X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Ftactics%2Fparamodulation%2Futils.ml;fp=helm%2Focaml%2Ftactics%2Fparamodulation%2Futils.ml;h=0000000000000000000000000000000000000000;hb=55b82bd235d82ff7f0a40d980effe1efde1f5073;hp=b212d0faba862c580355b4db09b98ef6142120b7;hpb=771ee8b9d122fa963881c876e86f90531bb7434f;p=helm.git

diff --git a/helm/ocaml/tactics/paramodulation/utils.ml b/helm/ocaml/tactics/paramodulation/utils.ml
deleted file mode 100644
index b212d0fab..000000000
--- a/helm/ocaml/tactics/paramodulation/utils.ml
+++ /dev/null
@@ -1,707 +0,0 @@
-(* Copyright (C) 2005, HELM Team.
- * 
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- * 
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- * 
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA  02111-1307, USA.
- * 
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-(* $Id$ *)
-
-let debug = true;;
-
-let debug_print s = if debug then prerr_endline (Lazy.force s);;
-
-let print_metasenv metasenv =
-  String.concat "\n--------------------------\n"
-    (List.map (fun (i, context, term) ->
-                 (string_of_int i) ^ " [\n" ^ (CicPp.ppcontext context) ^
-                   "\n] " ^  (CicPp.ppterm term))
-       metasenv)
-;;
-
-
-
-
-let print_subst ?(prefix="\n") subst =
-    String.concat prefix
-     (List.map
-       (fun (i, (c, t, ty)) ->
-          Printf.sprintf "?%d -> %s : %s" i
-            (CicPp.ppterm t) (CicPp.ppterm ty))
-       subst)
-;;  
-
-type comparison = Lt | Le | Eq | Ge | Gt | Incomparable;;
-    
-let string_of_comparison = function
-  | Lt -> "<"
-  | Le -> "<="
-  | Gt -> ">"
-  | Ge -> ">="
-  | Eq -> "="
-  | Incomparable -> "I"
-
-module OrderedTerm =
-struct
-  type t = Cic.term
-      
-  let compare = Pervasives.compare
-end
-
-module TermSet = Set.Make(OrderedTerm);;
-module TermMap = Map.Make(OrderedTerm);;
-
-let symbols_of_term term =
-  let module C = Cic in
-  let rec aux map = function
-    | C.Meta _ -> map
-    | C.Appl l ->
-        List.fold_left (fun res t -> (aux res t)) map l
-    | t ->
-        let map = 
-          try
-            let c = TermMap.find t map in
-            TermMap.add t (c+1) map
-          with Not_found ->
-            TermMap.add t 1 map
-        in
-        map
-  in
-  aux TermMap.empty term
-;;
-
-
-let metas_of_term term =
-  let module C = Cic in
-  let rec aux = function
-    | C.Meta _ as t -> TermSet.singleton t
-    | C.Appl l ->
-        List.fold_left (fun res t -> TermSet.union res (aux t)) TermSet.empty l
-    | t -> TermSet.empty (* TODO: maybe add other cases? *)
-  in
-  aux term
-;;
-
-
-(************************* rpo ********************************)
-let number = [
-  UriManager.uri_of_string "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1)",3;
-  UriManager.uri_of_string "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)",6;
-  UriManager.uri_of_string "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)",9;
-  HelmLibraryObjects.Peano.pred_URI, 12;
-  HelmLibraryObjects.Peano.plus_URI, 15;
-  HelmLibraryObjects.Peano.minus_URI, 18;
-  HelmLibraryObjects.Peano.mult_URI, 21;
-  UriManager.uri_of_string "cic:/matita/nat/nat/nat.ind#xpointer(1/1)",103;
-  UriManager.uri_of_string "cic:/matita/nat/nat/nat.ind#xpointer(1/1/1)",106;
-  UriManager.uri_of_string "cic:/matita/nat/nat/nat.ind#xpointer(1/1/2)",109;
-  UriManager.uri_of_string "cic:/matita/nat/nat/pred.con",112;
-  UriManager.uri_of_string "cic:/matita/nat/plus/plus.con",115;
-  UriManager.uri_of_string "cic:/matita/nat/minus/minus.con",118;
-  UriManager.uri_of_string "cic:/matita/nat/times/times.con",121;
-  ]
-;;
-
-let atomic t =
-  match t with
-      Cic.Const _ 
-    | Cic.MutInd _ 
-    | Cic.MutConstruct _ 
-    | Cic.Rel _ -> true
-    | _ -> false
-
-let sig_order_const t1 t2 =
-  try
-    let u1 = CicUtil.uri_of_term t1 in
-    let u2 = CicUtil.uri_of_term t2 in  
-    let n1 = List.assoc u1 number in
-    let n2 = List.assoc u2 number in
-    if n1 < n2 then Lt
-    else if n1 > n2 then Gt
-    else 
-      begin
-	prerr_endline ("t1 = "^(CicPp.ppterm t1));
-	prerr_endline ("t2 = "^(CicPp.ppterm t2)); 
-	assert false
-      end
-  with 
-      Invalid_argument _ 
-    | Not_found -> Incomparable
-
-let sig_order t1 t2 =
-  match t1, t2 with
-      Cic.Rel n, Cic.Rel m when n < m -> Gt (* inverted order *)
-    | Cic.Rel n, Cic.Rel m when n = m -> Incomparable
-    | Cic.Rel n, Cic.Rel m when n > m -> Lt
-    | Cic.Rel _, _ -> Gt
-    | _, Cic.Rel _ -> Lt
-    | _,_ -> sig_order_const t1 t2
-
-let rec rpo_lt t1 t2 =
-  let module C = Cic in 
-  let first_trie =
-    match t1,t2 with 
-	C.Meta (_, _), C.Meta (_,_) -> false
-      | C.Meta (_,_) , t2 -> TermSet.mem t1 (metas_of_term t2)
-      | t1, C.Meta (_,_) -> false
-      | C.Appl [h1;a1],C.Appl [h2;a2] when h1=h2 -> 
-	  rpo_lt a1 a2
-      | C.Appl (h1::arg1),C.Appl (h2::arg2) when h1=h2 ->
-	  if lex_lt arg1 arg2 then
-	    check_lt arg1 t2 
-	  else false
-      | C.Appl (h1::arg1),C.Appl (h2::arg2) -> 
-	  (match sig_order h1 h2 with
-	     | Lt -> check_lt arg1 t2
-	     | _ -> false)
-      | C.Appl (h1::arg1), t2 when atomic t2 ->
-	  (match sig_order h1 t2 with
-	     | Lt -> check_lt arg1 t2
-	     | _ -> false)
-      | t1 , C.Appl (h2::arg2) when atomic t1 ->
-	  (match sig_order t1 h2 with
-	     | Lt -> true
-             | _ -> false )
-      | C.Appl [] , _ -> assert false 
-      | _ , C.Appl [] -> assert false
-      | t1, t2 when (atomic t1 && atomic t2 && t1<>t2) ->
-	  (match sig_order t1 t2 with
-	     | Lt -> true
-	     | _ -> false)
-      | _,_ -> false
-  in
-  if first_trie then true else
-  match t2 with
-      C.Appl (_::args) ->
-	List.exists (fun a -> t1 = a || rpo_lt t1 a) args
-    | _ -> false
- 
-and lex_lt l1 l2 = 
-  match l1,l2 with
-      [],[] -> false
-    | [],_ -> assert false
-    | _, [] -> assert false
-    | a1::l1, a2::l2 when a1 = a2 -> lex_lt l1 l2
-    | a1::_, a2::_ -> rpo_lt a1 a2
- 
-and check_lt l t =
-  List.fold_left 
-    (fun b a -> b && (rpo_lt a t))
-    true l
-;;
-
-let rpo t1 t2 =
-  if rpo_lt t2 t1 then Gt
-  else if rpo_lt t1 t2 then Lt
-  else Incomparable
-
-
-(*********************** fine rpo *****************************)
-
-(* (weight of constants, [(meta, weight_of_meta)]) *)
-type weight = int * (int * int) list;;
-
-let string_of_weight (cw, mw) =
-  let s =
-    String.concat ", "
-      (List.map (function (m, w) -> Printf.sprintf "(%d,%d)" m w) mw)
-  in
-  Printf.sprintf "[%d; %s]" cw s
-
-
-let weight_of_term ?(consider_metas=true) term =
-  let module C = Cic in
-  let vars_dict = Hashtbl.create 5 in
-  let rec aux = function
-    | C.Meta (metano, _) when consider_metas ->
-        (try
-           let oldw = Hashtbl.find vars_dict metano in
-           Hashtbl.replace vars_dict metano (oldw+1)
-         with Not_found ->
-           Hashtbl.add vars_dict metano 1);
-        0
-    | C.Meta _ -> 0 (* "variables" are lighter than constants and functions...*)
-                  
-    | C.Var (_, ens)
-    | C.Const (_, ens)
-    | C.MutInd (_, _, ens)
-    | C.MutConstruct (_, _, _, ens) ->
-        List.fold_left (fun w (u, t) -> (aux t) + w) 1 ens
-          
-    | C.Cast (t1, t2)
-    | C.Lambda (_, t1, t2)
-    | C.Prod (_, t1, t2)
-    | C.LetIn (_, t1, t2) ->
-        let w1 = aux t1 in
-        let w2 = aux t2 in
-        w1 + w2 + 1
-          
-    | C.Appl l -> List.fold_left (+) 0 (List.map aux l)
-        
-    | C.MutCase (_, _, outt, t, pl) ->
-        let w1 = aux outt in
-        let w2 = aux t in
-        let w3 = List.fold_left (+) 0 (List.map aux pl) in
-        w1 + w2 + w3 + 1
-          
-    | C.Fix (_, fl) ->
-        List.fold_left (fun w (n, i, t1, t2) -> (aux t1) + (aux t2) + w) 1 fl
-          
-    | C.CoFix (_, fl) ->
-        List.fold_left (fun w (n, t1, t2) -> (aux t1) + (aux t2) + w) 1 fl
-          
-    | _ -> 1
-  in
-  let w = aux term in
-  let l =
-    Hashtbl.fold (fun meta metaw resw -> (meta, metaw)::resw) vars_dict [] in
-  let compare w1 w2 = 
-    match w1, w2 with
-    | (m1, _), (m2, _) -> m2 - m1 
-  in 
-  (w, List.sort compare l) (* from the biggest meta to the smallest (0) *)
-;;
-
-
-module OrderedInt = struct
-  type t = int
-
-  let compare = Pervasives.compare
-end
-
-module IntSet = Set.Make(OrderedInt)
-
-let compute_equality_weight ty left right =
-  let metasw = ref 0 in
-  let weight_of t =
-    let w, m = (weight_of_term ~consider_metas:true t) in
-    metasw := !metasw + (2 * (List.length m));
-    w
-  in
-  (* Warning: the following let cannot be expanded since it forces the
-     right evaluation order!!!! *)
-  let w = (weight_of ty) + (weight_of left) + (weight_of right) in
-  w + !metasw
-;;
-
-
-(* returns a "normalized" version of the polynomial weight wl (with type
- * weight list), i.e. a list sorted ascending by meta number,
- * from 0 to maxmeta. wl must be sorted descending by meta number. Example:
- * normalize_weight 5 (3, [(3, 2); (1, 1)]) ->
- *      (3, [(1, 1); (2, 0); (3, 2); (4, 0); (5, 0)]) *)
-let normalize_weight maxmeta (cw, wl) =
-  let rec aux = function
-    | 0 -> []
-    | m -> (m, 0)::(aux (m-1))
-  in
-  let tmpl = aux maxmeta in
-  let wl =
-    List.sort
-      (fun (m, _) (n, _) -> Pervasives.compare m n)
-      (List.fold_left
-         (fun res (m, w) -> (m, w)::(List.remove_assoc m res)) tmpl wl)
-  in
-  (cw, wl)
-;;
-
-
-let normalize_weights (cw1, wl1) (cw2, wl2) =
-  let rec aux wl1 wl2 =
-    match wl1, wl2 with
-    | [], [] -> [], []
-    | (m, w)::tl1, (n, w')::tl2 when m = n ->
-        let res1, res2 = aux tl1 tl2 in
-        (m, w)::res1, (n, w')::res2
-    | (m, w)::tl1, ((n, w')::_ as wl2) when m < n ->
-        let res1, res2 = aux tl1 wl2 in
-        (m, w)::res1, (m, 0)::res2
-    | ((m, w)::_ as wl1), (n, w')::tl2 when m > n ->
-        let res1, res2 = aux wl1 tl2 in
-        (n, 0)::res1, (n, w')::res2
-    | [], (n, w)::tl2 ->
-        let res1, res2 = aux [] tl2 in
-        (n, 0)::res1, (n, w)::res2
-    | (m, w)::tl1, [] ->
-        let res1, res2 = aux tl1 [] in
-        (m, w)::res1, (m, 0)::res2
-    | _, _ -> assert false
-  in
-  let cmp (m, _) (n, _) = compare m n in
-  let wl1, wl2 = aux (List.sort cmp wl1) (List.sort cmp wl2) in
-  (cw1, wl1), (cw2, wl2)
-;;
-
-        
-let compare_weights ?(normalize=false)
-    ((h1, w1) as weight1) ((h2, w2) as weight2)=
-  let (h1, w1), (h2, w2) =
-    if normalize then
-      normalize_weights weight1 weight2
-    else
-      (h1, w1), (h2, w2)
-  in
-  let res, diffs =
-    try
-      List.fold_left2
-        (fun ((lt, eq, gt), diffs) w1 w2 ->
-           match w1, w2 with
-           | (meta1, w1), (meta2, w2) when meta1 = meta2 ->
-               let diffs = (w1 - w2) + diffs in 
-               let r = compare w1 w2 in
-               if r < 0 then (lt+1, eq, gt), diffs
-               else if r = 0 then (lt, eq+1, gt), diffs
-               else (lt, eq, gt+1), diffs
-           | (meta1, w1), (meta2, w2) ->
-               debug_print
-                 (lazy
-                    (Printf.sprintf "HMMM!!!! %s, %s\n"
-                       (string_of_weight weight1) (string_of_weight weight2)));
-               assert false)
-        ((0, 0, 0), 0) w1 w2
-    with Invalid_argument _ ->
-      debug_print
-        (lazy
-           (Printf.sprintf "Invalid_argument: %s{%s}, %s{%s}, normalize = %s\n"
-              (string_of_weight (h1, w1)) (string_of_weight weight1)
-              (string_of_weight (h2, w2)) (string_of_weight weight2)
-              (string_of_bool normalize)));
-      assert false
-  in
-  let hdiff = h1 - h2 in 
-  match res with
-  | (0, _, 0) ->
-      if hdiff < 0 then Lt
-      else if hdiff > 0 then Gt
-      else Eq (* Incomparable *)
-  | (m, _, 0) ->
-      if hdiff <= 0 then Lt
-      else if (- diffs) >= hdiff then Le else Incomparable
-  | (0, _, m) ->
-      if hdiff >= 0 then Gt
-      else if diffs >= (- hdiff) then Ge else Incomparable
-  | (m, _, n) when m > 0 && n > 0 ->
-      Incomparable
-  | _ -> assert false 
-
-;;
-
-
-let rec aux_ordering ?(recursion=true) t1 t2 =
-  let module C = Cic in
-  let compare_uris u1 u2 =
-    let res =
-      compare (UriManager.string_of_uri u1) (UriManager.string_of_uri u2) in
-    if res < 0 then Lt
-    else if res = 0 then Eq
-    else Gt
-  in
-  match t1, t2 with
-  | C.Meta _, _
-  | _, C.Meta _ -> Incomparable
-
-  | t1, t2 when t1 = t2 -> Eq
-
-  | C.Rel n, C.Rel m -> if n > m then Lt else Gt
-  | C.Rel _, _ -> Lt
-  | _, C.Rel _ -> Gt
-
-  | C.Const (u1, _), C.Const (u2, _) -> compare_uris u1 u2
-  | C.Const _, _ -> Lt
-  | _, C.Const _ -> Gt
-
-  | C.MutInd (u1, _, _), C.MutInd (u2, _, _) -> compare_uris u1 u2
-  | C.MutInd _, _ -> Lt
-  | _, C.MutInd _ -> Gt
-
-  | C.MutConstruct (u1, _, _, _), C.MutConstruct (u2, _, _, _) ->
-      compare_uris u1 u2
-  | C.MutConstruct _, _ -> Lt
-  | _, C.MutConstruct _ -> Gt
-
-  | C.Appl l1, C.Appl l2 when recursion ->
-      let rec cmp t1 t2 =
-        match t1, t2 with
-        | [], [] -> Eq
-        | _, [] -> Gt
-        | [], _ -> Lt
-        | hd1::tl1, hd2::tl2 ->
-            let o = aux_ordering hd1 hd2 in
-            if o = Eq then cmp tl1 tl2
-            else o
-      in
-      cmp l1 l2
-  | C.Appl (h1::t1), C.Appl (h2::t2) when not recursion ->
-      aux_ordering h1 h2
-        
-  | t1, t2 ->
-      debug_print
-        (lazy
-           (Printf.sprintf "These two terms are not comparable:\n%s\n%s\n\n"
-              (CicPp.ppterm t1) (CicPp.ppterm t2)));
-      Incomparable
-;;
-
-
-(* w1, w2 are the weights, they should already be normalized... *)
-let nonrec_kbo_w (t1, w1) (t2, w2) =
-  match compare_weights w1 w2 with
-  | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
-  | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
-  | Eq -> aux_ordering t1 t2
-  | res -> res
-;;
-
-    
-let nonrec_kbo t1 t2 =
-  let w1 = weight_of_term t1 in
-  let w2 = weight_of_term t2 in
-  (* 
-  prerr_endline ("weight1 :"^(string_of_weight w1));
-  prerr_endline ("weight2 :"^(string_of_weight w2)); 
-  *)
-  match compare_weights ~normalize:true w1 w2 with
-  | Le -> if aux_ordering t1 t2 = Lt then Lt else Incomparable
-  | Ge -> if aux_ordering t1 t2 = Gt then Gt else Incomparable
-  | Eq -> aux_ordering t1 t2
-  | res -> res
-;;
-
-
-let rec kbo t1 t2 =
-  let aux = aux_ordering ~recursion:false in
-  let w1 = weight_of_term t1
-  and w2 = weight_of_term t2 in
-  let rec cmp t1 t2 =
-    match t1, t2 with
-    | [], [] -> Eq
-    | _, [] -> Gt
-    | [], _ -> Lt
-    | hd1::tl1, hd2::tl2 ->
-        let o =
-          kbo hd1 hd2
-        in
-        if o = Eq then cmp tl1 tl2
-        else o
-  in
-  let comparison = compare_weights ~normalize:true w1 w2 in
-  match comparison with
-  | Le ->
-      let r = aux t1 t2 in
-      if r = Lt then Lt
-      else if r = Eq then (
-        match t1, t2 with
-        | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
-            if cmp tl1 tl2 = Lt then Lt else Incomparable
-        | _, _ ->  Incomparable
-      ) else Incomparable
-  | Ge ->
-      let r = aux t1 t2 in
-      if r = Gt then Gt
-      else if r = Eq then (
-        match t1, t2 with
-        | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
-            if cmp tl1 tl2 = Gt then Gt else Incomparable
-        | _, _ ->  Incomparable
-      ) else Incomparable
-  | Eq ->
-      let r = aux t1 t2 in
-      if r = Eq then (
-        match t1, t2 with
-        | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
-            cmp tl1 tl2
-        | _, _ ->  Incomparable
-      ) else r 
-  | res -> res
-;;
-          
-let rec ao t1 t2 =
-  let get_hd t =
-    match t with
-	Cic.MutConstruct(uri,tyno,cno,_) -> Some(uri,tyno,cno)
-      | Cic.Appl(Cic.MutConstruct(uri,tyno,cno,_)::_) -> 
-	  Some(uri,tyno,cno)
-      | _ -> None in
-  let aux = aux_ordering ~recursion:false in
-  let w1 = weight_of_term t1
-  and w2 = weight_of_term t2 in
-  let rec cmp t1 t2 =
-    match t1, t2 with
-    | [], [] -> Eq
-    | _, [] -> Gt
-    | [], _ -> Lt
-    | hd1::tl1, hd2::tl2 ->
-        let o =
-          ao hd1 hd2
-        in
-        if o = Eq then cmp tl1 tl2
-        else o
-  in
-  match get_hd t1, get_hd t2 with
-      Some(_),None -> Lt
-    | None,Some(_) -> Gt
-    | _ ->
-	let comparison = compare_weights ~normalize:true w1 w2 in
-	  match comparison with
-	    | Le ->
-		let r = aux t1 t2 in
-		  if r = Lt then Lt
-		  else if r = Eq then (
-		    match t1, t2 with
-		      | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
-			  if cmp tl1 tl2 = Lt then Lt else Incomparable
-		      | _, _ ->  Incomparable
-		  ) else Incomparable
-	    | Ge ->
-		let r = aux t1 t2 in
-		  if r = Gt then Gt
-		  else if r = Eq then (
-		    match t1, t2 with
-		      | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
-			  if cmp tl1 tl2 = Gt then Gt else Incomparable
-		      | _, _ ->  Incomparable
-		  ) else Incomparable
-	    | Eq ->
-		let r = aux t1 t2 in
-		  if r = Eq then (
-		    match t1, t2 with
-		      | Cic.Appl (h1::tl1), Cic.Appl (h2::tl2) when h1 = h2 ->
-			  cmp tl1 tl2
-		      | _, _ ->  Incomparable
-		  ) else r 
-	    | res -> res
-;;
-
-let names_of_context context = 
-  List.map
-    (function
-       | None -> None
-       | Some (n, e) -> Some n)
-    context
-;;
-
-
-let rec lpo t1 t2 =
-  let module C = Cic in
-  match t1, t2 with
-  | t1, t2 when t1 = t2 -> Eq
-  | t1, (C.Meta _ as m) ->
-      if TermSet.mem m (metas_of_term t1) then Gt else Incomparable
-  | (C.Meta _ as m), t2 ->
-      if TermSet.mem m (metas_of_term t2) then Lt else Incomparable
-  | C.Appl (hd1::tl1), C.Appl (hd2::tl2) -> (
-      let res =
-        let f o r t =
-          if r then true else
-            match lpo t o with
-            | Gt | Eq -> true
-            | _ -> false
-        in
-        let res1 = List.fold_left (f t2) false tl1 in
-        if res1 then Gt
-        else let res2 = List.fold_left (f t1) false tl2 in
-        if res2 then Lt
-        else Incomparable
-      in
-      if res <> Incomparable then
-        res
-      else
-        let f o r t =
-          if not r then false else
-            match lpo o t with
-            | Gt -> true
-            | _ -> false
-        in
-        match aux_ordering hd1 hd2 with
-        | Gt ->
-            let res = List.fold_left (f t1) false tl2 in
-            if res then Gt
-            else Incomparable
-        | Lt ->
-            let res = List.fold_left (f t2) false tl1 in
-            if res then Lt
-            else Incomparable
-        | Eq -> (
-            let lex_res =
-              try
-                List.fold_left2
-                  (fun r t1 t2 -> if r <> Eq then r else lpo t1 t2)
-                  Eq tl1 tl2
-              with Invalid_argument _ ->
-                Incomparable
-            in
-            match lex_res with
-            | Gt ->
-                if List.fold_left (f t1) false tl2 then Gt
-                else Incomparable
-            | Lt ->
-                if List.fold_left (f t2) false tl1 then Lt
-                else Incomparable
-            | _ -> Incomparable
-          )
-        | _ -> Incomparable
-    )
-  | t1, t2 -> aux_ordering t1 t2
-;;
-
-
-(* settable by the user... *)
-let compare_terms = ref nonrec_kbo;; 
-(* let compare_terms = ref ao;; *)
-(* let compare_terms = ref rpo;; *)
-
-let guarded_simpl ?(debug=false) context t =
-  if !compare_terms == nonrec_kbo then t
-  else
-    let t' = ProofEngineReduction.simpl context t in
-    if t = t' then t else
-      begin
-	let simpl_order = !compare_terms t t' in
-	if debug then
-	  prerr_endline ("comparing "^(CicPp.ppterm t)^(CicPp.ppterm t'));
-	if simpl_order = Gt then (if debug then prerr_endline "GT";t')
-	else (if debug then prerr_endline "NO_GT";t)
-      end
-;;
-
-type equality_sign = Negative | Positive;;
-
-let string_of_sign = function
-  | Negative -> "Negative"
-  | Positive -> "Positive"
-;;
-
-
-type pos = Left | Right 
-
-let string_of_pos = function
-  | Left -> "Left"
-  | Right -> "Right"
-;;
-
-
-let eq_ind_URI () = LibraryObjects.eq_ind_URI ~eq:(LibraryObjects.eq_URI ())
-let eq_ind_r_URI () = LibraryObjects.eq_ind_r_URI ~eq:(LibraryObjects.eq_URI ())
-let sym_eq_URI () = LibraryObjects.sym_eq_URI ~eq:(LibraryObjects.eq_URI ())
-let eq_XURI () =
-  let s = UriManager.string_of_uri (LibraryObjects.eq_URI ()) in
-  UriManager.uri_of_string (s ^ "#xpointer(1/1/1)")
-let trans_eq_URI () = LibraryObjects.trans_eq_URI ~eq:(LibraryObjects.eq_URI ())