq = 
+let fix_metas bag newmeta eq = 
   let w, p, (ty, left, right, o), menv,_ = open_equality eq in
-  let subst, metasenv, newmeta = relocate newmeta menv in
+  let to_be_relocated = 
+(* List.map (fun i ,_,_ -> i) menv *)
+    HExtlib.list_uniq 
+      (List.sort Pervasives.compare 
+         (Utils.metas_of_term left @ Utils.metas_of_term right @
+         Utils.metas_of_term ty)) 
+  in
+  let subst, metasenv, newmeta = relocate newmeta menv to_be_relocated in
   let ty = Subst.apply_subst subst ty in
   let left = Subst.apply_subst subst left in
   let right = Subst.apply_subst subst right in
@@ -638,15 +917,17 @@ let fix_metas newmeta eq =
         Step (Subst.concat s subst,(r,id1,(pos,id2), pred))
   in
   let p = fix_proof p in
-  let eq = mk_equality (w, p, (ty, left, right, o), metasenv) in
-  newmeta+1, eq  
+  let eq' = mk_equality bag (w, p, (ty, left, right, o), metasenv) in
+  newmeta+1, eq'  
 
 exception NotMetaConvertible;;
 
 let meta_convertibility_aux table t1 t2 =
   let module C = Cic in
-  let rec aux ((table_l, table_r) as table) t1 t2 =
+  let rec aux ((table_l,table_r) as table) t1 t2 =
     match t1, t2 with
+    | C.Meta (m1, tl1), C.Meta (m2, tl2) when m1 = m2 -> table
+    | C.Meta (m1, tl1), C.Meta (m2, tl2) when m1 < m2 -> aux table t2 t1
     | C.Meta (m1, tl1), C.Meta (m2, tl2) ->
         let m1_binding, table_l =
           try List.assoc m1 table_l, table_l
@@ -657,18 +938,7 @@ let meta_convertibility_aux table t1 t2 =
         in
         if (m1_binding <> m2) || (m2_binding <> m1) then
           raise NotMetaConvertible
-        else (
-          try
-            List.fold_left2
-              (fun res t1 t2 ->
-                 match t1, t2 with
-                 | None, Some _ | Some _, None -> raise NotMetaConvertible
-                 | None, None -> res
-                 | Some t1, Some t2 -> (aux res t1 t2))
-              (table_l, table_r) tl1 tl2
-          with Invalid_argument _ ->
-            raise NotMetaConvertible
-        )
+        else table_l,table_r
     | C.Var (u1, ens1), C.Var (u2, ens2)
     | C.Const (u1, ens1), C.Const (u2, ens2) when (UriManager.eq u1 u2) ->
         aux_ens table ens1 ens2
@@ -744,12 +1014,12 @@ let meta_convertibility_eq eq1 eq2 =
     true
   else
     try
-      let table = meta_convertibility_aux ([], []) left left' in
+      let table = meta_convertibility_aux ([],[]) left left' in
       let _ = meta_convertibility_aux table right right' in
       true
     with NotMetaConvertible ->
       try
-        let table = meta_convertibility_aux ([], []) left right' in
+        let table = meta_convertibility_aux ([],[]) left right' in
         let _ = meta_convertibility_aux table right left' in
         true
       with NotMetaConvertible ->
@@ -762,7 +1032,7 @@ let meta_convertibility t1 t2 =
     true
   else
     try
-      ignore(meta_convertibility_aux ([], []) t1 t2);
+      ignore(meta_convertibility_aux ([],[]) t1 t2);
       true
     with NotMetaConvertible ->
       false
@@ -771,21 +1041,20 @@ let meta_convertibility t1 t2 =
 exception TermIsNotAnEquality;;
 
 let term_is_equality term =
-  let iseq uri = UriManager.eq uri (LibraryObjects.eq_URI ()) in
   match term with
-  | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _] when iseq uri -> true
+  | Cic.Appl [Cic.MutInd (uri, _, _); _; _; _] 
+    when LibraryObjects.is_eq_URI uri -> true
   | _ -> false
 ;;
 
-let equality_of_term proof term =
-  let eq_uri = LibraryObjects.eq_URI () in
-  let iseq uri = UriManager.eq uri eq_uri in
+let equality_of_term bag proof term =
   match term with
-  | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] when iseq uri ->
+  | Cic.Appl [Cic.MutInd (uri, _, _); ty; t1; t2] 
+    when LibraryObjects.is_eq_URI uri ->
       let o = !Utils.compare_terms t1 t2 in
       let stat = (ty,t1,t2,o) in
       let w = Utils.compute_equality_weight stat in
-      let e = mk_equality (w, Exact proof, stat,[]) in
+      let e = mk_equality bag (w, Exact proof, stat,[]) in
       e
   | _ ->
       raise TermIsNotAnEquality
@@ -793,24 +1062,26 @@ let equality_of_term proof term =
 
 let is_weak_identity eq = 
   let _,_,(_,left, right,_),_,_ = open_equality eq in
-  left = right || meta_convertibility left right 
+   left = right 
+   (* doing metaconv here is meaningless *)
 ;;
 
 let is_identity (_, context, ugraph) eq = 
   let _,_,(ty,left,right,_),menv,_ = open_equality eq in
-  left = right ||
-  (* (meta_convertibility left right)) *)
-  fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
+  (* doing metaconv here is meaningless *)
+  left = right
+(*   fst (CicReduction.are_convertible ~metasenv:menv context left right ugraph)
+ *   *)
 ;;
 
 
-let term_of_equality equality =
+let term_of_equality eq_uri equality =
   let _, _, (ty, left, right, _), menv, _= open_equality equality in
   let eq i = function Cic.Meta (j, _) -> i = j | _ -> false in
   let argsno = List.length menv in
   let t =
     CicSubstitution.lift argsno
-      (Cic.Appl [Cic.MutInd (LibraryObjects.eq_URI (), 0, []); ty; left; right])
+      (Cic.Appl [Cic.MutInd (eq_uri, 0, []); ty; left; right])
   in
   snd (
     List.fold_right
@@ -826,3 +1097,242 @@ let term_of_equality equality =
       menv (argsno, t))
 ;;
 
+let symmetric bag eq_ty l id uri m =
+  let eq = Cic.MutInd(uri,0,[]) in
+  let pred = 
+    Cic.Lambda (Cic.Name "Sym",eq_ty,
+     Cic.Appl [CicSubstitution.lift 1 eq ;
+               CicSubstitution.lift 1 eq_ty;
+               Cic.Rel 1;CicSubstitution.lift 1 l]) 
+  in
+  let prefl = 
+    Exact (Cic.Appl
+      [Cic.MutConstruct(uri,0,1,[]);eq_ty;l]) 
+  in
+  let id1 = 
+    let eq = mk_equality bag (0,prefl,(eq_ty,l,l,Utils.Eq),m) in
+    let (_,_,_,_,id) = open_equality eq in
+    id
+  in
+  Step(Subst.empty_subst,
+    (Demodulation,id1,(Utils.Left,id),pred))
+;;
+
+module IntOT = struct
+  type t = int
+  let compare = Pervasives.compare
+end
+
+module IntSet = Set.Make(IntOT);;
+
+let n_purged = ref 0;;
+
+let collect ((id_to_eq,_) as bag) alive1 alive2 alive3 =
+(*   let _ = <:start<collect>> in *)
+  let deps_of id = 
+    let p,_,_ = proof_of_id bag id in  
+    match p with
+    | Exact _ -> IntSet.empty
+    | Step (_,(_,id1,(_,id2),_)) ->
+          IntSet.add id1 (IntSet.add id2 IntSet.empty)
+  in
+  let rec close s = 
+    let news = IntSet.fold (fun id s -> IntSet.union (deps_of id) s) s s in
+    if IntSet.equal news s then s else close news
+  in
+  let l_to_s s l = List.fold_left (fun s x -> IntSet.add x s) s l in
+  let alive_set = l_to_s (l_to_s (l_to_s IntSet.empty alive2) alive1) alive3 in
+  let closed_alive_set = close alive_set in
+  let to_purge = 
+    Hashtbl.fold 
+      (fun k _ s -> 
+        if not (IntSet.mem k closed_alive_set) then
+          k::s else s) id_to_eq []
+  in
+  n_purged := !n_purged + List.length to_purge;
+  List.iter (Hashtbl.remove id_to_eq) to_purge;
+(*   let _ = <:stop<collect>> in ()   *)
+;;
+
+let id_of e = 
+  let _,_,_,_,id = open_equality e in id
+;;
+
+let get_stats () = "" 
+(*
+  <:show<Equality.>> ^ 
+  "# of purged eq by the collector: " ^ string_of_int !n_purged ^ "\n"
+*)
+;;
+
+let rec pp_proofterm name t context = 
+  let rec skip_lambda tys ctx = function
+    | Cic.Lambda (n,s,t) -> skip_lambda (s::tys) ((Some n)::ctx) t
+    | t -> ctx,tys,t
+  in
+  let rename s name = 
+    match name with 
+    | Cic.Name s1 -> Cic.Name (s ^ s1)
+    | _ -> assert false
+  in
+  let rec skip_letin ctx = function
+    | Cic.LetIn (n,b,t) -> 
+        pp_proofterm (Some (rename "Lemma " n)) b ctx:: 
+          skip_letin ((Some n)::ctx) t
+    | t -> 
+        let ppterm t = CicPp.pp t ctx in
+        let rec pp inner = function
+          | Cic.Appl [Cic.Const (uri,[]);_;l;m;r;p1;p2] 
+              when Pcre.pmatch ~pat:"trans_eq" (UriManager.string_of_uri uri)->
+                if not inner then
+                  ("     " ^ ppterm l) :: pp true p1 @ 
+                            [ "   = " ^ ppterm m ] @ pp true p2 @ 
+                            [ "   = " ^ ppterm r ]
+                else
+                   pp true p1 @ 
+                            [ "   = " ^ ppterm m ] @ pp true p2 
+          | Cic.Appl [Cic.Const (uri,[]);_;l;m;p] 
+              when Pcre.pmatch ~pat:"sym_eq" (UriManager.string_of_uri uri)->
+                pp true p
+          | Cic.Appl [Cic.Const (uri,[]);_;_;_;_;_;p] 
+              when Pcre.pmatch ~pat:"eq_f" (UriManager.string_of_uri uri)->
+                pp true p
+          | Cic.Appl [Cic.Const (uri,[]);_;_;_;_;_;p] 
+              when Pcre.pmatch ~pat:"eq_f1" (UriManager.string_of_uri uri)->
+                pp true p
+          | Cic.Appl [Cic.MutConstruct (uri,_,_,[]);_;_;t;p] 
+              when Pcre.pmatch ~pat:"ex.ind" (UriManager.string_of_uri uri)->
+                      [ "witness " ^ ppterm t ] @ pp true p
+          | Cic.Appl (t::_) ->[ " [by " ^ ppterm t ^ "]"]
+          | t ->[ " [by " ^ ppterm t ^ "]"]
+        in
+        let rec compat = function
+          | a::b::tl -> (b ^ a) :: compat tl
+          | h::[] -> [h]
+          | [] -> []
+        in
+        let compat l = List.hd l :: compat (List.tl l) in
+        compat (pp false t) @ ["";""]
+  in      
+  let names, tys, body = skip_lambda [] context t in
+  let ppname name = (match name with Some (Cic.Name s) -> s | _ -> "") in
+  ppname name ^ ":\n" ^
+  (if context = [] then
+     let rec pp_l ctx = function
+          | (t,name)::tl -> 
+              "   " ^ ppname name ^ ": " ^ CicPp.pp t ctx ^ "\n" ^ 
+              pp_l (name::ctx) tl
+          | [] -> "\n\n"
+     in
+       pp_l [] (List.rev (List.combine tys names))
+   else "")
+    ^
+  String.concat "\n" (skip_letin names body)
+;;
+
+let pp_proofterm t = 
+  "\n\n" ^ 
+  pp_proofterm (Some (Cic.Name "Hypothesis")) t []
+;;
+
+let initial_nameset_list = [
+ "x"; "y"; "z"; "t"; "u"; "v"; "a"; "b"; "c"; "d"; 
+ "e"; "l"; "m"; "n"; "o"; "p"; "q"; "r"; 
+]
+
+module S = Set.Make(String)
+
+let initial_nameset = List.fold_right S.add initial_nameset_list S.empty, [];;
+
+let freshname (nameset, subst) term = 
+  let m = CicUtil.metas_of_term term in
+  let nameset, subst = 
+    List.fold_left 
+      (fun (set,rc) (m,_) -> 
+        if List.mem_assoc m rc then set,rc else
+        let name = S.choose set in
+        let set = S.remove name set in
+        set, 
+        (m,Cic.Const(UriManager.uri_of_string 
+             ("cic:/"^name^".con"),[]))::rc)
+      (nameset,subst) m
+  in
+  let term = 
+   ProofEngineReduction.replace
+    ~equality:(fun i t -> match t with Cic.Meta (j,_) -> i=j| _ -> false) 
+    ~what:(List.map fst subst) 
+    ~with_what:(List.map snd subst) ~where:term
+  in
+  (nameset, subst), term
+;;
+
+let remove_names_in_context (set,subst) names =
+  List.fold_left
+    (fun s n -> 
+      match n with Some (Cic.Name n) -> S.remove n s | _ -> s) 
+    set names, subst
+;;
+
+let string_of_id2 (id_to_eq,_) names nameset id = 
+  if id = 0 then "" else 
+  try
+    let (_,_,(_,l,r,_),_,_) = open_equality (Hashtbl.find id_to_eq id) in
+    let nameset, l = freshname nameset l in
+    let nameset, r = freshname nameset r in
+    Printf.sprintf "%s = %s" (CicPp.pp l names) (CicPp.pp r names)
+  with
+      Not_found -> assert false
+;;
+
+let draw_proof bag names goal_proof proof id =
+  let b = Buffer.create 100 in
+  let fmt = Format.formatter_of_buffer b in 
+  let sint = string_of_int in
+  let fst3 (x,_,_) = x in
+  let visited = ref [] in
+  let nameset = remove_names_in_context initial_nameset names in
+  let rec fact id = function
+    | Exact t -> 
+        if not (List.mem id !visited) then
+          begin
+          visited := id :: !visited;
+          let nameset, t = freshname nameset t in
+          let t = CicPp.pp t names in
+          GraphvizPp.Dot.node (sint id) 
+          ~attrs:["label",t^":"^string_of_id2 bag names nameset id;
+          "shape","rectangle"] fmt;
+          end
+    | Step (_,(_,id1,(_,id2),_)) ->
+        GraphvizPp.Dot.edge (sint id) (sint id1) fmt;
+        GraphvizPp.Dot.edge (sint id) (sint id2) fmt;
+        let p1,_,_ = proof_of_id bag id1 in
+        let p2,_,_ = proof_of_id bag id2 in
+        fact id1 p1;
+        fact id2 p2;
+        if not (List.mem id !visited); then
+          begin
+          visited := id :: !visited;
+          GraphvizPp.Dot.node (sint id) 
+          ~attrs:["label",sint id^":"^string_of_id2 bag names nameset id;
+                  "shape","ellipse"] fmt
+          end
+  in
+  let sleft acc (_,_,id,_,_) =
+    if acc != 0 then GraphvizPp.Dot.edge (sint acc) (sint id) fmt;
+    fact id (fst3 (proof_of_id bag id));
+    id
+  in
+  GraphvizPp.Dot.header ~node_attrs:["fontsize","10"; ] fmt;
+  ignore(List.fold_left sleft id goal_proof);
+  GraphvizPp.Dot.trailer fmt;
+  let oc = open_out "/tmp/matita_paramod.dot" in
+  Buffer.output_buffer oc b;
+  close_out oc;
+  Utils.debug_print (lazy "dot!");
+  ignore(Unix.system 
+    "dot -Tps -o /tmp/matita_paramod.eps /tmp/matita_paramod.dot"
+(* "cat /tmp/matita_paramod.dot| tred | dot -Tps -o /tmp/matita_paramod.eps" *)
+  );
+  ignore(Unix.system "gv /tmp/matita_paramod.eps");
+;;
+