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
183 include Hcons.Make (struct
184 type t = State.t * QNameSet.t * Formula.t
185 let equal (a, b, c) (d, e, f) =
186 a == d && b == e && c == f
188 HASHINT4 (PRIME1, a, ((QNameSet.uid b) :> int), ((Formula.uid c) :> int))
191 let q, l, f = t.node in
192 fprintf ppf "%a, %a %s %a"
195 Pretty.double_right_arrow
200 module TransList : sig
201 include Hlist.S with type elt = Transition.t
202 val print : Format.formatter -> ?sep:string -> t -> unit
205 include Hlist.Make(Transition)
206 let print ppf ?(sep="\n") l =
208 let q, lab, f = Transition.node t in
209 fprintf ppf "%a, %a → %a%s"
212 Formula.print f sep) l
219 mutable states : StateSet.t;
220 mutable starting_states : StateSet.t;
221 mutable selecting_states: StateSet.t;
222 transitions: (State.t, (QNameSet.t*Formula.t) list) Hashtbl.t;
223 mutable ranked_states : StateSet.t array
228 let get_states a = a.states
229 let get_starting_states a = a.starting_states
230 let get_selecting_states a = a.selecting_states
231 let get_states_by_rank a = a.ranked_states
232 let get_max_rank a = Array.length a.ranked_states - 1
234 let _pr_buff = Buffer.create 50
235 let _str_fmt = formatter_of_buffer _pr_buff
236 let _flush_str_fmt () = pp_print_flush _str_fmt ();
237 let s = Buffer.contents _pr_buff in
238 Buffer.clear _pr_buff; s
241 let _ = _flush_str_fmt() in
243 "Internal UID: %i@\n\
245 Number of states: %i@\n\
246 Starting states: %a@\n\
247 Selection states: %a@\n\
248 Ranked states: %a@\n\
249 Alternating transitions:@\n"
251 StateSet.print a.states
252 (StateSet.cardinal a.states)
253 StateSet.print a.starting_states
254 StateSet.print a.selecting_states
255 (let r = ref 0 in Pretty.print_array ~sep:", " (fun ppf s ->
256 fprintf ppf "%i:%a" !r StateSet.print s; incr r)) a.ranked_states;
259 (fun q t acc -> List.fold_left (fun acc (s , f) -> (q,s,f)::acc) acc t)
263 let sorted_trs = List.stable_sort (fun (q1, s1, _) (q2, s2, _) ->
264 let c = State.compare q2 q1 in if c == 0 then QNameSet.compare s2 s1 else c)
267 let _ = _flush_str_fmt () in
268 let strs_strings, max_pre, max_all =
269 List.fold_left (fun (accl, accp, acca) (q, s, f) ->
270 let s1 = State.print _str_fmt q; _flush_str_fmt () in
271 let s2 = QNameSet.print _str_fmt s; _flush_str_fmt () in
272 let s3 = Formula.print _str_fmt f; _flush_str_fmt () in
273 let pre = Pretty.length s1 + Pretty.length s2 in
274 let all = Pretty.length s3 in
275 ( (q, s1, s2, s3) :: accl, max accp pre, max acca all)
276 ) ([], 0, 0) sorted_trs
278 let line = Pretty.line (max_all + max_pre + 6) in
279 let prev_q = ref State.dummy in
280 fprintf fmt "%s@\n" line;
281 List.iter (fun (q, s1, s2, s3) ->
282 if !prev_q != q && !prev_q != State.dummy then fprintf fmt "%s@\n" line;
284 fprintf fmt "%s, %s" s1 s2;
286 (Pretty.padding (max_pre - Pretty.length s1 - Pretty.length s2));
287 fprintf fmt " %s %s@\n" Pretty.right_arrow s3;
289 fprintf fmt "%s@\n" line
292 let get_trans a tag states =
293 StateSet.fold (fun q acc0 ->
295 let trs = Hashtbl.find a.transitions q in
296 List.fold_left (fun acc1 (labs, phi) ->
297 if QNameSet.mem tag labs then
298 TransList.cons (Transition.make (q, labs, phi)) acc1
300 with Not_found -> acc0
301 ) states TransList.nil
304 let get_form a tag q =
306 let trs = Hashtbl.find a.transitions q in
307 List.fold_left (fun aphi (labs, phi) ->
308 if QNameSet.mem tag labs then Formula.or_ aphi phi else aphi
311 Not_found -> Formula.false_
314 [complete transitions a] ensures that for each state q
315 and each symbols s in the alphabet, a transition q, s exists.
316 (adding q, s -> F when necessary).
319 let complete_transitions a =
320 StateSet.iter (fun q ->
321 if StateSet.mem q a.starting_states then ()
323 let qtrans = Hashtbl.find a.transitions q in
325 List.fold_left (fun rem (labels, _) ->
326 QNameSet.diff rem labels) QNameSet.any qtrans
329 if QNameSet.is_empty rem then qtrans
331 (rem, Formula.false_) :: qtrans
333 Hashtbl.replace a.transitions q nqtrans
336 (* [cleanup_states] remove states that do not lead to a
339 let cleanup_states a =
340 let memo = ref StateSet.empty in
342 if not (StateSet.mem q !memo) then begin
343 memo := StateSet.add q !memo;
344 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
345 List.iter (fun (_, phi) ->
346 StateSet.iter loop (Formula.get_states phi)) trs
349 StateSet.iter loop a.selecting_states;
350 let unused = StateSet.diff a.states !memo in
351 StateSet.iter (fun q -> Hashtbl.remove a.transitions q) unused;
354 (* [normalize_negations a] removes negative atoms in the formula
355 complementing the sub-automaton in the negative states.
356 [TODO check the meaning of negative upward arrows]
359 let normalize_negations auto =
360 let memo_state = Hashtbl.create 17 in
361 let todo = Queue.create () in
363 match Formula.expr f with
364 Boolean.True | Boolean.False -> if b then f else Formula.not_ f
365 | Boolean.Or(f1, f2) ->
366 (if b then Formula.or_ else Formula.and_)(flip b f1) (flip b f2)
367 | Boolean.And(f1, f2) ->
368 (if b then Formula.and_ else Formula.or_)(flip b f1) (flip b f2)
369 | Boolean.Atom(a, b') -> begin
370 match a.Atom.node with
372 if b == b' then begin
373 (* a appears positively, either no negation or double negation *)
374 if not (Hashtbl.mem memo_state (q,b)) then Queue.add (q,true) todo;
375 Formula.mk_atom (Move(m, q))
377 (* need to reverse the atom
378 either we have a positive state deep below a negation
379 or we have a negative state in a positive formula
380 b' = sign of the state
381 b = sign of the enclosing formula
385 (* does the inverted state of q exist ? *)
386 Hashtbl.find memo_state (q, false)
389 (* create a new state and add it to the todo queue *)
390 let nq = State.make () in
391 auto.states <- StateSet.add nq auto.states;
392 Hashtbl.add memo_state (q, false) nq;
393 Queue.add (q, false) todo; nq
395 Formula.mk_atom (Move (m,not_q))
397 | _ -> if b then f else Formula.not_ f
400 (* states that are not reachable from a selection stat are not interesting *)
401 StateSet.iter (fun q -> Queue.add (q, true) todo) auto.selecting_states;
403 while not (Queue.is_empty todo) do
404 let (q, b) as key = Queue.pop todo in
405 if not (StateSet.mem q auto.starting_states) then
408 Hashtbl.find memo_state key
411 let nq = if b then q else
412 let nq = State.make () in
413 auto.states <- StateSet.add nq auto.states;
416 Hashtbl.add memo_state key nq; nq
418 let trans = try Hashtbl.find auto.transitions q with Not_found -> [] in
419 let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
420 Hashtbl.replace auto.transitions q' trans';
424 (* [compute_dependencies auto] returns a hash table storing for each
425 states [q] a Move.table containing the set of states on which [q]
426 depends (loosely). [q] depends on [q'] if there is a transition
427 [q, {...} -> phi], where [q'] occurs in [phi].
429 let compute_dependencies auto =
430 let edges = Hashtbl.create 17 in
432 (fun q -> Hashtbl.add edges q (Move.create_table StateSet.empty))
433 auto.starting_states;
434 Hashtbl.iter (fun q trans ->
435 let moves = try Hashtbl.find edges q with Not_found ->
436 let m = Move.create_table StateSet.empty in
437 Hashtbl.add edges q m;
440 List.iter (fun (_, phi) ->
441 let m_phi = Formula.get_states_by_move phi in
442 Move.iter (fun m set ->
443 Move.set moves m (StateSet.union set (Move.get moves m)))
444 m_phi) trans) auto.transitions;
449 let compute_rank auto =
450 let dependencies = compute_dependencies auto in
451 let upward = [ `Stay ; `Parent ; `Previous_sibling ] in
452 let downward = [ `Stay; `First_child; `Next_sibling ] in
453 let swap dir = if dir == upward then downward else upward in
454 let is_satisfied q t =
455 Move.for_all (fun _ set -> StateSet.(is_empty (remove q set))) t
457 let update_dependencies dir initacc =
460 Hashtbl.fold (fun q deps acc ->
461 let to_remove = StateSet.union acc initacc in
464 Move.set deps m (StateSet.diff (Move.get deps m) to_remove)
467 if is_satisfied q deps then StateSet.add q acc else acc
470 if acc == new_acc then new_acc else loop new_acc
472 let satisfied = loop StateSet.empty in
473 StateSet.iter (fun q ->
474 Hashtbl.remove dependencies q) satisfied;
477 let current_states = ref StateSet.empty in
478 let rank_list = ref [] in
480 let current_dir = ref upward in
481 let detect_cycle = ref 0 in
482 while Hashtbl.length dependencies != 0 do
483 let new_sat = update_dependencies !current_dir !current_states in
484 if StateSet.is_empty new_sat then incr detect_cycle;
485 if !detect_cycle > 2 then assert false;
486 rank_list := (!rank, new_sat) :: !rank_list;
488 current_dir := swap !current_dir;
489 current_states := StateSet.union new_sat !current_states;
491 let by_rank = Hashtbl.create 17 in
492 List.iter (fun (r,s) ->
493 let set = try Hashtbl.find by_rank r with Not_found -> StateSet.empty in
494 Hashtbl.replace by_rank r (StateSet.union s set)) !rank_list;
495 auto.ranked_states <-
496 Array.init (Hashtbl.length by_rank) (fun i -> Hashtbl.find by_rank i)
503 let next = Uid.make_maker ()
509 states = StateSet.empty;
510 starting_states = StateSet.empty;
511 selecting_states = StateSet.empty;
512 transitions = Hashtbl.create MED_H_SIZE;
513 ranked_states = [| |]
518 let add_state a ?(starting=false) ?(selecting=false) q =
519 a.states <- StateSet.add q a.states;
520 if starting then a.starting_states <- StateSet.add q a.starting_states;
521 if selecting then a.selecting_states <- StateSet.add q a.selecting_states
523 let add_trans a q s f =
524 if not (StateSet.mem q a.states) then add_state a q;
525 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
527 List.fold_left (fun (acup, atrs) (labs, phi) ->
528 let lab1 = QNameSet.inter labs s in
529 let lab2 = QNameSet.diff labs s in
531 if QNameSet.is_empty lab1 then []
532 else [ (lab1, Formula.or_ phi f) ]
535 if QNameSet.is_empty lab2 then []
536 else [ (lab2, Formula.or_ phi f) ]
538 (QNameSet.union acup labs, tr1@ tr2 @ atrs)
539 ) (QNameSet.empty, []) trs
541 let rem = QNameSet.diff s cup in
542 let ntrs = if QNameSet.is_empty rem then ntrs
543 else (rem, f) :: ntrs
545 Hashtbl.replace a.transitions q ntrs
548 complete_transitions a;
549 normalize_negations a;
556 StateSet.fold (fun q a -> StateSet.add (f q) a) s StateSet.empty
558 let map_hash fk fv h =
559 let h' = Hashtbl.create (Hashtbl.length h) in
560 let () = Hashtbl.iter (fun k v -> Hashtbl.add h' (fk k) (fv v)) h in
563 let rec map_form f phi =
564 match Formula.expr phi with
565 | Boolean.Or(phi1, phi2) -> Formula.or_ (map_form f phi1) (map_form f phi2)
566 | Boolean.And(phi1, phi2) -> Formula.and_ (map_form f phi1) (map_form f phi2)
567 | Boolean.Atom({ Atom.node = Move(m,q); _}, b) ->
568 let a = Formula.mk_atom (Move (m,f q)) in
569 if b then a else Formula.not_ a
572 let rename_states mapper a =
573 let rename q = try Hashtbl.find mapper q with Not_found -> q in
574 { Builder.make () with
575 states = map_set rename a.states;
576 starting_states = map_set rename a.starting_states;
577 selecting_states = map_set rename a.selecting_states;
582 (List.map (fun (labels, form) -> (labels, map_form rename form)) l))
584 ranked_states = Array.map (map_set rename) a.ranked_states
588 let mapper = Hashtbl.create MED_H_SIZE in
590 StateSet.iter (fun q -> Hashtbl.add mapper q (State.make())) a.states
592 rename_states mapper a
600 (fun q phi -> Formula.(or_ (stay q) phi))
601 a1.selecting_states Formula.false_
603 Hashtbl.iter (fun q trs -> Hashtbl.add a1.transitions q trs)
607 Hashtbl.replace a1.transitions q [(QNameSet.any, link_phi)])
610 states = StateSet.union a1.states a2.states;
611 selecting_states = a2.selecting_states;
612 transitions = a1.transitions;
620 states = StateSet.union a1.states a2.states;
621 selecting_states = StateSet.union a1.selecting_states a2.selecting_states;
622 starting_states = StateSet.union a1.starting_states a2.starting_states;
625 Hashtbl.iter (fun k v -> Hashtbl.add a1.transitions k v) a2.transitions
632 let link a1 a2 q link_phi =
634 states = StateSet.union a1.states a2.states;
635 selecting_states = StateSet.singleton q;
636 starting_states = StateSet.union a1.starting_states a2.starting_states;
639 Hashtbl.iter (fun k v -> Hashtbl.add a1.transitions k v) a2.transitions
641 Hashtbl.add a1.transitions q [(QNameSet.any, link_phi)];
650 let q = State.make () in
653 (fun q phi -> Formula.(or_ (stay q) phi))
654 (StateSet.union a1.selecting_states a2.selecting_states)
657 link a1 a2 q link_phi
662 let q = State.make () in
665 (fun q phi -> Formula.(and_ (stay q) phi))
666 (StateSet.union a1.selecting_states a2.selecting_states)
669 link a1 a2 q link_phi
673 let q = State.make () in
676 (fun q phi -> Formula.(and_ (not_(stay q)) phi))
680 let () = Hashtbl.add a.transitions q [(QNameSet.any, link_phi)] in
683 selecting_states = StateSet.singleton q;
686 normalize_negations a; compute_rank a; a
688 let diff a1 a2 = inter a1 (neg a2)