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 (***********************************************************************)
19 type predicate = | First_child
26 | Is of (Tree.NodeKind.t)
30 let is_move p = match p with
31 | First_child | Next_sibling
32 | Parent | Previous_sibling | Stay -> true
36 type atom = predicate * bool * State.t
38 module Atom : (Formula.ATOM with type data = atom) =
44 let equal n1 n2 = n1 = n2
45 let hash n = Hashtbl.hash n
48 include Hcons.Make(Node)
51 let p, b, q = a.node in
52 if not b then fprintf ppf "%s" Pretty.lnot;
54 | First_child -> fprintf ppf "FC(%a)" State.print q
55 | Next_sibling -> fprintf ppf "NS(%a)" State.print q
56 | Parent -> fprintf ppf "FC%s(%a)" Pretty.inverse State.print q
57 | Previous_sibling -> fprintf ppf "NS%s(%a)" Pretty.inverse State.print q
58 | Stay -> fprintf ppf "%s(%a)" Pretty.epsilon State.print q
59 | Is_first_child -> fprintf ppf "FC%s?" Pretty.inverse
60 | Is_next_sibling -> fprintf ppf "NS%s?" Pretty.inverse
61 | Is k -> fprintf ppf "is-%a?" Tree.NodeKind.print k
62 | Has_first_child -> fprintf ppf "FC?"
63 | Has_next_sibling -> fprintf ppf "NS?"
66 let p, b, q = a.node in
74 include Formula.Make(Atom)
76 let mk_atom a b c = atom_ (Atom.make (a,b,c))
77 let mk_kind k = mk_atom (Is k) true State.dummy
79 (mk_atom Has_first_child true State.dummy)
81 let has_next_sibling =
82 (mk_atom Has_next_sibling true State.dummy)
85 (mk_atom Is_first_child true State.dummy)
88 (mk_atom Is_next_sibling true State.dummy)
91 (mk_atom (Is Attribute) true State.dummy)
94 (mk_atom (Is Element) true State.dummy)
96 let is_processing_instruction =
97 (mk_atom (Is ProcessingInstruction) true State.dummy)
100 (mk_atom (Is Comment) true State.dummy)
104 (mk_atom First_child true q)
109 (mk_atom Next_sibling true q)
114 (mk_atom Parent true q)
117 let previous_sibling q =
119 (mk_atom Previous_sibling true q)
123 (mk_atom Stay true q)
128 | Formula.Atom a -> let _, _, q = Atom.node a in
129 if q != State.dummy then StateSet.add q acc else acc
136 module Transition = Hcons.Make (struct
137 type t = State.t * QNameSet.t * SFormula.t
138 let equal (a, b, c) (d, e, f) =
139 a == d && b == e && c == f
141 HASHINT4 (PRIME1, a, ((QNameSet.uid b) :> int), ((SFormula.uid c) :> int))
145 module TransList : sig
146 include Hlist.S with type elt = Transition.t
147 val print : Format.formatter -> ?sep:string -> t -> unit
150 include Hlist.Make(Transition)
151 let print ppf ?(sep="\n") l =
153 let q, lab, f = Transition.node t in
154 fprintf ppf "%a, %a -> %a%s" State.print q QNameSet.print lab SFormula.print f sep) l
159 type node_summary = int
160 let dummy_summary = -1
170 let has_right (s : node_summary) : bool =
172 let has_left (s : node_summary) : bool =
173 Obj.magic ((s lsr 1) land 1)
175 let is_right (s : node_summary) : bool =
176 Obj.magic ((s lsr 2) land 1)
178 let is_left (s : node_summary) : bool =
179 Obj.magic ((s lsr 3) land 1)
181 let kind (s : node_summary ) : Tree.NodeKind.t =
184 let node_summary is_left is_right has_left has_right kind =
185 ((Obj.magic kind) lsl 4) lor
186 ((Obj.magic is_left) lsl 3) lor
187 ((Obj.magic is_right) lsl 2) lor
188 ((Obj.magic has_left) lsl 1) lor
189 (Obj.magic has_right)
197 summary : node_summary;
200 module Config = Hcons.Make(struct
205 c.unsat == d.unsat &&
207 c.summary == d.summary
210 HASHINT4((c.sat.StateSet.id :> int),
211 (c.unsat.StateSet.id :> int),
212 (c.todo.TransList.id :> int),
219 mutable states : StateSet.t;
220 mutable selection_states: StateSet.t;
221 transitions: (State.t, (QNameSet.t*SFormula.t) list) Hashtbl.t;
222 mutable cache2 : TransList.t Cache.N2.t;
223 mutable cache4 : Config.t Cache.N4.t;
226 let next = Uid.make_maker ()
228 let dummy2 = TransList.cons
229 (Transition.make (State.dummy,QNameSet.empty, SFormula.false_))
235 Config.make { sat = StateSet.empty;
236 unsat = StateSet.empty;
237 todo = TransList.nil;
238 summary = dummy_summary
243 let auto = { id = next ();
245 selection_states = ss;
246 transitions = Hashtbl.create 17;
247 cache2 = Cache.N2.create dummy2;
248 cache4 = Cache.N4.create dummy_config;
254 Cache.N2.iteri (fun _ _ _ b -> if b then incr n2) auto.cache2;
255 Cache.N4.iteri (fun _ _ _ _ _ b -> if b then incr n4) auto.cache4;
256 Logger.msg `STATS "automaton %i, cache2: %i entries, cache6: %i entries"
257 (auto.id :> int) !n2 !n4;
258 let c2l, c2u = Cache.N2.stats auto.cache2 in
259 let c4l, c4u = Cache.N4.stats auto.cache4 in
261 "cache2: length: %i, used: %i, occupation: %f"
262 c2l c2u (float c2u /. float c2l);
264 "cache4: length: %i, used: %i, occupation: %f"
265 c4l c4u (float c4u /. float c4l)
271 a.cache4 <- Cache.N4.create (Cache.N4.dummy a.cache4)
275 a.cache2 <- Cache.N2.create (Cache.N2.dummy a.cache2)
278 let get_trans_aux a tag states =
279 StateSet.fold (fun q acc0 ->
281 let trs = Hashtbl.find a.transitions q in
282 List.fold_left (fun acc1 (labs, phi) ->
283 if QNameSet.mem tag labs then TransList.cons (Transition.make (q, labs, phi)) acc1 else acc1) acc0 trs
284 with Not_found -> acc0
285 ) states TransList.nil
288 let get_trans a tag states =
290 Cache.N2.find a.cache2
291 (tag.QName.id :> int) (states.StateSet.id :> int)
293 if trs == dummy2 then
294 let trs = get_trans_aux a tag states in
297 (tag.QName.id :> int)
298 (states.StateSet.id :> int) trs; trs)
301 let simplify_atom atom pos q { Config.node=config; _ } =
302 if (pos && StateSet.mem q config.sat)
303 || ((not pos) && StateSet.mem q config.unsat) then SFormula.true_
304 else if (pos && StateSet.mem q config.unsat)
305 || ((not pos) && StateSet.mem q config.sat) then SFormula.false_
308 let eval_form phi fcs nss ps ss summary =
310 begin match SFormula.expr phi with
311 Formula.True | Formula.False -> phi
313 let p, b, q = Atom.node a in begin
315 | First_child -> simplify_atom phi b q fcs
316 | Next_sibling -> simplify_atom phi b q nss
317 | Parent | Previous_sibling -> simplify_atom phi b q ps
318 | Stay -> simplify_atom phi b q ss
319 | Is_first_child -> SFormula.of_bool (b == (is_left summary))
320 | Is_next_sibling -> SFormula.of_bool (b == (is_right summary))
321 | Is k -> SFormula.of_bool (b == (k == (kind summary)))
322 | Has_first_child -> SFormula.of_bool (b == (has_left summary))
323 | Has_next_sibling -> SFormula.of_bool (b == (has_right summary))
325 | Formula.And(phi1, phi2) -> SFormula.and_ (loop phi1) (loop phi2)
326 | Formula.Or (phi1, phi2) -> SFormula.or_ (loop phi1) (loop phi2)
333 let eval_trans auto fcs nss ps ss =
334 let fcsid = (fcs.Config.id :> int) in
335 let nssid = (nss.Config.id :> int) in
336 let psid = (ps.Config.id :> int) in
337 let rec loop old_config =
338 let oid = (old_config.Config.id :> int) in
340 let res = Cache.N4.find auto.cache4 oid fcsid nssid psid in
341 if res != dummy_config then res
346 summary = old_summary } = old_config.Config.node
348 let sat, unsat, removed, kept, todo =
351 let q, lab, phi = Transition.node trs in
352 let a_sat, a_unsat, a_rem, a_kept, a_todo = acc in
353 if StateSet.mem q a_sat || StateSet.mem q a_unsat then acc else
355 eval_form phi fcs nss ps old_config old_summary
357 if SFormula.is_true new_phi then
358 StateSet.add q a_sat, a_unsat, StateSet.add q a_rem, a_kept, a_todo
359 else if SFormula.is_false new_phi then
360 a_sat, StateSet.add q a_unsat, StateSet.add q a_rem, a_kept, a_todo
362 let new_tr = Transition.make (q, lab, new_phi) in
363 (a_sat, a_unsat, a_rem, StateSet.add q a_kept, (TransList.cons new_tr a_todo))
364 ) old_todo (old_sat, old_unsat, StateSet.empty, StateSet.empty, TransList.nil)
366 (* States that have been removed from the todo list and not kept are now
368 let unsat = StateSet.union unsat (StateSet.diff removed kept) in
369 (* States that were found once to be satisfiable remain so *)
370 let unsat = StateSet.diff unsat sat in
371 let new_config = Config.make { old_config.Config.node with sat; unsat; todo; } in
372 Cache.N4.add auto.cache4 oid fcsid nssid psid new_config;
375 if res == old_config then res else loop res
380 [add_trans a q labels f] adds a transition [(q,labels) -> f] to the
381 automaton [a] but ensures that transitions remains pairwise disjoint
384 let add_trans a q s f =
385 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
387 List.fold_left (fun (acup, atrs) (labs, phi) ->
388 let lab1 = QNameSet.inter labs s in
389 let lab2 = QNameSet.diff labs s in
391 if QNameSet.is_empty lab1 then []
392 else [ (lab1, SFormula.or_ phi f) ]
395 if QNameSet.is_empty lab2 then []
396 else [ (lab2, SFormula.or_ phi f) ]
398 (QNameSet.union acup labs, tr1@ tr2 @ atrs)
399 ) (QNameSet.empty, []) trs
401 let rem = QNameSet.diff s cup in
402 let ntrs = if QNameSet.is_empty rem then ntrs
403 else (rem, f) :: ntrs
405 Hashtbl.replace a.transitions q ntrs
407 let _pr_buff = Buffer.create 50
408 let _str_fmt = formatter_of_buffer _pr_buff
409 let _flush_str_fmt () = pp_print_flush _str_fmt ();
410 let s = Buffer.contents _pr_buff in
411 Buffer.clear _pr_buff; s
415 "Internal UID: %i@\n\
417 Selection states: %a@\n\
418 Alternating transitions:@\n"
420 StateSet.print a.states
421 StateSet.print a.selection_states;
424 (fun q t acc -> List.fold_left (fun acc (s , f) -> (q,s,f)::acc) acc t)
428 let sorted_trs = List.stable_sort (fun (q1, s1, _) (q2, s2, _) ->
429 let c = State.compare q1 q2 in - (if c == 0 then QNameSet.compare s1 s2 else c))
432 let _ = _flush_str_fmt () in
433 let strs_strings, max_pre, max_all = List.fold_left (fun (accl, accp, acca) (q, s, f) ->
434 let s1 = State.print _str_fmt q; _flush_str_fmt () in
435 let s2 = QNameSet.print _str_fmt s; _flush_str_fmt () in
436 let s3 = SFormula.print _str_fmt f; _flush_str_fmt () in
437 let pre = Pretty.length s1 + Pretty.length s2 in
438 let all = Pretty.length s3 in
439 ( (q, s1, s2, s3) :: accl, max accp pre, max acca all)
440 ) ([], 0, 0) sorted_trs
442 let line = Pretty.line (max_all + max_pre + 6) in
443 let prev_q = ref State.dummy in
444 fprintf fmt "%s@\n" line;
445 List.iter (fun (q, s1, s2, s3) ->
446 if !prev_q != q && !prev_q != State.dummy then fprintf fmt "%s@\n" line;
448 fprintf fmt "%s, %s" s1 s2;
449 fprintf fmt "%s" (Pretty.padding (max_pre - Pretty.length s1 - Pretty.length s2));
450 fprintf fmt " %s %s@\n" Pretty.right_arrow s3;
452 fprintf fmt "%s@\n" line
455 [complete transitions a] ensures that for each state q
456 and each symbols s in the alphabet, a transition q, s exists.
457 (adding q, s -> F when necessary).
460 let complete_transitions a =
461 StateSet.iter (fun q ->
462 let qtrans = Hashtbl.find a.transitions q in
464 List.fold_left (fun rem (labels, _) ->
465 QNameSet.diff rem labels) QNameSet.any qtrans
468 if QNameSet.is_empty rem then qtrans
470 (rem, SFormula.false_) :: qtrans
472 Hashtbl.replace a.transitions q nqtrans
475 let cleanup_states a =
476 let memo = ref StateSet.empty in
478 if not (StateSet.mem q !memo) then begin
479 memo := StateSet.add q !memo;
480 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
481 List.iter (fun (_, phi) ->
482 StateSet.iter loop (SFormula.get_states phi)) trs
485 StateSet.iter loop a.selection_states;
486 let unused = StateSet.diff a.states !memo in
487 StateSet.iter (fun q -> Hashtbl.remove a.transitions q) unused;
490 (* [normalize_negations a] removes negative atoms in the formula
491 complementing the sub-automaton in the negative states.
492 [TODO check the meaning of negative upward arrows]
495 let normalize_negations auto =
496 let memo_state = Hashtbl.create 17 in
497 let todo = Queue.create () in
499 match SFormula.expr f with
500 Formula.True | Formula.False -> if b then f else SFormula.not_ f
501 | Formula.Or(f1, f2) -> (if b then SFormula.or_ else SFormula.and_)(flip b f1) (flip b f2)
502 | Formula.And(f1, f2) -> (if b then SFormula.and_ else SFormula.or_)(flip b f1) (flip b f2)
503 | Formula.Atom(a) -> begin
504 let l, b', q = Atom.node a in
505 if q == State.dummy then if b then f else SFormula.not_ f
507 if b == b' then begin
508 (* a appears positively, either no negation or double negation *)
509 if not (Hashtbl.mem memo_state (q,b)) then Queue.add (q,true) todo;
510 SFormula.atom_ (Atom.make (l, true, q))
512 (* need to reverse the atom
513 either we have a positive state deep below a negation
514 or we have a negative state in a positive formula
515 b' = sign of the state
516 b = sign of the enclosing formula
520 (* does the inverted state of q exist ? *)
521 Hashtbl.find memo_state (q, false)
524 (* create a new state and add it to the todo queue *)
525 let nq = State.make () in
526 auto.states <- StateSet.add nq auto.states;
527 Hashtbl.add memo_state (q, false) nq;
528 Queue.add (q, false) todo; nq
530 SFormula.atom_ (Atom.make (l, true, not_q))
534 (* states that are not reachable from a selection stat are not interesting *)
535 StateSet.iter (fun q -> Queue.add (q, true) todo) auto.selection_states;
537 while not (Queue.is_empty todo) do
538 let (q, b) as key = Queue.pop todo in
541 Hashtbl.find memo_state key
544 let nq = if b then q else
545 let nq = State.make () in
546 auto.states <- StateSet.add nq auto.states;
549 Hashtbl.add memo_state key nq; nq
551 let trans = Hashtbl.find auto.transitions q in
552 let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
553 Hashtbl.replace auto.transitions q' trans';