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 move = [ `First_child
28 type 'a table = 'a array
33 | `Previous_sibling -> 3
39 | 3 -> `Previous_sibling
43 let create_table a = Array.make 5 a
44 let get m k = m.(idx k)
45 let set m k v = m.(idx k) <- v
46 let iter f m = Array.iteri (fun i v -> f (ridx i) v) m
49 iter (fun i v -> acc := f i v !acc) m;
53 iter (fun i v -> if not (p i v) then raise Exit) m;
57 let for_all2 p m1 m2 =
62 if not (p (ridx i) v1 v2) then raise Exit
70 iter (fun i v -> if p i v then raise Exit) m;
76 `First_child -> fprintf ppf "%s" Pretty.down_arrow
77 | `Next_sibling -> fprintf ppf "%s" Pretty.right_arrow
78 | `Parent -> fprintf ppf "%s" Pretty.up_arrow
79 | `Previous_sibling -> fprintf ppf "%s" Pretty.left_arrow
80 | `Stay -> fprintf ppf "%s" Pretty.bullet
82 let print_table pr_e ppf m =
83 iter (fun i v -> fprintf ppf "%a: %a" print i pr_e v;
84 if (idx i) < 4 then fprintf ppf ", ") m
87 type predicate = Move of move * State.t
90 | Is of Tree.NodeKind.t
100 let equal n1 n2 = n1 = n2
101 let hash n = Hashtbl.hash n
104 include Hcons.Make(Node)
109 fprintf ppf "%a%a" Move.print m State.print q
110 | Is_first_child -> fprintf ppf "%s?" Pretty.up_arrow
111 | Is_next_sibling -> fprintf ppf "%s?" Pretty.left_arrow
112 | Is k -> fprintf ppf "is-%a?" Tree.NodeKind.print k
113 | Has_first_child -> fprintf ppf "%s?" Pretty.down_arrow
114 | Has_next_sibling -> fprintf ppf "%s?" Pretty.right_arrow
121 include Boolean.Make(Atom)
123 let mk_atom a = atom_ (Atom.make a)
124 let is k = mk_atom (Is k)
126 let has_first_child = mk_atom Has_first_child
128 let has_next_sibling = mk_atom Has_next_sibling
130 let is_first_child = mk_atom Is_first_child
132 let is_next_sibling = mk_atom Is_next_sibling
134 let is_attribute = mk_atom (Is Attribute)
136 let is_element = mk_atom (Is Element)
138 let is_processing_instruction = mk_atom (Is ProcessingInstruction)
140 let is_comment = mk_atom (Is Comment)
142 let mk_move m q = mk_atom (Move(m,q))
145 (mk_move `First_child q)
150 (mk_move `Next_sibling q)
158 let previous_sibling q =
160 (mk_move `Previous_sibling q)
163 let stay q = mk_move `Stay q
165 let get_states_by_move phi =
166 let table = Move.create_table StateSet.empty in
169 | Boolean.Atom ({ Atom.node = Move(v,q) ; _ }, _) ->
170 let s = Move.get table v in
171 Move.set table v (StateSet.add q s)
176 let table = get_states_by_move phi in
177 Move.fold (fun _ s acc -> StateSet.union s acc) table StateSet.empty
179 let rec rename_state phi qfrom qto =
183 | Or (phi1, phi2) -> or_ (rename_state phi1 qfrom qto) (rename_state phi2 qfrom qto)
184 | And (phi1, phi2) -> and_ (rename_state phi1 qfrom qto) (rename_state phi2 qfrom qto)
185 | Atom ({ Atom.node = Move(m, q); }, b) when q == qfrom ->
186 let atm = mk_move m qto in if b then atm else not_ atm
192 include Hcons.Make (struct
193 type t = State.t * QNameSet.t * Formula.t
194 let equal (a, b, c) (d, e, f) =
195 a == d && b == e && c == f
196 let hash ((a, b, c) : t) =
197 HASHINT4 (PRIME1, ((a) :> int), ((QNameSet.uid b) :> int), ((Formula.uid c) :> int))
200 let q, l, f = t.node in
201 fprintf ppf "%a, %a %s %a"
209 module TransList : sig
210 include Hlist.S with type elt = Transition.t
211 val print : ?sep:string -> Format.formatter -> t -> unit
214 include Hlist.Make(Transition)
215 let print ?(sep="\n") ppf l =
217 fprintf ppf "%a%s" Transition.print t sep) l
224 mutable states : StateSet.t;
225 mutable starting_states : StateSet.t;
226 mutable selecting_states: StateSet.t;
227 transitions: (State.t, (QNameSet.t*Formula.t) list) Hashtbl.t;
228 mutable ranked_states : StateSet.t array
233 let get_states a = a.states
234 let get_starting_states a = a.starting_states
235 let get_selecting_states a = a.selecting_states
236 let get_states_by_rank a = a.ranked_states
237 let get_max_rank a = Array.length a.ranked_states - 1
239 let _pr_buff = Buffer.create 50
240 let _str_fmt = formatter_of_buffer _pr_buff
241 let _flush_str_fmt () = pp_print_flush _str_fmt ();
242 let s = Buffer.contents _pr_buff in
243 Buffer.clear _pr_buff; s
246 let _ = _flush_str_fmt() in
248 "Internal UID: %i@\n\
250 Number of states: %i@\n\
251 Starting states: %a@\n\
252 Selection states: %a@\n\
253 Ranked states: %a@\n\
254 Alternating transitions:@\n"
256 StateSet.print a.states
257 (StateSet.cardinal a.states)
258 StateSet.print a.starting_states
259 StateSet.print a.selecting_states
260 (let r = ref 0 in Pretty.print_array ~sep:", " (fun ppf s ->
261 fprintf ppf "%i:%a" !r StateSet.print s; incr r)) a.ranked_states;
264 (fun q t acc -> List.fold_left (fun acc (s , f) -> (q,s,f)::acc) acc t)
268 let sorted_trs = List.stable_sort (fun (q1, s1, _) (q2, s2, _) ->
269 let c = State.compare q2 q1 in if c == 0 then QNameSet.compare s2 s1 else c)
272 let _ = _flush_str_fmt () in
273 let strs_strings, max_pre, max_all =
274 List.fold_left (fun (accl, accp, acca) (q, s, f) ->
275 let s1 = State.print _str_fmt q; _flush_str_fmt () in
276 let s2 = QNameSet.print _str_fmt s; _flush_str_fmt () in
277 let s3 = Formula.print _str_fmt f; _flush_str_fmt () in
278 let pre = Pretty.length s1 + Pretty.length s2 in
279 let all = Pretty.length s3 in
280 ( (q, s1, s2, s3) :: accl, max accp pre, max acca all)
281 ) ([], 0, 0) sorted_trs
283 let line = Pretty.line (max_all + max_pre + 6) in
284 let prev_q = ref State.dummy_state in
285 fprintf fmt "%s@\n" line;
286 List.iter (fun (q, s1, s2, s3) ->
287 if !prev_q != q && !prev_q != State.dummy_state then fprintf fmt "%s@\n" line;
289 fprintf fmt "%s, %s" s1 s2;
291 (Pretty.padding (max_pre - Pretty.length s1 - Pretty.length s2));
292 fprintf fmt " %s %s@\n" Pretty.left_arrow s3;
294 fprintf fmt "%s@\n" line
297 let get_trans a tag states =
298 StateSet.fold (fun q acc0 ->
300 let trs = Hashtbl.find a.transitions q in
301 List.fold_left (fun acc1 (labs, phi) ->
302 if QNameSet.mem tag labs then
303 TransList.cons (Transition.make (q, labs, phi)) acc1
305 with Not_found -> acc0
306 ) states TransList.nil
309 let get_form a tag q =
311 let trs = Hashtbl.find a.transitions q in
312 List.fold_left (fun aphi (labs, phi) ->
313 if QNameSet.mem tag labs then Formula.or_ aphi phi else aphi
316 Not_found -> Formula.false_
319 [complete transitions a] ensures that for each state q
320 and each symbols s in the alphabet, a transition q, s exists.
321 (adding q, s -> F when necessary).
324 let complete_transitions a =
325 StateSet.iter (fun q ->
326 if StateSet.mem q a.starting_states then ()
328 let qtrans = Hashtbl.find a.transitions q in
330 List.fold_left (fun rem (labels, _) ->
331 QNameSet.diff rem labels) QNameSet.any qtrans
334 if QNameSet.is_empty rem then qtrans
336 (rem, Formula.false_) :: qtrans
338 Hashtbl.replace a.transitions q nqtrans
341 (* [cleanup_states] remove states that do not lead to a
344 let cleanup_states a =
345 let memo = ref StateSet.empty in
347 if not (StateSet.mem q !memo) then begin
348 memo := StateSet.add q !memo;
349 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
350 List.iter (fun (_, phi) ->
351 StateSet.iter loop (Formula.get_states phi)) trs
354 StateSet.iter loop a.selecting_states;
355 let unused = StateSet.diff a.states !memo in
356 StateSet.iter (fun q -> Hashtbl.remove a.transitions q) unused;
359 (* [normalize_negations a] removes negative atoms in the formula
360 complementing the sub-automaton in the negative states.
361 [TODO check the meaning of negative upward arrows]
364 let normalize_negations auto =
365 let memo_state = Hashtbl.create 17 in
366 let todo = Queue.create () in
368 match Formula.expr f with
369 Boolean.True | Boolean.False -> if b then f else Formula.not_ f
370 | Boolean.Or(f1, f2) ->
371 (if b then Formula.or_ else Formula.and_)(flip b f1) (flip b f2)
372 | Boolean.And(f1, f2) ->
373 (if b then Formula.and_ else Formula.or_)(flip b f1) (flip b f2)
374 | Boolean.Atom(a, b') -> begin
375 match a.Atom.node with
377 if b == b' then begin
378 (* a appears positively, either no negation or double negation *)
379 if not (Hashtbl.mem memo_state (q,b)) then Queue.add (q,true) todo;
380 Formula.mk_atom (Move(m, q))
382 (* need to reverse the atom
383 either we have a positive state deep below a negation
384 or we have a negative state in a positive formula
385 b' = sign of the state
386 b = sign of the enclosing formula
390 (* does the inverted state of q exist ? *)
391 Hashtbl.find memo_state (q, false)
394 (* create a new state and add it to the todo queue *)
395 let nq = State.next () in
396 auto.states <- StateSet.add nq auto.states;
397 Hashtbl.add memo_state (q, false) nq;
398 Queue.add (q, false) todo; nq
400 Formula.mk_atom (Move (m,not_q))
402 | _ -> if b then f else Formula.not_ f
405 (* states that are not reachable from a selection stat are not interesting *)
406 StateSet.iter (fun q -> Queue.add (q, true) todo) auto.selecting_states;
408 while not (Queue.is_empty todo) do
409 let (q, b) as key = Queue.pop todo in
410 if not (StateSet.mem q auto.starting_states) then
413 Hashtbl.find memo_state key
416 let nq = if b then q else
417 let nq = State.next () in
418 auto.states <- StateSet.add nq auto.states;
421 Hashtbl.add memo_state key nq; nq
423 let trans = try Hashtbl.find auto.transitions q with Not_found -> [] in
424 let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
425 Hashtbl.replace auto.transitions q' trans';
429 exception Found of State.t * State.t
431 let simplify_epsilon auto =
432 let rec loop old_states =
433 if old_states != auto.states then begin
434 let old_states = auto.states in
437 (fun qfrom v -> match v with
439 if labels == QNameSet.any then begin
440 match (Formula.expr phi) with
441 Boolean.Atom ( {Atom.node = Move(`Stay, qto); _ }, true) -> raise (Found (qfrom, qto))
446 with Found (qfrom, qto) ->
447 Hashtbl.remove auto.transitions qfrom;
448 let new_trans = Hashtbl.fold (fun q tr_lst acc ->
450 List.map (fun (lab, phi) ->
451 (lab, Formula.rename_state phi qfrom qto))
454 (q, new_tr_lst) :: acc) auto.transitions []
456 Hashtbl.reset auto.transitions;
457 List.iter (fun (q, l) -> Hashtbl.add auto.transitions q l) new_trans;
458 auto.states <- StateSet.remove qfrom auto.states;
459 if (StateSet.mem qfrom auto.starting_states) then
460 auto.starting_states <- StateSet.add qto (StateSet.remove qfrom auto.starting_states);
461 if (StateSet.mem qfrom auto.selecting_states) then
462 auto.selecting_states <- StateSet.add qto (StateSet.remove qfrom auto.selecting_states);
470 (* [compute_dependencies auto] returns a hash table storing for each
471 states [q] a Move.table containing the set of states on which [q]
472 depends (loosely). [q] depends on [q'] if there is a transition
473 [q, {...} -> phi], where [q'] occurs in [phi].
475 let compute_dependencies auto =
476 let edges = Hashtbl.create 17 in
478 (fun q -> Hashtbl.add edges q (Move.create_table StateSet.empty))
479 auto.starting_states;
480 Hashtbl.iter (fun q trans ->
481 let moves = try Hashtbl.find edges q with Not_found ->
482 let m = Move.create_table StateSet.empty in
483 Hashtbl.add edges q m;
486 List.iter (fun (_, phi) ->
487 let m_phi = Formula.get_states_by_move phi in
488 Move.iter (fun m set ->
489 Move.set moves m (StateSet.union set (Move.get moves m)))
490 m_phi) trans) auto.transitions;
494 let state_prerequisites dir auto q =
495 Hashtbl.fold (fun q' trans acc ->
496 List.fold_left (fun acc (_, phi) ->
497 let m_phi = Formula.get_states_by_move phi in
498 if StateSet.mem q (Move.get m_phi dir)
499 then StateSet.add q' acc else acc)
500 acc trans) auto.transitions StateSet.empty
502 let compute_rank auto =
503 let dependencies = compute_dependencies auto in
504 let upward = [ `Stay ; `Parent ; `Previous_sibling ] in
505 let downward = [ `Stay; `First_child; `Next_sibling ] in
506 let swap dir = if dir == upward then downward else upward in
507 let is_satisfied dir q t =
508 Move.for_all (fun d set ->
509 if List.mem d dir then
510 StateSet.(is_empty (remove q set))
511 else StateSet.is_empty set) t
513 let update_dependencies dir initacc =
516 Hashtbl.fold (fun q deps acc ->
517 let to_remove = StateSet.union acc initacc in
520 Move.set deps m (StateSet.diff (Move.get deps m) to_remove)
523 if is_satisfied dir q deps then StateSet.add q acc else acc
526 if acc == new_acc then new_acc else loop new_acc
528 let satisfied = loop StateSet.empty in
529 StateSet.iter (fun q ->
530 Hashtbl.remove dependencies q) satisfied;
533 let current_states = ref StateSet.empty in
534 let rank_list = ref [] in
536 let current_dir = ref upward in
537 let detect_cycle = ref 0 in
538 while Hashtbl.length dependencies != 0 do
539 let new_sat = update_dependencies !current_dir !current_states in
540 if StateSet.is_empty new_sat then incr detect_cycle;
541 if !detect_cycle > 2 then assert false;
542 rank_list := (!rank, new_sat) :: !rank_list;
544 current_dir := swap !current_dir;
545 current_states := StateSet.union new_sat !current_states;
547 let by_rank = Hashtbl.create 17 in
548 List.iter (fun (r,s) ->
549 let set = try Hashtbl.find by_rank r with Not_found -> StateSet.empty in
550 Hashtbl.replace by_rank r (StateSet.union s set)) !rank_list;
551 auto.ranked_states <-
552 Array.init (Hashtbl.length by_rank) (fun i -> Hashtbl.find by_rank i)
559 let next = Uid.make_maker ()
565 states = StateSet.empty;
566 starting_states = StateSet.empty;
567 selecting_states = StateSet.empty;
568 transitions = Hashtbl.create MED_H_SIZE;
569 ranked_states = [| |]
574 let add_state a ?(starting=false) ?(selecting=false) q =
575 a.states <- StateSet.add q a.states;
576 if starting then a.starting_states <- StateSet.add q a.starting_states;
577 if selecting then a.selecting_states <- StateSet.add q a.selecting_states
579 let add_trans a q s f =
580 if not (StateSet.mem q a.states) then add_state a q;
581 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
583 List.fold_left (fun (acup, atrs) (labs, phi) ->
584 let lab1 = QNameSet.inter labs s in
585 let lab2 = QNameSet.diff labs s in
587 if QNameSet.is_empty lab1 then []
588 else [ (lab1, Formula.or_ phi f) ]
591 if QNameSet.is_empty lab2 then []
592 else [ (lab2, Formula.or_ phi f) ]
594 (QNameSet.union acup labs, tr1@ tr2 @ atrs)
595 ) (QNameSet.empty, []) trs
597 let rem = QNameSet.diff s cup in
598 let ntrs = if QNameSet.is_empty rem then ntrs
599 else (rem, f) :: ntrs
601 Hashtbl.replace a.transitions q ntrs
606 complete_transitions a;
607 normalize_negations a;
615 StateSet.fold (fun q a -> StateSet.add (f q) a) s StateSet.empty
617 let map_hash fk fv h =
618 let h' = Hashtbl.create (Hashtbl.length h) in
619 let () = Hashtbl.iter (fun k v -> Hashtbl.add h' (fk k) (fv v)) h in
622 let rec map_form f phi =
623 match Formula.expr phi with
624 | Boolean.Or(phi1, phi2) -> Formula.or_ (map_form f phi1) (map_form f phi2)
625 | Boolean.And(phi1, phi2) -> Formula.and_ (map_form f phi1) (map_form f phi2)
626 | Boolean.Atom({ Atom.node = Move(m,q); _}, b) ->
627 let a = Formula.mk_atom (Move (m,f q)) in
628 if b then a else Formula.not_ a
631 let rename_states mapper a =
632 let rename q = try Hashtbl.find mapper q with Not_found -> q in
633 { Builder.make () with
634 states = map_set rename a.states;
635 starting_states = map_set rename a.starting_states;
636 selecting_states = map_set rename a.selecting_states;
641 (List.map (fun (labels, form) -> (labels, map_form rename form)) l))
643 ranked_states = Array.map (map_set rename) a.ranked_states
647 let mapper = Hashtbl.create MED_H_SIZE in
649 StateSet.iter (fun q -> Hashtbl.add mapper q (State.next())) a.states
651 rename_states mapper a
659 (fun q phi -> Formula.(or_ (stay q) phi))
660 a1.selecting_states Formula.false_
662 Hashtbl.iter (fun q trs -> Hashtbl.add a1.transitions q trs)
666 Hashtbl.replace a1.transitions q [(QNameSet.any, link_phi)])
669 states = StateSet.union a1.states a2.states;
670 selecting_states = a2.selecting_states;
671 transitions = a1.transitions;
679 states = StateSet.union a1.states a2.states;
680 selecting_states = StateSet.union a1.selecting_states a2.selecting_states;
681 starting_states = StateSet.union a1.starting_states a2.starting_states;
684 Hashtbl.iter (fun k v -> Hashtbl.add a1.transitions k v) a2.transitions
691 let link a1 a2 q link_phi =
693 states = StateSet.union a1.states a2.states;
694 selecting_states = StateSet.singleton q;
695 starting_states = StateSet.union a1.starting_states a2.starting_states;
698 Hashtbl.iter (fun k v -> Hashtbl.add a1.transitions k v) a2.transitions
700 Hashtbl.add a1.transitions q [(QNameSet.any, link_phi)];
709 let q = State.next () in
712 (fun q phi -> Formula.(or_ (stay q) phi))
713 (StateSet.union a1.selecting_states a2.selecting_states)
716 link a1 a2 q link_phi
721 let q = State.next () in
724 (fun q phi -> Formula.(and_ (stay q) phi))
725 (StateSet.union a1.selecting_states a2.selecting_states)
728 link a1 a2 q link_phi
732 let q = State.next () in
735 (fun q phi -> Formula.(and_ (not_(stay q)) phi))
739 let () = Hashtbl.add a.transitions q [(QNameSet.any, link_phi)] in
742 selecting_states = StateSet.singleton q;
745 normalize_negations a; compute_rank a; a
747 let diff a1 a2 = inter a1 (neg a2)