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 2013-02-08 18:43:08 CET by Kim Nguyen>
24 type move = [ `Left | `Right | `Up1 | `Up2 | `Epsilon ]
25 type state_ctx = { mutable left : StateSet.t;
26 mutable right : StateSet.t;
27 mutable up1 : StateSet.t;
28 mutable up2 : StateSet.t;
29 mutable epsilon : StateSet.t}
31 type pred_ = move * bool * State.t
33 module Move : (Formula.PREDICATE with type data = pred_ and type ctx = state_ctx ) =
38 type t = move * bool * State.t
39 let equal n1 n2 = n1 = n2
40 let hash n = Hashtbl.hash n
45 let make_ctx a b c d e =
46 { left = a; right = b; up1 = c; up2 = d; epsilon = e }
48 include Hcons.Make(Node)
51 let _ = flush_str_formatter() in
52 let fmt = str_formatter in
54 let m, b, s = a.node in
57 | `Left -> Pretty.down_arrow, Pretty.subscript 1
58 | `Right -> Pretty.down_arrow, Pretty.subscript 2
59 | `Epsilon -> Pretty.epsilon, ""
60 | `Up1 -> Pretty.up_arrow, Pretty.subscript 1
61 | `Up2 -> Pretty.up_arrow, Pretty.subscript 2
63 fprintf fmt "%s%s" dir num;
65 let str = flush_str_formatter() in
66 if b then fprintf ppf "%s" str
67 else Pretty.pp_overline ppf str
70 let l, b, s = p.node in
72 exception NegativeAtom of (move*State.t)
74 let l, b, s = p.node in
75 if b then raise (NegativeAtom(l,s));
82 | `Epsilon -> ctx.epsilon
86 module SFormula = Formula.Make(Move)
89 mutable states : StateSet.t;
90 mutable top_states : StateSet.t;
91 mutable bottom_states: StateSet.t;
92 mutable selection_states: StateSet.t;
93 transitions: (State.t, (QNameSet.t*SFormula.t) list) Hashtbl.t;
96 let next = Uid.make_maker ()
98 let create () = { id = next ();
99 states = StateSet.empty;
100 top_states = StateSet.empty;
101 bottom_states = StateSet.empty;
102 selection_states = StateSet.empty;
103 transitions = Hashtbl.create 17;
108 [add_trans a q labels f] adds a transition [(q,labels) -> f] to the
109 automaton [a] but ensures that transitions remains pairwise disjoint
112 let add_trans a q s f =
113 let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
115 List.fold_left (fun (acup, atrs) (labs, phi) ->
116 let lab1 = QNameSet.inter labs s in
117 let lab2 = QNameSet.diff labs s in
119 if QNameSet.is_empty lab1 then []
120 else [ (lab1, SFormula.or_ phi f) ]
123 if QNameSet.is_empty lab2 then []
124 else [ (lab2, SFormula.or_ phi f) ]
126 (QNameSet.union acup labs, tr1@ tr2 @ atrs)
127 ) (QNameSet.empty, []) trs
129 let rem = QNameSet.diff s cup in
130 let ntrs = if QNameSet.is_empty rem then ntrs
131 else (rem, f) :: ntrs
133 Hashtbl.replace a.transitions q ntrs
141 Bottom states: %a@\n\
142 Selection states: %a@\n\
143 Alternating transitions:@\n"
145 StateSet.print a.states
146 StateSet.print a.top_states
147 StateSet.print a.bottom_states
148 StateSet.print a.selection_states;
151 (fun q t acc -> List.fold_left (fun acc (s , f) -> (q,s,f)::acc) acc t)
155 let sorted_trs = List.stable_sort (fun (q1, s1, phi1) (q2, s2, phi2) ->
156 let c = State.compare q1 q2 in - (if c == 0 then QNameSet.compare s1 s2 else c))
159 let sfmt = str_formatter in
160 let _ = flush_str_formatter () in
161 let strs_strings, maxs = List.fold_left (fun (accl, accm) (q, s, f) ->
162 let s1 = State.print sfmt q; flush_str_formatter () in
163 let s2 = QNameSet.print sfmt s; flush_str_formatter () in
164 let s3 = SFormula.print sfmt f; flush_str_formatter () in
165 ( (s1, s2, s3) :: accl,
167 accm (2 + String.length s1 + String.length s2))
170 List.iter (fun (s1, s2, s3) ->
171 fprintf fmt "%s, %s" s1 s2;
172 fprintf fmt "%s" (Pretty.padding (maxs - String.length s1 - String.length s2 - 2));
173 fprintf fmt "%s %s@\n" Pretty.right_arrow s3) strs_strings
176 [complete transitions a] ensures that for each state q
177 and each symbols s in the alphabet, a transition q, s exists.
178 (adding q, s -> F when necessary).
181 let complete_transitions a =
182 StateSet.iter (fun q ->
183 let qtrans = Hashtbl.find a.transitions q in
185 List.fold_left (fun rem (labels, _) ->
186 QNameSet.diff rem labels) QNameSet.any qtrans
189 if QNameSet.is_empty rem then qtrans
191 (rem, SFormula.false_) :: qtrans
193 Hashtbl.replace a.transitions q nqtrans
196 (* [normalize_negations a] removes negative atoms in the formula
197 complementing the sub-automaton in the negative states.
198 [TODO check the meaning of negative upward arrows]
200 let normalize_negations a =
201 let memo_state = Hashtbl.create 17 in
202 let todo = Queue.create () in
204 match SFormula.expr f with
205 Formula.True | Formula.False -> if b then f else SFormula.not_ f
206 | Formula.Or(f1, f2) -> (if b then SFormula.or_ else SFormula.and_)(flip b f1) (flip b f2)
207 | Formula.And(f1, f2) -> (if b then SFormula.and_ else SFormula.or_)(flip b f1) (flip b f2)
208 | Formula.Atom(a) -> begin
209 let l, b', q = Move.node a in
210 if b == b' then begin
211 (* a appears positively, either no negation or double negation *)
212 if not (Hashtbl.mem memo_state (q,b)) then Queue.add (q,true) todo;
213 SFormula.atom_ (Move.make (l, true, q))
215 (* need to reverse the atom
216 either we have a positive state deep below a negation
217 or we have a negative state in a positive formula
218 b' = sign of the state
219 b = sign of the containing formula
223 (* does the inverted state of q exist ? *)
224 Hashtbl.find memo_state (q, false)
227 (* create a new state and add it to the todo queue *)
228 let nq = State.make () in
229 Hashtbl.add memo_state (q, false) nq;
230 Queue.add (q, false) todo; nq
232 SFormula.atom_ (Move.make (l, true, not_q))
236 StateSet.iter (fun q -> Queue.add (q, true) todo) a.top_states;
237 while not (Queue.is_empty todo) do
238 let (q, b) as key = Queue.pop todo in
241 Hashtbl.find memo_state key
244 let nq = if b then q else State.make () in
245 Hashtbl.add memo_state key nq; nq
247 let trans = Hashtbl.find a.transitions q in
248 let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
249 Hashtbl.replace a.transitions q' trans'
251 Hashtbl.iter (fun (q, b) q' ->
252 if not (b || StateSet.mem q a.bottom_states) then
253 a.bottom_states <- StateSet.add q' a.bottom_states