X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fcomponents%2Fng_paramodulation%2Forderings.ml;h=7743e3726c024f55f9213dfa26f08f0c168b4630;hb=94c7a260ca00f045a3ec1b371f19de757f83003b;hp=3da8477a961d8cb93d84d5889fb2c98f276daf2d;hpb=b60b04a930b208dc0bf8876305c4fa5ea2aeb619;p=helm.git

diff --git a/helm/software/components/ng_paramodulation/orderings.ml b/helm/software/components/ng_paramodulation/orderings.ml
index 3da8477a9..7743e3726 100644
--- a/helm/software/components/ng_paramodulation/orderings.ml
+++ b/helm/software/components/ng_paramodulation/orderings.ml
@@ -11,21 +11,48 @@
 
 (* $Id$ *)
 
-type aux_comparison = XEQ | XLE | XGE | XLT | XGT | XINCOMPARABLE
+type aux_comparison = XEQ | XLE | XGE | XLT | XGT | XINCOMPARABLE | XINVERTIBLE
 
-module Orderings (B : Terms.Blob) = struct
+module type Blob =
+  sig 
+    include Terms.Blob 
 
-  type weight = int * (int * int) list;;
+    (* This order relation should be:
+     * - stable for instantiation
+     * - total on ground terms
+     *
+     *)
+    val compare_terms : 
+          t Terms.foterm -> t Terms.foterm -> Terms.comparison
+
+    val compute_unit_clause_weight : 't Terms.unit_clause -> int
+
+    val compute_goal_weight : 't Terms.unit_clause -> int
+
+    val name : string
+
+  end
   
-  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
-  ;;
+type weight = int * (int * int) list;;
+  
+let rec eq_foterm f x y =
+    x == y ||
+    match x, y with
+    | Terms.Leaf t1, Terms.Leaf t2 -> f t1 t2
+    | Terms.Var i, Terms.Var j -> i = j
+    | Terms.Node l1, Terms.Node l2 -> List.for_all2 (eq_foterm f) l1 l2
+    | _ -> false
+;;
+  
+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 term =
+let weight_of_term term =
     let vars_dict = Hashtbl.create 5 in
     let rec aux = function
       | Terms.Var i -> 
@@ -44,156 +71,234 @@ module Orderings (B : Terms.Blob) = struct
     in
     let compare w1 w2 = 
       match w1, w2 with
-      | (m1, _), (m2, _) -> m2 - m1 
+      | (m1, _), (m2, _) -> m1 - m2
     in 
-    (w, List.sort compare l) (* from the biggest meta to the smallest (0) *)
-  ;;
+    (w, List.sort compare l) (* from the smallest meta to the bigest *)
+;;
   
-  let compute_unit_clause_weight = 
+let compute_unit_clause_weight (_,l, _, _) = 
     let weight_of_polynomial w m =
       let factor = 2 in      
       w + factor * List.fold_left (fun acc (_,occ) -> acc+occ) 0 m
     in
-    function
+    match l with
     | Terms.Predicate t -> 
         let w, m = weight_of_term t in 
         weight_of_polynomial w m
-    | Terms.Equation (_,x,_,Terms.Lt)
+    | Terms.Equation (_,x,_,Terms.Lt) 
     | Terms.Equation (x,_,_,Terms.Gt) ->
         let w, m = weight_of_term x in 
         weight_of_polynomial w m
     | Terms.Equation (l,r,_,Terms.Eq) 
-    | Terms.Equation (l,r,_,Terms.Incomparable) ->
+    | Terms.Equation (l,r,_,Terms.Incomparable) 
+    | Terms.Equation (l,r,_,Terms.Invertible) ->
         let wl, ml = weight_of_term l in 
         let wr, mr = weight_of_term r in 
         weight_of_polynomial (wl+wr) (ml@mr)
-  ;;
-  
-  (* 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)
+;;
+
+(* UNUSED for now *)
+let compute_goal_weight (_,l, _, _) = 
+    let weight_of_polynomial w m =
+      let factor = 2 in      
+      w + factor * List.fold_left (fun acc (_,occ) -> acc+occ) 0 m
     in
-    (cw, wl)
+    match l with
+    | Terms.Predicate t -> 
+        let w, m = weight_of_term t in 
+        weight_of_polynomial w m
+    | Terms.Equation (l,r,_,_) ->
+        let wl, ml = weight_of_term l in 
+        let wr, mr = weight_of_term r in 
+        let wl = weight_of_polynomial wl ml in
+        let wr = weight_of_polynomial wr mr in
+          - (abs (wl-wr))
   ;;
+
+let compute_goal_weight = compute_unit_clause_weight;;
   
+(* Riazanov: 3.1.5 pag 38 *)
+(* Compare weights normalized in a new way :
+ * Variables should be sorted from the lowest index to the highest
+ * Variables which do not occur in the term should not be present
+ * in the normalized polynomial
+ *)
+let compare_weights (h1, w1) (h2, w2) =
+  let rec aux hdiff (lt, gt) diffs w1 w2 =
+    match w1, w2 with
+      | ((var1, w1)::tl1) as l1, (((var2, w2)::tl2) as l2) ->
+          if var1 = var2 then
+            let diffs = (w1 - w2) + diffs in
+            let r = Pervasives.compare w1 w2 in
+            let lt = lt or (r < 0) in
+            let gt = gt or (r > 0) in
+              if lt && gt then XINCOMPARABLE else
+                aux hdiff (lt, gt) diffs tl1 tl2
+          else if var1 < var2 then
+            if lt then XINCOMPARABLE else
+              aux hdiff (false,true) (diffs+w1) tl1 l2        
+          else
+            if gt then XINCOMPARABLE else
+              aux hdiff (true,false) (diffs-w2) l1 tl2
+      | [], (_,w2)::tl2 ->
+          if gt then XINCOMPARABLE else
+            aux hdiff (true,false) (diffs-w2) [] tl2
+      | (_,w1)::tl1, [] ->
+          if lt then XINCOMPARABLE else
+            aux hdiff (false,true) (diffs+w1) tl1 []
+      | [], [] ->
+          if lt then
+            if hdiff <= 0 then XLT
+            else if (- diffs) >= hdiff then XLE else XINCOMPARABLE
+          else if gt then
+            if hdiff >= 0 then XGT
+            else if diffs >= (- hdiff) then XGE else XINCOMPARABLE
+          else
+            if hdiff < 0 then XLT
+            else if hdiff > 0 then XGT
+            else XEQ
+  in
+    aux (h1-h2) (false,false) 0 w1 w2
+;;
+
+(* Riazanov: p. 40, relation >>> 
+ * if head_only=true then it is not >>> but helps case 2 of 3.14 p 39 *)
+let rec aux_ordering b_compare ?(head_only=false) t1 t2 =
+  match t1, t2 with
+  (* We want to discard any identity equality. *
+   * If we give back XEQ, no inference rule    *
+   * will be applied on this equality          *)
+  | Terms.Var i, Terms.Var j when i = j ->
+      XEQ
+  (* 1. *)
+  | Terms.Var _, _
+  | _, Terms.Var _ -> XINCOMPARABLE
+  (* 2.a *)
+  | Terms.Leaf a1, Terms.Leaf a2 -> 
+      let cmp = b_compare a1 a2 in
+      if cmp = 0 then XEQ else if cmp < 0 then XLT else XGT
+  | Terms.Leaf _, Terms.Node _ -> XLT
+  | Terms.Node _, Terms.Leaf _ -> XGT
+  (* 2.b *)
+  | Terms.Node l1, Terms.Node l2 ->
+      let rec cmp t1 t2 =
+        match t1, t2 with
+        | [], [] -> XEQ
+        | _, [] -> (* XGT *) assert false (* hd symbols were eq *)
+        | [], _ -> (* XLT *) assert false (* hd symbols were eq *)
+        | hd1::tl1, hd2::tl2 ->
+            let o = aux_ordering b_compare ~head_only hd1 hd2 in
+            if o = XEQ && not head_only then cmp tl1 tl2 else o
+      in
+      cmp l1 l2
+;;
   
-  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)
-  ;;
-  
-  (* Riazanov: 3.1.5 pag 38 *)
-  (* TODO: optimize early detection of XINCOMPARABLE case *)
-  let compare_weights (h1, w1) (h2, w2) =
-    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
-             | _ -> assert false)
-          ((0, 0, 0), 0) w1 w2
-      with Invalid_argument _ -> assert false
+let compare_terms o x y = 
+    match o x y with
+      | XINCOMPARABLE -> Terms.Incomparable
+      | XGT -> Terms.Gt
+      | XLT -> Terms.Lt
+      | XEQ -> Terms.Eq
+      | XINVERTIBLE -> Terms.Invertible
+      | _ -> assert false
+;;
+
+module NRKBO (B : Terms.Blob) = struct
+  let name = "nrkbo"
+  include B 
+
+  module Pp = Pp.Pp(B)
+
+  let eq_foterm = eq_foterm B.eq;;
+
+exception UnificationFailure of string Lazy.t;;
+
+
+(* DUPLICATE CODE FOR TESTS (see FoUnif)  *)
+  let alpha_eq s t =
+    let rec equiv subst s t =
+      let s = match s with Terms.Var i -> FoSubst.lookup i subst | _ -> s
+      and t = match t with Terms.Var i -> FoSubst.lookup i subst | _ -> t
+        
+      in
+      match s, t with
+        | s, t when eq_foterm s t -> subst
+        | Terms.Var i, Terms.Var j
+            when (not (List.exists (fun (_,k) -> k=t) subst)) ->
+            let subst = FoSubst.build_subst i t subst in
+              subst
+        | Terms.Node l1, Terms.Node l2 -> (
+            try
+              List.fold_left2
+                (fun subst' s t -> equiv subst' s t)
+                subst l1 l2
+            with Invalid_argument _ ->
+              raise (UnificationFailure (lazy "Inference.unification.unif"))
+          )
+        | _, _ ->
+            raise (UnificationFailure (lazy "Inference.unification.unif"))
     in
-    let hdiff = h1 - h2 in 
-    match res with
-    | (0, _, 0) ->
-        if hdiff < 0 then XLT
-        else if hdiff > 0 then XGT
-        else XEQ 
-    | (m, _, 0) ->
-        if hdiff <= 0 then XLT
-        else if (- diffs) >= hdiff then XLE else XINCOMPARABLE
-    | (0, _, m) ->
-        if hdiff >= 0 then XGT
-        else if diffs >= (- hdiff) then XGE else XINCOMPARABLE
-    | (m, _, n) when m > 0 && n > 0 -> XINCOMPARABLE
-    | _ -> assert false 
-  ;;
-  
-  (* Riazanov: p. 40, relation >>> 
-   * if head_only=true then it is not >>> but helps case 2 of 3.14 p 39 *)
-  let rec aux_ordering ?(head_only=false) t1 t2 =
-    match t1, t2 with
-    (* 1. *)
-    | Terms.Var _, _
-    | _, Terms.Var _ -> XINCOMPARABLE
-    (* 2.a *)
-    | Terms.Leaf a1, Terms.Leaf a2 -> 
-        let cmp = B.compare a1 a2 in
-        if cmp = 0 then XEQ else if cmp < 0 then XLT else XGT
-    | Terms.Leaf _, Terms.Node _ -> XLT
-    | Terms.Node _, Terms.Leaf _ -> XGT
-    (* 2.b *)
-    | Terms.Node l1, Terms.Node l2 ->
-        let rec cmp t1 t2 =
-          match t1, t2 with
-          | [], [] -> XEQ
-          | _, [] -> XGT
-          | [], _ -> XLT
-          | hd1::tl1, hd2::tl2 ->
-              let o = aux_ordering ~head_only hd1 hd2 in
-              if o = XEQ && not head_only then cmp tl1 tl2 else o
-        in
-        cmp l1 l2
+      equiv FoSubst.id_subst s t
+;;
+
+let relocate maxvar varlist subst =
+    List.fold_right
+      (fun i (maxvar, varlist, s) -> 
+         maxvar+1, maxvar::varlist, FoSubst.build_subst i (Terms.Var maxvar) s)
+      varlist (maxvar+1, [], subst)
   ;;
+
+  let are_invertible l r =
+    let varlist = (Terms.vars_of_term l)@(Terms.vars_of_term r) in
+    let maxvar = List.fold_left max 0 varlist in
+    let _,_,subst = relocate maxvar varlist FoSubst.id_subst in
+    let newl = FoSubst.apply_subst subst l in
+    let newr = FoSubst.apply_subst subst r in
+      try (let subst = alpha_eq l newr in eq_foterm newl (FoSubst.apply_subst subst r)) with
+	  UnificationFailure _ -> false
+;;
+
+  let compute_unit_clause_weight = compute_unit_clause_weight;;
+  let compute_goal_weight = compute_goal_weight;;
   
   (* Riazanov: p. 40, relation >_n *)
   let nonrec_kbo t1 t2 =
     let w1 = weight_of_term t1 in
     let w2 = weight_of_term t2 in
-    let w1, w2 = normalize_weights w1 w2 in
     match compare_weights w1 w2 with
     | XLE ->  (* this is .> *)
-        if aux_ordering t1 t2 = XLT then XLT else XINCOMPARABLE
+        if aux_ordering B.compare t1 t2 = XLT then XLT else XINCOMPARABLE
     | XGE -> 
-        if aux_ordering t1 t2 = XGT then XGT else XINCOMPARABLE
-    | XEQ -> aux_ordering t1 t2
+        if aux_ordering B.compare t1 t2 = XGT then XGT else XINCOMPARABLE
+    | XEQ -> let res = aux_ordering B.compare t1 t2 in
+	if res = XINCOMPARABLE && are_invertible t1 t2 then XINVERTIBLE
+	else res
     | res -> res
   ;;
+
+  let compare_terms = compare_terms nonrec_kbo;;
+
+  let profiler = HExtlib.profile ~enable:true "compare_terms(nrkbo)";;
+  let compare_terms x y =
+    profiler.HExtlib.profile (compare_terms x) y
+  ;;
+
+end
   
+module KBO (B : Terms.Blob) = struct
+  let name = "kbo"
+  include B 
+
+  module Pp = Pp.Pp(B)
+
+  let eq_foterm = eq_foterm B.eq;;
+
+  let compute_unit_clause_weight = compute_unit_clause_weight;;
+  let compute_goal_weight = compute_goal_weight;;
+
   (* Riazanov: p. 38, relation > *)
   let rec kbo t1 t2 =
-    let aux = aux_ordering ~head_only:true in
+    let aux = aux_ordering B.compare ~head_only:true in
     let rec cmp t1 t2 =
       match t1, t2 with
       | [], [] -> XEQ
@@ -206,7 +311,6 @@ module Orderings (B : Terms.Blob) = struct
     in
     let w1 = weight_of_term t1 in
     let w2 = weight_of_term t2 in
-    let w1, w2 = normalize_weights w1 w2 in
     let comparison = compare_weights w1 w2 in
     match comparison with
     | XLE ->
@@ -231,19 +335,99 @@ module Orderings (B : Terms.Blob) = struct
         let r = aux t1 t2 in
         if r = XEQ then (
           match t1, t2 with
+	  | Terms.Var i, Terms.Var j when i=j -> XEQ
           | Terms.Node (_::tl1), Terms.Node (_::tl2) -> cmp tl1 tl2
           | _, _ ->  XINCOMPARABLE
         ) else r 
     | res -> res
   ;;
+
+  let compare_terms = compare_terms kbo;;
+
+  let profiler = HExtlib.profile ~enable:true "compare_terms(kbo)";;
+  let compare_terms x y =
+    profiler.HExtlib.profile (compare_terms x) y
+  ;;
+
+end
+
+module LPO (B : Terms.Blob) = struct
+  let name = "lpo"
+  include B 
+
+  module Pp = Pp.Pp(B)
+
+  let eq_foterm = eq_foterm B.eq;;
+
+  let compute_unit_clause_weight = compute_unit_clause_weight;;
+  let compute_goal_weight = compute_goal_weight;;
+
+  let rec lpo s t =
+    match s,t with
+      | s, t when eq_foterm s t ->
+          XEQ
+      | Terms.Var _, Terms.Var _ ->
+          XINCOMPARABLE
+      | _, Terms.Var i ->
+          if (List.mem i (Terms.vars_of_term s)) then XGT
+          else XINCOMPARABLE
+      | Terms.Var i,_ ->
+          if (List.mem i (Terms.vars_of_term t)) then XLT
+          else XINCOMPARABLE
+      | Terms.Node (hd1::tl1), Terms.Node (hd2::tl2) ->
+          let rec ge_subterm t ol = function
+            | [] -> (false, ol)
+            | x::tl ->
+                let res = lpo x t in
+                match res with
+                  | XGT | XEQ -> (true,res::ol)
+                  | o -> ge_subterm t (o::ol) tl
+          in
+          let (res, l_ol) = ge_subterm t [] tl1 in
+            if res then XGT
+            else let (res, r_ol) = ge_subterm s [] tl2 in
+              if res then XLT
+              else begin
+                let rec check_subterms t = function
+                  | _,[] -> true
+                  | o::ol,_::tl ->
+                      if o = XLT then check_subterms t (ol,tl)
+                      else false
+                  | [], x::tl ->
+                      if lpo x t = XLT then check_subterms t ([],tl)
+                      else false
+                in
+                match aux_ordering B.compare hd1 hd2 with
+                  | XGT -> if check_subterms s (r_ol,tl2) then XGT
+                    else XINCOMPARABLE
+                  | XLT -> if check_subterms t (l_ol,tl1) then XLT
+                    else XINCOMPARABLE
+                  | XEQ -> 
+                      let lex = List.fold_left2
+                        (fun acc si ti -> if acc = XEQ then lpo si ti else acc)
+                        XEQ tl1 tl2
+                      in
+                 (match lex with
+                    | XGT ->
+                        if List.for_all (fun x -> lpo s x = XGT) tl2 then XGT
+                      else XINCOMPARABLE
+                    | XLT ->
+                        if List.for_all (fun x -> lpo x t = XLT) tl1 then XLT
+                      else XINCOMPARABLE
+                    | o -> o)   
+              | XINCOMPARABLE -> XINCOMPARABLE
+              | _ -> assert false
+          end
+      | _,_ -> aux_ordering B.compare s t
             
-  let compare_terms x y = 
-    match nonrec_kbo x y with
-    | XINCOMPARABLE -> Terms.Incomparable
-    | XGT -> Terms.Gt
-    | XLT -> Terms.Lt
-    | XEQ -> Terms.Eq
-    | _ -> assert false
-  ;; 
+  ;;
+
+  let compare_terms = compare_terms lpo;;
+
+  let profiler = HExtlib.profile ~enable:true "compare_terms(lpo)";;
+  let compare_terms x y =
+    profiler.HExtlib.profile (compare_terms x) y
+  ;;
 
 end
+