X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=components%2Ftactics%2Fparamodulation%2Futils.ml;fp=components%2Ftactics%2Fparamodulation%2Futils.ml;h=affd4897f5b7a351906554746b4debc93accb3c3;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1

diff --git a/components/tactics/paramodulation/utils.ml b/components/tactics/paramodulation/utils.ml
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+(* 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 time = true;;
+let debug = false;;
+let debug_metas = false;; 
+let debug_res = false;;
+
+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"
+
+type environment = Cic.metasenv * Cic.context * CicUniv.universe_graph
+
+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
+    | C.Lambda(n,s,t) ->
+	TermSet.union (aux s) (aux t)
+    | C.Prod(n,s,t) ->
+	TermSet.union (aux s) (aux t)
+    | C.LetIn(n,s,ty,t) ->
+	TermSet.union (aux s) (TermSet.union (aux ty) (aux t))
+    | t -> TermSet.empty (* TODO: maybe add other cases? *)
+  in
+  aux term
+;;
+
+let rec remove_local_context =
+  function
+    | Cic.Meta (i,_) -> Cic.Meta (i,[])
+    | Cic.Appl l ->
+       Cic.Appl(List.map remove_local_context l)
+    | t -> t 
+
+
+(************************* 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) ?(count_metas_occurrences=false) 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);
+        if count_metas_occurrences then 1 else 0
+    | C.Meta _ ->  (* "variables" are lighter than constants and functions...*)
+        if count_metas_occurrences then 1 else 0         
+    | 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 goal_symbols = ref TermSet.empty
+
+let set_of_map m = 
+  TermMap.fold (fun k _ s -> TermSet.add k s) m TermSet.empty
+;;
+
+let set_goal_symbols term = 
+  let m = symbols_of_term term in
+  goal_symbols := (set_of_map m)
+;;
+
+let symbols_of_eq (ty,left,right,_) = 
+  let sty = set_of_map (symbols_of_term ty) in
+  let sl = set_of_map (symbols_of_term left) in
+  let sr = set_of_map (symbols_of_term right) in
+  TermSet.union sty (TermSet.union sl sr)
+;;
+
+let distance sgoal seq =
+  let s = TermSet.diff seq sgoal in
+  TermSet.cardinal s
+;;
+
+let compute_equality_weight (ty,left,right,o) =
+  let factor = 2 in
+  match o with
+    | Lt -> 
+	let w, m = (weight_of_term 
+	       ~consider_metas:true ~count_metas_occurrences:false right) in
+	  w + (factor * (List.length m)) ;
+    | Le -> assert false
+    | Gt -> 
+	let w, m = (weight_of_term 
+	       ~consider_metas:true ~count_metas_occurrences:false left) in
+	  w + (factor * (List.length m)) ;
+  | Ge -> assert false
+  | Eq 
+  | Incomparable -> 
+      let w1, m1 = (weight_of_term 
+	       ~consider_metas:true ~count_metas_occurrences:false right) in
+      let w2, m2 = (weight_of_term 
+	       ~consider_metas:true ~count_metas_occurrences:false left) in
+      w1 + w2 + (factor * (List.length m1)) + (factor * (List.length m2))
+;;
+
+let compute_equality_weight e =
+  let w = compute_equality_weight e in
+  let d = 0 in (* distance !goal_symbols (symbols_of_eq e) in *)
+(*
+  prerr_endline (Printf.sprintf "dist %s --- %s === %d" 
+   (String.concat ", " (List.map (CicPp.ppterm) (TermSet.elements
+     !goal_symbols)))
+   (String.concat ", " (List.map (CicPp.ppterm) (TermSet.elements
+     (symbols_of_eq e))))
+   d
+  );
+*)
+  w + d 
+;;
+
+(* old
+let compute_equality_weight (ty,left,right,o) =
+  let metasw = ref 0 in
+  let weight_of t =
+    let w, m = (weight_of_term 
+		  ~consider_metas:true ~count_metas_occurrences:false t) in
+    metasw := !metasw + (1 * (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 
+  (* let w = weight_of (Cic.Appl [ty;left;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
+	 debug_print (lazy ("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 pos = Left | Right 
+
+let string_of_pos = function
+  | Left -> "Left"
+  | Right -> "Right"
+;;
+
+let metas_of_term t = 
+  List.map fst (CicUtil.metas_of_term t)
+;;
+