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 2013-04-23 15:12:29 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
163 type node_summary = int
164 let dummy_summary = -1
174 let has_right (s : node_summary) : bool =
176 let has_left (s : node_summary) : bool =
177 Obj.magic ((s lsr 1) land 1)
179 let is_right (s : node_summary) : bool =
180 Obj.magic ((s lsr 2) land 1)
182 let is_left (s : node_summary) : bool =
183 Obj.magic ((s lsr 3) land 1)
185 let kind (s : node_summary ) : Tree.NodeKind.t =
188 let node_summary is_left is_right has_left has_right kind =
189 ((Obj.magic kind) lsl 4) lor
190 ((Obj.magic is_left) lsl 3) lor
191 ((Obj.magic is_right) lsl 2) lor
192 ((Obj.magic has_left) lsl 1) lor
193 (Obj.magic has_right)
201 summary : node_summary;
205 module Config = Hcons.Make(struct
210 c.unsat == d.unsat &&
212 c.summary == d.summary
215 HASHINT4((c.sat.StateSet.id :> int),
216 (c.unsat.StateSet.id :> int),
217 (c.todo.TransList.id :> int),
224 mutable states : StateSet.t;
225 mutable selection_states: StateSet.t;
226 transitions: (State.t, (QNameSet.t*SFormula.t) list) Hashtbl.t;
227 mutable cache2 : TransList.t Cache.N2.t;
228 mutable cache4 : Config.t Cache.N4.t;
231 let next = Uid.make_maker ()
233 let dummy2 = TransList.cons
234 (Transition.make (State.dummy,QNameSet.empty, SFormula.false_))
239 let dummy_config = Config.make { sat = StateSet.empty;
240 unsat = StateSet.empty;
241 todo = TransList.nil;
242 summary = dummy_summary;
248 let auto = { id = next ();
250 selection_states = ss;
251 transitions = Hashtbl.create 17;
252 cache2 = Cache.N2.create dummy2;
253 cache4 = Cache.N4.create dummy_config;
259 Cache.N2.iteri (fun _ _ _ b -> if b then incr n2) auto.cache2;
260 Cache.N4.iteri (fun _ _ _ _ _ b -> if b then incr n4) auto.cache4;
261 Format.eprintf "STATS: automaton %i, cache2: %i entries, cache6: %i entries\n%!"
262 (auto.id :> int) !n2 !n4;
263 let c2l, c2u = Cache.N2.stats auto.cache2 in
264 let c4l, c4u = Cache.N4.stats auto.cache4 in
265 Format.eprintf "STATS: cache2: length: %i, used: %i, occupation: %f\n%!" c2l c2u (float c2u /. float c2l);
266 Format.eprintf "STATS: cache4: length: %i, used: %i, occupation: %f\n%!" c4l c4u (float c4u /. float c4l)
272 a.cache2 <- Cache.N2.create (Cache.N2.dummy a.cache2);
273 a.cache4 <- Cache.N4.create (Cache.N4.dummy a.cache4)
276 let get_trans_aux a tag states =
277 StateSet.fold (fun q acc0 ->
279 let trs = Hashtbl.find a.transitions q in
280 List.fold_left (fun acc1 (labs, phi) ->
281 if QNameSet.mem tag labs then TransList.cons (Transition.make (q, labs, phi)) acc1 else acc1) acc0 trs
282 with Not_found -> acc0
283 ) states TransList.nil
286 let get_trans a tag states =
288 Cache.N2.find a.cache2
289 (tag.QName.id :> int) (states.StateSet.id :> int)
291 if trs == dummy2 then
292 let trs = get_trans_aux a tag states in
295 (tag.QName.id :> int)
296 (states.StateSet.id :> int) trs; trs)
301 let eval_form phi fcs nss ps ss is_left is_right has_left has_right kind =
303 begin match SFormula.expr phi with
304 Formula.True | Formula.False -> phi
306 let p, b, q = Atom.node a in begin
309 if b == StateSet.mem q fcs then SFormula.true_ else phi
311 if b == StateSet.mem q nss then SFormula.true_ else phi
312 | Parent | Previous_sibling ->
313 if b == StateSet.mem q ps then SFormula.true_ else phi
315 if b == StateSet.mem q ss then SFormula.true_ else phi
316 | Is_first_child -> SFormula.of_bool (b == is_left)
317 | Is_next_sibling -> SFormula.of_bool (b == is_right)
318 | Is k -> SFormula.of_bool (b == (k == kind))
319 | Has_first_child -> SFormula.of_bool (b == has_left)
320 | Has_next_sibling -> SFormula.of_bool (b == has_right)
322 | Formula.And(phi1, phi2) -> SFormula.and_ (loop phi1) (loop phi2)
323 | Formula.Or (phi1, phi2) -> SFormula.or_ (loop phi1) (loop phi2)
328 let int_of_conf is_left is_right has_left has_right kind =
329 ((Obj.magic kind) lsl 4) lor
330 ((Obj.magic is_left) lsl 3) lor
331 ((Obj.magic is_right) lsl 2) lor
332 ((Obj.magic has_left) lsl 1) lor
333 (Obj.magic has_right)
335 let eval_trans auto ltrs fcs nss ps ss is_left is_right has_left has_right kind =
336 let n = int_of_conf is_left is_right has_left has_right kind
337 and k = (fcs.StateSet.id :> int)
338 and l = (nss.StateSet.id :> int)
339 and m = (ps.StateSet.id :> int) in
340 let rec loop ltrs ss =
341 let i = (ltrs.TransList.id :> int)
342 and j = (ss.StateSet.id :> int) in
343 let (new_ltrs, new_ss) as res =
344 let res = Cache.N6.find auto.cache6 i j k l m n in
345 if res == dummy6 then
347 TransList.fold (fun trs (acct, accs) ->
348 let q, lab, phi = Transition.node trs in
349 if StateSet.mem q accs then (acct, accs) else
353 is_left is_right has_left has_right kind
355 if SFormula.is_true new_phi then
356 (acct, StateSet.add q accs)
357 else if SFormula.is_false new_phi then
360 let new_tr = Transition.make (q, lab, new_phi) in
361 (TransList.cons new_tr acct, accs)
362 ) ltrs (TransList.nil, ss)
364 Cache.N6.add auto.cache6 i j k l m n res; res
368 if new_ss == ss then res else
375 let simplify_atom atom pos q { Config.node=config; _ } =
376 if (pos && StateSet.mem q config.sat)
377 || ((not pos) && StateSet.mem q config.unsat) then SFormula.true_
378 else if (pos && StateSet.mem q config.unsat)
379 || ((not pos) && StateSet.mem q config.sat) then SFormula.false_
382 let eval_form phi fcs nss ps ss summary =
384 begin match SFormula.expr phi with
385 Formula.True | Formula.False -> phi
387 let p, b, q = Atom.node a in begin
389 | First_child -> simplify_atom phi b q fcs
390 | Next_sibling -> simplify_atom phi b q nss
391 | Parent | Previous_sibling -> simplify_atom phi b q ps
392 | Stay -> simplify_atom phi b q ss
393 | Is_first_child -> SFormula.of_bool (b == (is_left summary))
394 | Is_next_sibling -> SFormula.of_bool (b == (is_right summary))
395 | Is k -> SFormula.of_bool (b == (k == (kind summary)))
396 | Has_first_child -> SFormula.of_bool (b == (has_left summary))
397 | Has_next_sibling -> SFormula.of_bool (b == (has_right summary))
399 | Formula.And(phi1, phi2) -> SFormula.and_ (loop phi1) (loop phi2)
400 | Formula.Or (phi1, phi2) -> SFormula.or_ (loop phi1) (loop phi2)
407 let eval_trans auto fcs nss ps ss =
408 let fcsid = (fcs.Config.id :> int) in
409 let nssid = (nss.Config.id :> int) in
410 let psid = (ps.Config.id :> int) in
411 let rec loop old_config =
412 let oid = (old_config.Config.id :> int) in
414 let res = Cache.N4.find auto.cache4 oid fcsid nssid psid in
415 if res != dummy_config then res
420 summary = old_summary } = old_config.Config.node
422 let sat, unsat, removed, kept, todo =
425 let q, lab, phi = Transition.node trs in
426 let a_sat, a_unsat, a_rem, a_kept, a_todo = acc in
427 if StateSet.mem q a_sat || StateSet.mem q a_unsat then acc else
429 eval_form phi fcs nss ps old_config old_summary
431 if SFormula.is_true new_phi then
432 StateSet.add q a_sat, a_unsat, StateSet.add q a_rem, a_kept, a_todo
433 else if SFormula.is_false new_phi then
434 a_sat, StateSet.add q a_unsat, StateSet.add q a_rem, a_kept, a_todo
436 let new_tr = Transition.make (q, lab, new_phi) in
437 (a_sat, a_unsat, a_rem, StateSet.add q a_kept, (TransList.cons new_tr a_todo))
438 ) old_todo (old_sat, old_unsat, StateSet.empty, StateSet.empty, TransList.nil)
440 (* States that have been removed from the todo list and not kept are now
442 let unsat = StateSet.union unsat (StateSet.diff removed kept) in
443 (* States that were found once to be satisfiable remain so *)
444 let unsat = StateSet.diff unsat sat in
445 let new_config = Config.make { sat; unsat; todo ; summary = old_summary ; round = 0 } in
446 Cache.N4.add auto.cache4 oid fcsid nssid psid new_config;
449 if res == old_config then res else loop res
454 [add_trans a q labels f] adds a transition [(q,labels) -> f] to the
455 automaton [a] but ensures that transitions remains pairwise disjoint
458 let add_trans a q s f =
459 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
461 List.fold_left (fun (acup, atrs) (labs, phi) ->
462 let lab1 = QNameSet.inter labs s in
463 let lab2 = QNameSet.diff labs s in
465 if QNameSet.is_empty lab1 then []
466 else [ (lab1, SFormula.or_ phi f) ]
469 if QNameSet.is_empty lab2 then []
470 else [ (lab2, SFormula.or_ phi f) ]
472 (QNameSet.union acup labs, tr1@ tr2 @ atrs)
473 ) (QNameSet.empty, []) trs
475 let rem = QNameSet.diff s cup in
476 let ntrs = if QNameSet.is_empty rem then ntrs
477 else (rem, f) :: ntrs
479 Hashtbl.replace a.transitions q ntrs
481 let _pr_buff = Buffer.create 50
482 let _str_fmt = formatter_of_buffer _pr_buff
483 let _flush_str_fmt () = pp_print_flush _str_fmt ();
484 let s = Buffer.contents _pr_buff in
485 Buffer.clear _pr_buff; s
489 "Internal UID: %i@\n\
491 Selection states: %a@\n\
492 Alternating transitions:@\n"
494 StateSet.print a.states
495 StateSet.print a.selection_states;
498 (fun q t acc -> List.fold_left (fun acc (s , f) -> (q,s,f)::acc) acc t)
502 let sorted_trs = List.stable_sort (fun (q1, s1, _) (q2, s2, _) ->
503 let c = State.compare q1 q2 in - (if c == 0 then QNameSet.compare s1 s2 else c))
506 let _ = _flush_str_fmt () in
507 let strs_strings, max_pre, max_all = List.fold_left (fun (accl, accp, acca) (q, s, f) ->
508 let s1 = State.print _str_fmt q; _flush_str_fmt () in
509 let s2 = QNameSet.print _str_fmt s; _flush_str_fmt () in
510 let s3 = SFormula.print _str_fmt f; _flush_str_fmt () in
511 let pre = Pretty.length s1 + Pretty.length s2 in
512 let all = Pretty.length s3 in
513 ( (q, s1, s2, s3) :: accl, max accp pre, max acca all)
514 ) ([], 0, 0) sorted_trs
516 let line = Pretty.line (max_all + max_pre + 6) in
517 let prev_q = ref State.dummy in
518 fprintf fmt "%s@\n" line;
519 List.iter (fun (q, s1, s2, s3) ->
520 if !prev_q != q && !prev_q != State.dummy then fprintf fmt "%s@\n" line;
522 fprintf fmt "%s, %s" s1 s2;
523 fprintf fmt "%s" (Pretty.padding (max_pre - Pretty.length s1 - Pretty.length s2));
524 fprintf fmt " %s %s@\n" Pretty.right_arrow s3;
526 fprintf fmt "%s@\n" line
529 [complete transitions a] ensures that for each state q
530 and each symbols s in the alphabet, a transition q, s exists.
531 (adding q, s -> F when necessary).
534 let complete_transitions a =
535 StateSet.iter (fun q ->
536 let qtrans = Hashtbl.find a.transitions q in
538 List.fold_left (fun rem (labels, _) ->
539 QNameSet.diff rem labels) QNameSet.any qtrans
542 if QNameSet.is_empty rem then qtrans
544 (rem, SFormula.false_) :: qtrans
546 Hashtbl.replace a.transitions q nqtrans
549 let cleanup_states a =
550 let memo = ref StateSet.empty in
552 if not (StateSet.mem q !memo) then begin
553 memo := StateSet.add q !memo;
554 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
555 List.iter (fun (_, phi) ->
556 StateSet.iter loop (SFormula.get_states phi)) trs
559 StateSet.iter loop a.selection_states;
560 let unused = StateSet.diff a.states !memo in
561 StateSet.iter (fun q -> Hashtbl.remove a.transitions q) unused;
564 (* [normalize_negations a] removes negative atoms in the formula
565 complementing the sub-automaton in the negative states.
566 [TODO check the meaning of negative upward arrows]
569 let normalize_negations auto =
570 let memo_state = Hashtbl.create 17 in
571 let todo = Queue.create () in
573 match SFormula.expr f with
574 Formula.True | Formula.False -> if b then f else SFormula.not_ f
575 | Formula.Or(f1, f2) -> (if b then SFormula.or_ else SFormula.and_)(flip b f1) (flip b f2)
576 | Formula.And(f1, f2) -> (if b then SFormula.and_ else SFormula.or_)(flip b f1) (flip b f2)
577 | Formula.Atom(a) -> begin
578 let l, b', q = Atom.node a in
579 if q == State.dummy then if b then f else SFormula.not_ f
581 if b == b' then begin
582 (* a appears positively, either no negation or double negation *)
583 if not (Hashtbl.mem memo_state (q,b)) then Queue.add (q,true) todo;
584 SFormula.atom_ (Atom.make (l, true, q))
586 (* need to reverse the atom
587 either we have a positive state deep below a negation
588 or we have a negative state in a positive formula
589 b' = sign of the state
590 b = sign of the enclosing formula
594 (* does the inverted state of q exist ? *)
595 Hashtbl.find memo_state (q, false)
598 (* create a new state and add it to the todo queue *)
599 let nq = State.make () in
600 auto.states <- StateSet.add nq auto.states;
601 Hashtbl.add memo_state (q, false) nq;
602 Queue.add (q, false) todo; nq
604 SFormula.atom_ (Atom.make (l, true, not_q))
608 (* states that are not reachable from a selection stat are not interesting *)
609 StateSet.iter (fun q -> Queue.add (q, true) todo) auto.selection_states;
611 while not (Queue.is_empty todo) do
612 let (q, b) as key = Queue.pop todo in
615 Hashtbl.find memo_state key
618 let nq = if b then q else
619 let nq = State.make () in
620 auto.states <- StateSet.add nq auto.states;
623 Hashtbl.add memo_state key nq; nq
625 let trans = Hashtbl.find auto.transitions q in
626 let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
627 Hashtbl.replace auto.transitions q' trans';