1 (***********************************************************************)
5 (* Kim Nguyen, LRI UMR8623 *)
6 (* Université Paris-Sud & CNRS *)
8 (* Copyright 2010-2013 Université Paris-Sud and Centre National de la *)
9 (* Recherche Scientifique. All rights reserved. This file is *)
10 (* distributed under the terms of the GNU Lesser General Public *)
11 (* License, with the special exception on linking described in file *)
14 (***********************************************************************)
17 Time-stamp: <Last modified on 2013-04-18 17:05:32 CEST by Kim Nguyen>
23 type predicate = | First_child
30 | Is of (Tree.NodeKind.t)
34 let is_move p = match p with
35 | First_child | Next_sibling
36 | Parent | Previous_sibling | Stay -> true
40 type atom = predicate * bool * State.t
42 module Atom : (Formula.ATOM with type data = atom) =
48 let equal n1 n2 = n1 = n2
49 let hash n = Hashtbl.hash n
52 include Hcons.Make(Node)
55 let p, b, q = a.node in
56 if not b then fprintf ppf "%s" Pretty.lnot;
58 | First_child -> fprintf ppf "FC(%a)" State.print q
59 | Next_sibling -> fprintf ppf "NS(%a)" State.print q
60 | Parent -> fprintf ppf "FC%s(%a)" Pretty.inverse State.print q
61 | Previous_sibling -> fprintf ppf "NS%s(%a)" Pretty.inverse State.print q
62 | Stay -> fprintf ppf "%s(%a)" Pretty.epsilon State.print q
63 | Is_first_child -> fprintf ppf "FC%s?" Pretty.inverse
64 | Is_next_sibling -> fprintf ppf "NS%s?" Pretty.inverse
65 | Is k -> fprintf ppf "is-%a?" Tree.NodeKind.print k
66 | Has_first_child -> fprintf ppf "FC?"
67 | Has_next_sibling -> fprintf ppf "NS?"
70 let p, b, q = a.node in
78 include Formula.Make(Atom)
80 let mk_atom a b c = atom_ (Atom.make (a,b,c))
81 let mk_kind k = mk_atom (Is k) true State.dummy
83 (mk_atom Has_first_child true State.dummy)
85 let has_next_sibling =
86 (mk_atom Has_next_sibling true State.dummy)
89 (mk_atom Is_first_child true State.dummy)
92 (mk_atom Is_next_sibling true State.dummy)
95 (mk_atom (Is Attribute) true State.dummy)
98 (mk_atom (Is Element) true State.dummy)
100 let is_processing_instruction =
101 (mk_atom (Is ProcessingInstruction) true State.dummy)
104 (mk_atom (Is Comment) true State.dummy)
108 (mk_atom First_child true q)
113 (mk_atom Next_sibling true q)
118 (mk_atom Parent true q)
121 let previous_sibling q =
123 (mk_atom Previous_sibling true q)
127 (mk_atom Stay true q)
132 | Formula.Atom a -> let _, _, q = Atom.node a in
133 if q != State.dummy then StateSet.add q acc else acc
140 module Transition = Hcons.Make (struct
141 type t = State.t * QNameSet.t * SFormula.t
142 let equal (a, b, c) (d, e, f) =
143 a == d && b == e && c == f
145 HASHINT4 (PRIME1, a, ((QNameSet.uid b) :> int), ((SFormula.uid c) :> int))
149 module TransList : sig
150 include Hlist.S with type elt = Transition.t
151 val print : Format.formatter -> ?sep:string -> t -> unit
154 include Hlist.Make(Transition)
155 let print ppf ?(sep="\n") l =
157 let q, lab, f = Transition.node t in
158 fprintf ppf "%a, %a -> %a%s" State.print q QNameSet.print lab SFormula.print f sep) l
164 mutable states : StateSet.t;
165 mutable selection_states: StateSet.t;
166 transitions: (State.t, (QNameSet.t*SFormula.t) list) Hashtbl.t;
167 mutable cache2 : TransList.t Cache.N2.t;
168 mutable cache6 : (TransList.t*StateSet.t) Cache.N6.t;
171 let next = Uid.make_maker ()
173 let dummy2 = TransList.cons
174 (Transition.make (State.dummy,QNameSet.empty, SFormula.false_))
177 let dummy6 = (dummy2, StateSet.empty)
181 let auto = { id = next ();
183 selection_states = ss;
184 transitions = Hashtbl.create 17;
185 cache2 = Cache.N2.create dummy2;
186 cache6 = Cache.N6.create dummy6;
192 Cache.N2.iteri (fun _ _ _ b -> if b then incr n2) auto.cache2;
193 Cache.N6.iteri (fun _ _ _ _ _ _ _ b -> if b then incr n6) auto.cache6;
194 Format.eprintf "INFO: automaton %i, cache2: %i entries, cache6: %i entries\n%!"
195 (auto.id :> int) !n2 !n6;
196 let c2l, c2u = Cache.N2.stats auto.cache2 in
197 let c6l, c6u = Cache.N6.stats auto.cache6 in
198 Format.eprintf "INFO: cache2: length: %i, used: %i, occupation: %f\n%!" c2l c2u (float c2u /. float c2l);
199 Format.eprintf "INFO: cache6: length: %i, used: %i, occupation: %f\n%!" c6l c6u (float c6u /. float c6l)
205 a.cache2 <- Cache.N2.create dummy2;
206 a.cache6 <- Cache.N6.create dummy6
209 let get_trans_aux a tag states =
210 StateSet.fold (fun q acc0 ->
212 let trs = Hashtbl.find a.transitions q in
213 List.fold_left (fun acc1 (labs, phi) ->
214 if QNameSet.mem tag labs then TransList.cons (Transition.make (q, labs, phi)) acc1 else acc1) acc0 trs
215 with Not_found -> acc0
216 ) states TransList.nil
219 let get_trans a tag states =
221 Cache.N2.find a.cache2
222 (tag.QName.id :> int) (states.StateSet.id :> int)
224 if trs == dummy2 then
225 let trs = get_trans_aux a tag states in
228 (tag.QName.id :> int)
229 (states.StateSet.id :> int) trs; trs)
234 let eval_form phi fcs nss ps ss is_left is_right has_left has_right kind =
236 begin match SFormula.expr phi with
237 Formula.True | Formula.False -> phi
239 let p, b, q = Atom.node a in begin
242 if b == StateSet.mem q fcs then SFormula.true_ else phi
244 if b == StateSet.mem q nss then SFormula.true_ else phi
245 | Parent | Previous_sibling ->
246 if b == StateSet.mem q ps then SFormula.true_ else phi
248 if b == StateSet.mem q ss then SFormula.true_ else phi
249 | Is_first_child -> SFormula.of_bool (b == is_left)
250 | Is_next_sibling -> SFormula.of_bool (b == is_right)
251 | Is k -> SFormula.of_bool (b == (k == kind))
252 | Has_first_child -> SFormula.of_bool (b == has_left)
253 | Has_next_sibling -> SFormula.of_bool (b == has_right)
255 | Formula.And(phi1, phi2) -> SFormula.and_ (loop phi1) (loop phi2)
256 | Formula.Or (phi1, phi2) -> SFormula.or_ (loop phi1) (loop phi2)
261 let int_of_conf is_left is_right has_left has_right kind =
262 ((Obj.magic kind) lsl 4) lor
263 ((Obj.magic is_left) lsl 3) lor
264 ((Obj.magic is_right) lsl 2) lor
265 ((Obj.magic has_left) lsl 1) lor
266 (Obj.magic has_right)
268 let eval_trans auto ltrs fcs nss ps ss is_left is_right has_left has_right kind =
269 let n = int_of_conf is_left is_right has_left has_right kind
270 and k = (fcs.StateSet.id :> int)
271 and l = (nss.StateSet.id :> int)
272 and m = (ps.StateSet.id :> int) in
273 let rec loop ltrs ss =
274 let i = (ltrs.TransList.id :> int)
275 and j = (ss.StateSet.id :> int) in
276 let (new_ltrs, new_ss) as res =
277 let res = Cache.N6.find auto.cache6 i j k l m n in
278 if res == dummy6 then
280 TransList.fold (fun trs (acct, accs) ->
281 let q, lab, phi = Transition.node trs in
282 if StateSet.mem q accs then (acct, accs) else
286 is_left is_right has_left has_right kind
288 if SFormula.is_true new_phi then
289 (acct, StateSet.add q accs)
290 else if SFormula.is_false new_phi then
293 let new_tr = Transition.make (q, lab, new_phi) in
294 (TransList.cons new_tr acct, accs)
295 ) ltrs (TransList.nil, ss)
297 Cache.N6.add auto.cache6 i j k l m n res; res
301 if new_ss == ss then res else
315 let eq_config c1 c2 =
316 c1.sat == c2.sat && c1.unsat == c2.unsat && c1.todo == c2.todo
318 let simplify_atom atom pos q config =
319 if (pos && StateSet.mem q config.sat)
320 || ((not pos) && StateSet.mem q config.unsat) then SFormula.true_
321 else if (pos && StateSet.mem q config.unsat)
322 || ((not pos) && StateSet.mem q config.sat) then SFormula.false_
326 let eval_form2 phi fcs nss ps ss is_left is_right has_left has_right kind =
328 begin match SFormula.expr phi with
329 Formula.True | Formula.False -> phi
331 let p, b, q = Atom.node a in begin
333 | First_child -> simplify_atom phi b q fcs
334 | Next_sibling -> simplify_atom phi b q nss
335 | Parent | Previous_sibling -> simplify_atom phi b q ps
336 | Stay -> simplify_atom phi b q ss
337 | Is_first_child -> SFormula.of_bool (b == is_left)
338 | Is_next_sibling -> SFormula.of_bool (b == is_right)
339 | Is k -> SFormula.of_bool (b == (k == kind))
340 | Has_first_child -> SFormula.of_bool (b == has_left)
341 | Has_next_sibling -> SFormula.of_bool (b == has_right)
343 | Formula.And(phi1, phi2) -> SFormula.and_ (loop phi1) (loop phi2)
344 | Formula.Or (phi1, phi2) -> SFormula.or_ (loop phi1) (loop phi2)
351 let eval_trans2 auto fcs nss ps ss is_left is_right has_left has_right kind =
352 let rec loop old_config =
353 let { sat = old_sat; unsat = old_unsat; todo = old_todo } = old_config in
354 let sat, unsat, removed, kept, todo =
357 let q, lab, phi = Transition.node trs in
358 let a_sat, a_unsat, a_rem, a_kept, a_todo = acc in
359 if StateSet.mem q a_sat || StateSet.mem q a_unsat then acc else
362 phi fcs nss ps old_config
363 is_left is_right has_left has_right kind
365 if SFormula.is_true new_phi then
366 StateSet.add q a_sat, a_unsat, StateSet.add q a_rem, a_kept, a_todo
367 else if SFormula.is_false new_phi then
368 a_sat, StateSet.add q a_unsat, StateSet.add q a_rem, a_kept, a_todo
370 let new_tr = Transition.make (q, lab, new_phi) in
371 (a_sat, a_unsat, a_rem, StateSet.add q a_kept, (TransList.cons new_tr a_todo))
372 ) old_todo (old_sat, old_unsat, StateSet.empty, StateSet.empty, TransList.nil)
374 (* States that have been removed from the todo list and not kept are now
376 let unsat = StateSet.union unsat (StateSet.diff removed kept) in
377 (* States that were found once to be satisfiable remain so *)
378 let unsat = StateSet.diff unsat sat in
379 let new_config = { sat; unsat; todo } in
380 if sat == old_sat && unsat == old_unsat && todo == old_todo then new_config
386 [add_trans a q labels f] adds a transition [(q,labels) -> f] to the
387 automaton [a] but ensures that transitions remains pairwise disjoint
390 let add_trans a q s f =
391 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
393 List.fold_left (fun (acup, atrs) (labs, phi) ->
394 let lab1 = QNameSet.inter labs s in
395 let lab2 = QNameSet.diff labs s in
397 if QNameSet.is_empty lab1 then []
398 else [ (lab1, SFormula.or_ phi f) ]
401 if QNameSet.is_empty lab2 then []
402 else [ (lab2, SFormula.or_ phi f) ]
404 (QNameSet.union acup labs, tr1@ tr2 @ atrs)
405 ) (QNameSet.empty, []) trs
407 let rem = QNameSet.diff s cup in
408 let ntrs = if QNameSet.is_empty rem then ntrs
409 else (rem, f) :: ntrs
411 Hashtbl.replace a.transitions q ntrs
413 let _pr_buff = Buffer.create 50
414 let _str_fmt = formatter_of_buffer _pr_buff
415 let _flush_str_fmt () = pp_print_flush _str_fmt ();
416 let s = Buffer.contents _pr_buff in
417 Buffer.clear _pr_buff; s
421 "\nInternal UID: %i@\n\
423 Selection states: %a@\n\
424 Alternating transitions:@\n"
426 StateSet.print a.states
427 StateSet.print a.selection_states;
430 (fun q t acc -> List.fold_left (fun acc (s , f) -> (q,s,f)::acc) acc t)
434 let sorted_trs = List.stable_sort (fun (q1, s1, _) (q2, s2, _) ->
435 let c = State.compare q1 q2 in - (if c == 0 then QNameSet.compare s1 s2 else c))
438 let _ = _flush_str_fmt () in
439 let strs_strings, max_pre, max_all = List.fold_left (fun (accl, accp, acca) (q, s, f) ->
440 let s1 = State.print _str_fmt q; _flush_str_fmt () in
441 let s2 = QNameSet.print _str_fmt s; _flush_str_fmt () in
442 let s3 = SFormula.print _str_fmt f; _flush_str_fmt () in
443 let pre = Pretty.length s1 + Pretty.length s2 in
444 let all = Pretty.length s3 in
445 ( (q, s1, s2, s3) :: accl, max accp pre, max acca all)
446 ) ([], 0, 0) sorted_trs
448 let line = Pretty.line (max_all + max_pre + 6) in
449 let prev_q = ref State.dummy in
450 List.iter (fun (q, s1, s2, s3) ->
451 if !prev_q != q && !prev_q != State.dummy then fprintf fmt " %s\n%!" line;
453 fprintf fmt " %s, %s" s1 s2;
454 fprintf fmt "%s" (Pretty.padding (max_pre - Pretty.length s1 - Pretty.length s2));
455 fprintf fmt " %s %s@\n%!" Pretty.right_arrow s3;
457 fprintf fmt " %s\n%!" line
460 [complete transitions a] ensures that for each state q
461 and each symbols s in the alphabet, a transition q, s exists.
462 (adding q, s -> F when necessary).
465 let complete_transitions a =
466 StateSet.iter (fun q ->
467 let qtrans = Hashtbl.find a.transitions q in
469 List.fold_left (fun rem (labels, _) ->
470 QNameSet.diff rem labels) QNameSet.any qtrans
473 if QNameSet.is_empty rem then qtrans
475 (rem, SFormula.false_) :: qtrans
477 Hashtbl.replace a.transitions q nqtrans
480 let cleanup_states a =
481 let memo = ref StateSet.empty in
483 if not (StateSet.mem q !memo) then begin
484 memo := StateSet.add q !memo;
485 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
486 List.iter (fun (_, phi) ->
487 StateSet.iter loop (SFormula.get_states phi)) trs
490 StateSet.iter loop a.selection_states;
491 let unused = StateSet.diff a.states !memo in
492 eprintf "Unused states %a\n%!" StateSet.print unused;
493 StateSet.iter (fun q -> Hashtbl.remove a.transitions q) unused;
496 (* [normalize_negations a] removes negative atoms in the formula
497 complementing the sub-automaton in the negative states.
498 [TODO check the meaning of negative upward arrows]
501 let normalize_negations auto =
502 eprintf "Automaton before normalize_trans:\n";
503 print err_formatter auto;
504 eprintf "--------------------\n%!";
506 let memo_state = Hashtbl.create 17 in
507 let todo = Queue.create () in
509 match SFormula.expr f with
510 Formula.True | Formula.False -> if b then f else SFormula.not_ f
511 | Formula.Or(f1, f2) -> (if b then SFormula.or_ else SFormula.and_)(flip b f1) (flip b f2)
512 | Formula.And(f1, f2) -> (if b then SFormula.and_ else SFormula.or_)(flip b f1) (flip b f2)
513 | Formula.Atom(a) -> begin
514 let l, b', q = Atom.node a in
515 if q == State.dummy then if b then f else SFormula.not_ f
517 if b == b' then begin
518 (* a appears positively, either no negation or double negation *)
519 if not (Hashtbl.mem memo_state (q,b)) then Queue.add (q,true) todo;
520 SFormula.atom_ (Atom.make (l, true, q))
522 (* need to reverse the atom
523 either we have a positive state deep below a negation
524 or we have a negative state in a positive formula
525 b' = sign of the state
526 b = sign of the enclosing formula
530 (* does the inverted state of q exist ? *)
531 Hashtbl.find memo_state (q, false)
534 (* create a new state and add it to the todo queue *)
535 let nq = State.make () in
536 auto.states <- StateSet.add nq auto.states;
537 Hashtbl.add memo_state (q, false) nq;
538 Queue.add (q, false) todo; nq
540 SFormula.atom_ (Atom.make (l, true, not_q))
544 (* states that are not reachable from a selection stat are not interesting *)
545 StateSet.iter (fun q -> Queue.add (q, true) todo) auto.selection_states;
547 while not (Queue.is_empty todo) do
548 let (q, b) as key = Queue.pop todo in
551 Hashtbl.find memo_state key
554 let nq = if b then q else
555 let nq = State.make () in
556 auto.states <- StateSet.add nq auto.states;
559 Hashtbl.add memo_state key nq; nq
561 let trans = Hashtbl.find auto.transitions q in
562 let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
563 Hashtbl.replace auto.transitions q' trans';