(***********************************************************************)
(*
- Time-stamp: <Last modified on 2013-02-07 10:02:38 CET by Kim Nguyen>
+ Time-stamp: <Last modified on 2013-02-08 18:43:08 CET by Kim Nguyen>
*)
+INCLUDE "utils.ml"
open Format
open Utils
type move = [ `Left | `Right | `Up1 | `Up2 | `Epsilon ]
-type state_ctx = { left : StateSet.t;
- right : StateSet.t;
- up1 : StateSet.t;
- up2 : StateSet.t;
- epsilon : StateSet.t}
-type ctx_ = { mutable positive : state_ctx;
- mutable negative : state_ctx }
+type state_ctx = { mutable left : StateSet.t;
+ mutable right : StateSet.t;
+ mutable up1 : StateSet.t;
+ mutable up2 : StateSet.t;
+ mutable epsilon : StateSet.t}
+
type pred_ = move * bool * State.t
-module Move : (Formula.PREDICATE with type data = pred_ and type ctx = ctx_ ) =
+module Move : (Formula.PREDICATE with type data = pred_ and type ctx = state_ctx ) =
struct
module Node =
let hash n = Hashtbl.hash n
end
- type ctx = ctx_
+ type ctx = state_ctx
+
let make_ctx a b c d e =
{ left = a; right = b; up1 = c; up2 = d; epsilon = e }
- include Hcons.Make(Node)
+ include Hcons.Make(Node)
let print ppf a =
let _ = flush_str_formatter() in
let neg p =
let l, b, s = p.node in
make (l, not b, s)
-
+ exception NegativeAtom of (move*State.t)
let eval ctx p =
let l, b, s = p.node in
- let nctx = if b then ctx.positive else ctx.negative in
+ if b then raise (NegativeAtom(l,s));
StateSet.mem s begin
match l with
- `Left -> nctx.left
- | `Right -> nctx.right
- | `Up1 -> nctx.up1
- | `Up2 -> nctx.up2
- | `Epsilon -> nctx.epsilon
+ `Left -> ctx.left
+ | `Right -> ctx.right
+ | `Up1 -> ctx.up1
+ | `Up2 -> ctx.up2
+ | `Epsilon -> ctx.epsilon
end
end
module SFormula = Formula.Make(Move)
-type t = {
+type 'a t = {
id : Uid.t;
mutable states : StateSet.t;
mutable top_states : StateSet.t;
transitions: (State.t, (QNameSet.t*SFormula.t) list) Hashtbl.t;
}
-
-
let next = Uid.make_maker ()
let create () = { id = next ();
transitions = Hashtbl.create 17;
}
+
+(*
+ [add_trans a q labels f] adds a transition [(q,labels) -> f] to the
+ automaton [a] but ensures that transitions remains pairwise disjoint
+*)
+
let add_trans a q s f =
let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
- let rem, ntrs =
- List.fold_left (fun (rem, atrs) ((labs, phi) as tr) ->
- let nlabs = QNameSet.inter labs rem in
- if QNameSet.is_empty nlabs then
- (rem, tr :: atrs)
- else
- let nrem = QNameSet.diff rem labs in
- nrem, (nlabs, SFormula.or_ phi f)::atrs
- ) (s, []) trs
+ let cup, ntrs =
+ List.fold_left (fun (acup, atrs) (labs, phi) ->
+ let lab1 = QNameSet.inter labs s in
+ let lab2 = QNameSet.diff labs s in
+ let tr1 =
+ if QNameSet.is_empty lab1 then []
+ else [ (lab1, SFormula.or_ phi f) ]
+ in
+ let tr2 =
+ if QNameSet.is_empty lab2 then []
+ else [ (lab2, SFormula.or_ phi f) ]
+ in
+ (QNameSet.union acup labs, tr1@ tr2 @ atrs)
+ ) (QNameSet.empty, []) trs
in
+ let rem = QNameSet.diff s cup in
let ntrs = if QNameSet.is_empty rem then ntrs
else (rem, f) :: ntrs
in
fprintf fmt "%s, %s" s1 s2;
fprintf fmt "%s" (Pretty.padding (maxs - String.length s1 - String.length s2 - 2));
fprintf fmt "%s %s@\n" Pretty.right_arrow s3) strs_strings
+
+(*
+ [complete transitions a] ensures that for each state q
+ and each symbols s in the alphabet, a transition q, s exists.
+ (adding q, s -> F when necessary).
+*)
+
+let complete_transitions a =
+ StateSet.iter (fun q ->
+ let qtrans = Hashtbl.find a.transitions q in
+ let rem =
+ List.fold_left (fun rem (labels, _) ->
+ QNameSet.diff rem labels) QNameSet.any qtrans
+ in
+ let nqtrans =
+ if QNameSet.is_empty rem then qtrans
+ else
+ (rem, SFormula.false_) :: qtrans
+ in
+ Hashtbl.replace a.transitions q nqtrans
+ ) a.states
+
+(* [normalize_negations a] removes negative atoms in the formula
+ complementing the sub-automaton in the negative states.
+ [TODO check the meaning of negative upward arrows]
+*)
+let normalize_negations a =
+ let memo_state = Hashtbl.create 17 in
+ let todo = Queue.create () in
+ let rec flip b f =
+ match SFormula.expr f with
+ Formula.True | Formula.False -> if b then f else SFormula.not_ f
+ | Formula.Or(f1, f2) -> (if b then SFormula.or_ else SFormula.and_)(flip b f1) (flip b f2)
+ | Formula.And(f1, f2) -> (if b then SFormula.and_ else SFormula.or_)(flip b f1) (flip b f2)
+ | Formula.Atom(a) -> begin
+ let l, b', q = Move.node a in
+ if b == b' then begin
+ (* a appears positively, either no negation or double negation *)
+ if not (Hashtbl.mem memo_state (q,b)) then Queue.add (q,true) todo;
+ SFormula.atom_ (Move.make (l, true, q))
+ end else begin
+ (* need to reverse the atom
+ either we have a positive state deep below a negation
+ or we have a negative state in a positive formula
+ b' = sign of the state
+ b = sign of the containing formula
+ *)
+ let not_q =
+ try
+ (* does the inverted state of q exist ? *)
+ Hashtbl.find memo_state (q, false)
+ with
+ Not_found ->
+ (* create a new state and add it to the todo queue *)
+ let nq = State.make () in
+ Hashtbl.add memo_state (q, false) nq;
+ Queue.add (q, false) todo; nq
+ in
+ SFormula.atom_ (Move.make (l, true, not_q))
+ end
+ end
+ in
+ StateSet.iter (fun q -> Queue.add (q, true) todo) a.top_states;
+ while not (Queue.is_empty todo) do
+ let (q, b) as key = Queue.pop todo in
+ let q' =
+ try
+ Hashtbl.find memo_state key
+ with
+ Not_found ->
+ let nq = if b then q else State.make () in
+ Hashtbl.add memo_state key nq; nq
+ in
+ let trans = Hashtbl.find a.transitions q in
+ let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
+ Hashtbl.replace a.transitions q' trans'
+ done;
+ Hashtbl.iter (fun (q, b) q' ->
+ if not (b || StateSet.mem q a.bottom_states) then
+ a.bottom_states <- StateSet.add q' a.bottom_states
+ ) memo_state
+
projects / tatoo.git / commitdiff