2 ||M|| This file is part of HELM, an Hypertextual, Electronic
3 ||A|| Library of Mathematics, developed at the Computer Science
4 ||T|| Department, University of Bologna, Italy.
6 ||T|| HELM is free software; you can redistribute it and/or
7 ||A|| modify it under the terms of the GNU General Public License
8 \ / version 2 or (at your option) any later version.
9 \ / This software is distributed as is, NO WARRANTY.
10 V_______________________________________________________________ *)
14 type aux_comparison = XEQ | XLE | XGE | XLT | XGT | XINCOMPARABLE | XINVERTIBLE
20 (* This order relation should be:
21 * - stable for instantiation
22 * - total on ground terms
26 t Terms.foterm -> t Terms.foterm -> Terms.comparison
28 val compute_clause_weight : 't Terms.clause -> int
34 type weight = int * (int * int) list;;
36 let rec eq_foterm f x y =
39 | Terms.Leaf t1, Terms.Leaf t2 -> f t1 t2
40 | Terms.Var i, Terms.Var j -> i = j
41 | Terms.Node l1, Terms.Node l2 -> List.for_all2 (eq_foterm f) l1 l2
45 let string_of_weight (cw, mw) =
48 (List.map (function (m, w) -> Printf.sprintf "(%d,%d)" m w) mw)
50 Printf.sprintf "[%d; %s]" cw s
53 let weight_of_term term =
54 let vars_dict = Hashtbl.create 5 in
55 let rec aux = function
58 let oldw = Hashtbl.find vars_dict i in
59 Hashtbl.replace vars_dict i (oldw+1)
61 Hashtbl.add vars_dict i 1);
64 | Terms.Node l -> List.fold_left (+) 0 (List.map aux l)
68 Hashtbl.fold (fun meta metaw resw -> (meta, metaw)::resw) vars_dict []
72 | (m1, _), (m2, _) -> m1 - m2
74 (w, List.sort compare l) (* from the smallest meta to the bigest *)
77 let compute_literal_weight l =
78 let weight_of_polynomial w m =
80 w + factor * List.fold_left (fun acc (_,occ) -> acc+occ) 0 m
83 | Terms.Predicate t ->
84 let w, m = weight_of_term t in
85 weight_of_polynomial w m
86 | Terms.Equation (_,x,_,Terms.Lt)
87 | Terms.Equation (x,_,_,Terms.Gt) ->
88 let w, m = weight_of_term x in
89 weight_of_polynomial w m
90 | Terms.Equation (l,r,_,Terms.Eq)
91 | Terms.Equation (l,r,_,Terms.Incomparable)
92 | Terms.Equation (l,r,_,Terms.Invertible) ->
93 let wl, ml = weight_of_term l in
94 let wr, mr = weight_of_term r in
95 weight_of_polynomial (wl+wr) (ml@mr)
98 let compute_clause_weight (_,nl,pl,_,_) =
99 List.fold_left (fun acc (lit,_) -> compute_literal_weight lit + acc) 0 (nl@pl)
101 let compute_goal_weight = compute_clause_weight;;
103 (* Riazanov: 3.1.5 pag 38 *)
104 (* Compare weights normalized in a new way :
105 * Variables should be sorted from the lowest index to the highest
106 * Variables which do not occur in the term should not be present
107 * in the normalized polynomial
109 let compare_weights (h1, w1) (h2, w2) =
110 let rec aux hdiff (lt, gt) diffs w1 w2 =
112 | ((var1, w1)::tl1) as l1, (((var2, w2)::tl2) as l2) ->
114 let diffs = (w1 - w2) + diffs in
115 let r = Pervasives.compare w1 w2 in
116 let lt = lt or (r < 0) in
117 let gt = gt or (r > 0) in
118 if lt && gt then XINCOMPARABLE else
119 aux hdiff (lt, gt) diffs tl1 tl2
120 else if var1 < var2 then
121 if lt then XINCOMPARABLE else
122 aux hdiff (false,true) (diffs+w1) tl1 l2
124 if gt then XINCOMPARABLE else
125 aux hdiff (true,false) (diffs-w2) l1 tl2
127 if gt then XINCOMPARABLE else
128 aux hdiff (true,false) (diffs-w2) [] tl2
130 if lt then XINCOMPARABLE else
131 aux hdiff (false,true) (diffs+w1) tl1 []
134 if hdiff <= 0 then XLT
135 else if (- diffs) >= hdiff then XLE else XINCOMPARABLE
137 if hdiff >= 0 then XGT
138 else if diffs >= (- hdiff) then XGE else XINCOMPARABLE
140 if hdiff < 0 then XLT
141 else if hdiff > 0 then XGT
144 aux (h1-h2) (false,false) 0 w1 w2
147 (* Riazanov: p. 40, relation >>>
148 * if head_only=true then it is not >>> but helps case 2 of 3.14 p 39 *)
149 let rec aux_ordering b_compare ?(head_only=false) t1 t2 =
151 (* We want to discard any identity equality. *
152 * If we give back XEQ, no inference rule *
153 * will be applied on this equality *)
154 | Terms.Var i, Terms.Var j when i = j ->
158 | _, Terms.Var _ -> XINCOMPARABLE
160 | Terms.Leaf a1, Terms.Leaf a2 ->
161 let cmp = b_compare a1 a2 in
162 if cmp = 0 then XEQ else if cmp < 0 then XLT else XGT
163 | Terms.Leaf _, Terms.Node _ -> XLT
164 | Terms.Node _, Terms.Leaf _ -> XGT
166 | Terms.Node l1, Terms.Node l2 ->
170 | _, [] -> (* XGT *) assert false (* hd symbols were eq *)
171 | [], _ -> (* XLT *) assert false (* hd symbols were eq *)
172 | hd1::tl1, hd2::tl2 ->
173 let o = aux_ordering b_compare ~head_only hd1 hd2 in
174 if o = XEQ && not head_only then cmp tl1 tl2 else o
179 let compare_terms o x y =
181 | XINCOMPARABLE -> Terms.Incomparable
185 | XINVERTIBLE -> Terms.Invertible
189 let are_invertible relocate alpha_eq l r =
190 let varlist = Terms.vars_of_term l in
191 let maxvar = List.fold_left max 0 varlist in
192 let _,_,subst = relocate maxvar varlist FoSubst.id_subst in
193 let l = FoSubst.apply_subst subst l in
194 try (ignore(alpha_eq l r);true) with
195 FoUnif.UnificationFailure _ -> false;;
197 module NRKBO (B : Terms.Blob) = struct
202 module Unif = FoUnif.FoUnif(B)
203 module Utils = FoUtils.Utils(B)
205 let eq_foterm = eq_foterm B.eq;;
207 let are_invertible = are_invertible Utils.relocate Unif.alpha_eq;;
209 let compute_clause_weight = compute_clause_weight;;
211 (* Riazanov: p. 40, relation >_n *)
212 let nonrec_kbo t1 t2 =
213 let w1 = weight_of_term t1 in
214 let w2 = weight_of_term t2 in
215 match compare_weights w1 w2 with
216 | XLE -> (* this is .> *)
217 if aux_ordering B.compare t1 t2 = XLT then XLT else XINCOMPARABLE
219 if aux_ordering B.compare t1 t2 = XGT then XGT else XINCOMPARABLE
220 | XEQ -> let res = aux_ordering B.compare t1 t2 in
221 if res = XINCOMPARABLE && are_invertible t1 t2 then XINVERTIBLE
226 let compare_terms = compare_terms nonrec_kbo;;
228 let profiler = HExtlib.profile ~enable:true "compare_terms(nrkbo)";;
229 let compare_terms x y =
230 profiler.HExtlib.profile (compare_terms x) y
235 module KBO (B : Terms.Blob) = struct
240 module Unif = FoUnif.FoUnif(B)
241 module Utils = FoUtils.Utils(B)
243 let eq_foterm = eq_foterm B.eq;;
245 let are_invertible = are_invertible Utils.relocate Unif.alpha_eq;;
247 let compute_clause_weight = compute_clause_weight;;
248 let compute_goal_weight = compute_goal_weight;;
250 (* Riazanov: p. 38, relation > *)
252 let aux = aux_ordering B.compare ~head_only:true in
258 | hd1::tl1, hd2::tl2 ->
259 let o = kbo hd1 hd2 in
260 if o = XEQ then cmp tl1 tl2
263 let w1 = weight_of_term t1 in
264 let w2 = weight_of_term t2 in
265 let comparison = compare_weights w1 w2 in
266 match comparison with
270 else if r = XEQ then (
272 | Terms.Node (_::tl1), Terms.Node (_::tl2) ->
273 if cmp tl1 tl2 = XLT then XLT else XINCOMPARABLE
274 | _, _ -> assert false
279 else if r = XEQ then (
281 | Terms.Node (_::tl1), Terms.Node (_::tl2) ->
282 if cmp tl1 tl2 = XGT then XGT else XINCOMPARABLE
283 | _, _ -> assert false
289 | Terms.Var i, Terms.Var j when i=j -> XEQ
290 | Terms.Node (_::tl1), Terms.Node (_::tl2) -> cmp tl1 tl2
291 | _, _ -> XINCOMPARABLE
296 let compare_terms = compare_terms kbo;;
298 let profiler = HExtlib.profile ~enable:true "compare_terms(kbo)";;
299 let compare_terms x y =
300 profiler.HExtlib.profile (compare_terms x) y
305 module LPO (B : Terms.Blob) = struct
310 module Unif = FoUnif.FoUnif(B)
311 module Utils = FoUtils.Utils(B)
313 let eq_foterm = eq_foterm B.eq;;
315 let are_invertible = are_invertible Utils.relocate Unif.alpha_eq;;
317 let compute_clause_weight = compute_clause_weight;;
318 let compute_goal_weight = compute_goal_weight;;
322 | s, t when eq_foterm s t ->
324 | Terms.Var _, Terms.Var _ ->
327 if (List.mem i (Terms.vars_of_term s)) then XGT
330 if (List.mem i (Terms.vars_of_term t)) then XLT
332 | Terms.Node (hd1::tl1), Terms.Node (hd2::tl2) ->
333 let rec ge_subterm t ol = function
338 | XGT | XEQ -> (true,res::ol)
339 | o -> ge_subterm t (o::ol) tl
341 let (res, l_ol) = ge_subterm t [] tl1 in
343 else let (res, r_ol) = ge_subterm s [] tl2 in
346 let rec check_subterms t = function
349 if o = XLT then check_subterms t (ol,tl)
352 if lpo x t = XLT then check_subterms t ([],tl)
355 match aux_ordering B.compare hd1 hd2 with
356 | XGT -> if check_subterms s (r_ol,tl2) then XGT
358 | XLT -> if check_subterms t (l_ol,tl1) then XLT
361 let lex = List.fold_left2
362 (fun acc si ti -> if acc = XEQ then lpo si ti else acc)
367 if List.for_all (fun x -> lpo s x = XGT) tl2 then XGT
370 if List.for_all (fun x -> lpo x t = XLT) tl1 then XLT
373 | XINCOMPARABLE -> XINCOMPARABLE
376 | _,_ -> aux_ordering B.compare s t
380 let compare_terms = compare_terms lpo;;
382 let profiler = HExtlib.profile ~enable:true "compare_terms(lpo)";;
383 let compare_terms x y =
384 profiler.HExtlib.profile (compare_terms x) y