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 2013-04-22 15:27:36 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;
204 module Config = Hcons.Make(struct
209 c.unsat == d.unsat &&
211 c.summary == d.summary
214 HASHINT4((c.sat.StateSet.id :> int),
215 (c.unsat.StateSet.id :> int),
216 (c.todo.TransList.id :> int),
223 mutable states : StateSet.t;
224 mutable selection_states: StateSet.t;
225 transitions: (State.t, (QNameSet.t*SFormula.t) list) Hashtbl.t;
226 mutable cache2 : TransList.t Cache.N2.t;
227 mutable cache4 : Config.t Cache.N4.t;
230 let next = Uid.make_maker ()
232 let dummy2 = TransList.cons
233 (Transition.make (State.dummy,QNameSet.empty, SFormula.false_))
238 let dummy_config = Config.make { sat = StateSet.empty;
239 unsat = StateSet.empty;
240 todo = TransList.nil;
241 summary = dummy_summary
246 let auto = { id = next ();
248 selection_states = ss;
249 transitions = Hashtbl.create 17;
250 cache2 = Cache.N2.create dummy2;
251 cache4 = Cache.N4.create dummy_config;
257 Cache.N2.iteri (fun _ _ _ b -> if b then incr n2) auto.cache2;
258 Cache.N4.iteri (fun _ _ _ _ _ b -> if b then incr n4) auto.cache4;
259 Format.eprintf "INFO: automaton %i, cache2: %i entries, cache6: %i entries\n%!"
260 (auto.id :> int) !n2 !n4;
261 let c2l, c2u = Cache.N2.stats auto.cache2 in
262 let c4l, c4u = Cache.N4.stats auto.cache4 in
263 Format.eprintf "INFO: cache2: length: %i, used: %i, occupation: %f\n%!" c2l c2u (float c2u /. float c2l);
264 Format.eprintf "INFO: cache4: length: %i, used: %i, occupation: %f\n%!" c4l c4u (float c4u /. float c4l)
270 a.cache2 <- Cache.N2.create (Cache.N2.dummy a.cache2);
271 a.cache4 <- Cache.N4.create (Cache.N4.dummy a.cache4)
274 let get_trans_aux a tag states =
275 StateSet.fold (fun q acc0 ->
277 let trs = Hashtbl.find a.transitions q in
278 List.fold_left (fun acc1 (labs, phi) ->
279 if QNameSet.mem tag labs then TransList.cons (Transition.make (q, labs, phi)) acc1 else acc1) acc0 trs
280 with Not_found -> acc0
281 ) states TransList.nil
284 let get_trans a tag states =
286 Cache.N2.find a.cache2
287 (tag.QName.id :> int) (states.StateSet.id :> int)
289 if trs == dummy2 then
290 let trs = get_trans_aux a tag states in
293 (tag.QName.id :> int)
294 (states.StateSet.id :> int) trs; trs)
299 let eval_form phi fcs nss ps ss is_left is_right has_left has_right kind =
301 begin match SFormula.expr phi with
302 Formula.True | Formula.False -> phi
304 let p, b, q = Atom.node a in begin
307 if b == StateSet.mem q fcs then SFormula.true_ else phi
309 if b == StateSet.mem q nss then SFormula.true_ else phi
310 | Parent | Previous_sibling ->
311 if b == StateSet.mem q ps then SFormula.true_ else phi
313 if b == StateSet.mem q ss then SFormula.true_ else phi
314 | Is_first_child -> SFormula.of_bool (b == is_left)
315 | Is_next_sibling -> SFormula.of_bool (b == is_right)
316 | Is k -> SFormula.of_bool (b == (k == kind))
317 | Has_first_child -> SFormula.of_bool (b == has_left)
318 | Has_next_sibling -> SFormula.of_bool (b == has_right)
320 | Formula.And(phi1, phi2) -> SFormula.and_ (loop phi1) (loop phi2)
321 | Formula.Or (phi1, phi2) -> SFormula.or_ (loop phi1) (loop phi2)
326 let int_of_conf is_left is_right has_left has_right kind =
327 ((Obj.magic kind) lsl 4) lor
328 ((Obj.magic is_left) lsl 3) lor
329 ((Obj.magic is_right) lsl 2) lor
330 ((Obj.magic has_left) lsl 1) lor
331 (Obj.magic has_right)
333 let eval_trans auto ltrs fcs nss ps ss is_left is_right has_left has_right kind =
334 let n = int_of_conf is_left is_right has_left has_right kind
335 and k = (fcs.StateSet.id :> int)
336 and l = (nss.StateSet.id :> int)
337 and m = (ps.StateSet.id :> int) in
338 let rec loop ltrs ss =
339 let i = (ltrs.TransList.id :> int)
340 and j = (ss.StateSet.id :> int) in
341 let (new_ltrs, new_ss) as res =
342 let res = Cache.N6.find auto.cache6 i j k l m n in
343 if res == dummy6 then
345 TransList.fold (fun trs (acct, accs) ->
346 let q, lab, phi = Transition.node trs in
347 if StateSet.mem q accs then (acct, accs) else
351 is_left is_right has_left has_right kind
353 if SFormula.is_true new_phi then
354 (acct, StateSet.add q accs)
355 else if SFormula.is_false new_phi then
358 let new_tr = Transition.make (q, lab, new_phi) in
359 (TransList.cons new_tr acct, accs)
360 ) ltrs (TransList.nil, ss)
362 Cache.N6.add auto.cache6 i j k l m n res; res
366 if new_ss == ss then res else
373 let simplify_atom atom pos q { Config.node=config; _ } =
374 if (pos && StateSet.mem q config.sat)
375 || ((not pos) && StateSet.mem q config.unsat) then SFormula.true_
376 else if (pos && StateSet.mem q config.unsat)
377 || ((not pos) && StateSet.mem q config.sat) then SFormula.false_
381 let eval_form phi fcs nss ps ss summary =
383 begin match SFormula.expr phi with
384 Formula.True | Formula.False -> phi
386 let p, b, q = Atom.node a in begin
388 | First_child -> simplify_atom phi b q fcs
389 | Next_sibling -> simplify_atom phi b q nss
390 | Parent | Previous_sibling -> simplify_atom phi b q ps
391 | Stay -> simplify_atom phi b q ss
392 | Is_first_child -> SFormula.of_bool (b == (is_left summary))
393 | Is_next_sibling -> SFormula.of_bool (b == (is_right summary))
394 | Is k -> SFormula.of_bool (b == (k == (kind summary)))
395 | Has_first_child -> SFormula.of_bool (b == (has_left summary))
396 | Has_next_sibling -> SFormula.of_bool (b == (has_right summary))
398 | Formula.And(phi1, phi2) -> SFormula.and_ (loop phi1) (loop phi2)
399 | Formula.Or (phi1, phi2) -> SFormula.or_ (loop phi1) (loop phi2)
406 let eval_trans auto fcs nss ps ss =
407 let fcsid = (fcs.Config.id :> int) in
408 let nssid = (nss.Config.id :> int) in
409 let psid = (ps.Config.id :> int) in
410 let rec loop old_config =
411 let oid = (old_config.Config.id :> int) in
413 let res = Cache.N4.find auto.cache4 oid fcsid nssid psid in
414 if res != dummy_config then res
419 summary = old_summary } = old_config.Config.node
421 let sat, unsat, removed, kept, todo =
424 let q, lab, phi = Transition.node trs in
425 let a_sat, a_unsat, a_rem, a_kept, a_todo = acc in
426 if StateSet.mem q a_sat || StateSet.mem q a_unsat then acc else
428 eval_form phi fcs nss ps old_config old_summary
430 if SFormula.is_true new_phi then
431 StateSet.add q a_sat, a_unsat, StateSet.add q a_rem, a_kept, a_todo
432 else if SFormula.is_false new_phi then
433 a_sat, StateSet.add q a_unsat, StateSet.add q a_rem, a_kept, a_todo
435 let new_tr = Transition.make (q, lab, new_phi) in
436 (a_sat, a_unsat, a_rem, StateSet.add q a_kept, (TransList.cons new_tr a_todo))
437 ) old_todo (old_sat, old_unsat, StateSet.empty, StateSet.empty, TransList.nil)
439 (* States that have been removed from the todo list and not kept are now
441 let unsat = StateSet.union unsat (StateSet.diff removed kept) in
442 (* States that were found once to be satisfiable remain so *)
443 let unsat = StateSet.diff unsat sat in
444 let new_config = Config.make { sat; unsat; todo ; summary = old_summary } in
445 Cache.N4.add auto.cache4 oid fcsid nssid psid new_config;
448 if res == old_config then res else loop res
453 [add_trans a q labels f] adds a transition [(q,labels) -> f] to the
454 automaton [a] but ensures that transitions remains pairwise disjoint
457 let add_trans a q s f =
458 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
460 List.fold_left (fun (acup, atrs) (labs, phi) ->
461 let lab1 = QNameSet.inter labs s in
462 let lab2 = QNameSet.diff labs s in
464 if QNameSet.is_empty lab1 then []
465 else [ (lab1, SFormula.or_ phi f) ]
468 if QNameSet.is_empty lab2 then []
469 else [ (lab2, SFormula.or_ phi f) ]
471 (QNameSet.union acup labs, tr1@ tr2 @ atrs)
472 ) (QNameSet.empty, []) trs
474 let rem = QNameSet.diff s cup in
475 let ntrs = if QNameSet.is_empty rem then ntrs
476 else (rem, f) :: ntrs
478 Hashtbl.replace a.transitions q ntrs
480 let _pr_buff = Buffer.create 50
481 let _str_fmt = formatter_of_buffer _pr_buff
482 let _flush_str_fmt () = pp_print_flush _str_fmt ();
483 let s = Buffer.contents _pr_buff in
484 Buffer.clear _pr_buff; s
488 "\nInternal UID: %i@\n\
490 Selection states: %a@\n\
491 Alternating transitions:@\n"
493 StateSet.print a.states
494 StateSet.print a.selection_states;
497 (fun q t acc -> List.fold_left (fun acc (s , f) -> (q,s,f)::acc) acc t)
501 let sorted_trs = List.stable_sort (fun (q1, s1, _) (q2, s2, _) ->
502 let c = State.compare q1 q2 in - (if c == 0 then QNameSet.compare s1 s2 else c))
505 let _ = _flush_str_fmt () in
506 let strs_strings, max_pre, max_all = List.fold_left (fun (accl, accp, acca) (q, s, f) ->
507 let s1 = State.print _str_fmt q; _flush_str_fmt () in
508 let s2 = QNameSet.print _str_fmt s; _flush_str_fmt () in
509 let s3 = SFormula.print _str_fmt f; _flush_str_fmt () in
510 let pre = Pretty.length s1 + Pretty.length s2 in
511 let all = Pretty.length s3 in
512 ( (q, s1, s2, s3) :: accl, max accp pre, max acca all)
513 ) ([], 0, 0) sorted_trs
515 let line = Pretty.line (max_all + max_pre + 6) in
516 let prev_q = ref State.dummy in
517 List.iter (fun (q, s1, s2, s3) ->
518 if !prev_q != q && !prev_q != State.dummy then fprintf fmt " %s\n%!" line;
520 fprintf fmt " %s, %s" s1 s2;
521 fprintf fmt "%s" (Pretty.padding (max_pre - Pretty.length s1 - Pretty.length s2));
522 fprintf fmt " %s %s@\n%!" Pretty.right_arrow s3;
524 fprintf fmt " %s\n%!" line
527 [complete transitions a] ensures that for each state q
528 and each symbols s in the alphabet, a transition q, s exists.
529 (adding q, s -> F when necessary).
532 let complete_transitions a =
533 StateSet.iter (fun q ->
534 let qtrans = Hashtbl.find a.transitions q in
536 List.fold_left (fun rem (labels, _) ->
537 QNameSet.diff rem labels) QNameSet.any qtrans
540 if QNameSet.is_empty rem then qtrans
542 (rem, SFormula.false_) :: qtrans
544 Hashtbl.replace a.transitions q nqtrans
547 let cleanup_states a =
548 let memo = ref StateSet.empty in
550 if not (StateSet.mem q !memo) then begin
551 memo := StateSet.add q !memo;
552 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
553 List.iter (fun (_, phi) ->
554 StateSet.iter loop (SFormula.get_states phi)) trs
557 StateSet.iter loop a.selection_states;
558 let unused = StateSet.diff a.states !memo in
559 eprintf "Unused states %a\n%!" StateSet.print unused;
560 StateSet.iter (fun q -> Hashtbl.remove a.transitions q) unused;
563 (* [normalize_negations a] removes negative atoms in the formula
564 complementing the sub-automaton in the negative states.
565 [TODO check the meaning of negative upward arrows]
568 let normalize_negations auto =
569 eprintf "Automaton before normalize_trans:\n";
570 print err_formatter auto;
571 eprintf "--------------------\n%!";
573 let memo_state = Hashtbl.create 17 in
574 let todo = Queue.create () in
576 match SFormula.expr f with
577 Formula.True | Formula.False -> if b then f else SFormula.not_ f
578 | Formula.Or(f1, f2) -> (if b then SFormula.or_ else SFormula.and_)(flip b f1) (flip b f2)
579 | Formula.And(f1, f2) -> (if b then SFormula.and_ else SFormula.or_)(flip b f1) (flip b f2)
580 | Formula.Atom(a) -> begin
581 let l, b', q = Atom.node a in
582 if q == State.dummy then if b then f else SFormula.not_ f
584 if b == b' then begin
585 (* a appears positively, either no negation or double negation *)
586 if not (Hashtbl.mem memo_state (q,b)) then Queue.add (q,true) todo;
587 SFormula.atom_ (Atom.make (l, true, q))
589 (* need to reverse the atom
590 either we have a positive state deep below a negation
591 or we have a negative state in a positive formula
592 b' = sign of the state
593 b = sign of the enclosing formula
597 (* does the inverted state of q exist ? *)
598 Hashtbl.find memo_state (q, false)
601 (* create a new state and add it to the todo queue *)
602 let nq = State.make () in
603 auto.states <- StateSet.add nq auto.states;
604 Hashtbl.add memo_state (q, false) nq;
605 Queue.add (q, false) todo; nq
607 SFormula.atom_ (Atom.make (l, true, not_q))
611 (* states that are not reachable from a selection stat are not interesting *)
612 StateSet.iter (fun q -> Queue.add (q, true) todo) auto.selection_states;
614 while not (Queue.is_empty todo) do
615 let (q, b) as key = Queue.pop todo in
618 Hashtbl.find memo_state key
621 let nq = if b then q else
622 let nq = State.make () in
623 auto.states <- StateSet.add nq auto.states;
626 Hashtbl.add memo_state key nq; nq
628 let trans = Hashtbl.find auto.transitions q in
629 let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
630 Hashtbl.replace auto.transitions q' trans';