(***********************************************************************)
(*                                                                     *)
(*                               TAToo                                 *)
(*                                                                     *)
(*                     Kim Nguyen, LRI UMR8623                         *)
(*                   Université Paris-Sud & CNRS                       *)
(*                                                                     *)
(*  Copyright 2010-2013 Université Paris-Sud and Centre National de la *)
(*  Recherche Scientifique. All rights reserved.  This file is         *)
(*  distributed under the terms of the GNU Lesser General Public       *)
(*  License, with the special exception on linking described in file   *)
(*  ../LICENSE.                                                        *)
(*                                                                     *)
(***********************************************************************)

(*
  Time-stamp: <Last modified on 2013-03-04 16:36:40 CET by Kim Nguyen>
*)

INCLUDE "utils.ml"
open Format
open Utils

type move = [ `Left | `Right | `Up1 | `Up2 | `Epsilon ]
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 = state_ctx ) =
struct

  module Node =
  struct
    type t = move * bool * State.t
    let equal n1 n2 = n1 = n2
    let hash n = Hashtbl.hash n
  end

  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) 

  let print ppf a =
    let _ = flush_str_formatter() in
    let fmt = str_formatter in

    let m, b, s = a.node in
    let dir,num =
      match  m with
      | `Left ->  Pretty.down_arrow, Pretty.subscript 1
      | `Right -> Pretty.down_arrow, Pretty.subscript 2
      | `Epsilon -> Pretty.epsilon, ""
      | `Up1 -> Pretty.up_arrow, Pretty.subscript 1
      | `Up2 -> Pretty.up_arrow, Pretty.subscript 2
    in
    fprintf fmt "%s%s" dir num;
    State.print fmt s;
    let str = flush_str_formatter() in
    if b then fprintf ppf "%s" str
    else Pretty.pp_overline ppf str

  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
    if b then raise (NegativeAtom(l,s));
    StateSet.mem s begin
      match l with
        `Left -> ctx.left
      | `Right -> ctx.right
      | `Up1 -> ctx.up1
      | `Up2 -> ctx.up2
      | `Epsilon -> ctx.epsilon
    end
end

module SFormula = Formula.Make(Move)
type t = {
  id : Uid.t;
  mutable states : StateSet.t;
(*  mutable top_states : StateSet.t;
  mutable bottom_states: StateSet.t; *)
  mutable selection_states: StateSet.t;
  transitions: (State.t, (QNameSet.t*SFormula.t) list) Hashtbl.t;
}

let next = Uid.make_maker ()

let create () = { id = next ();
                  states = StateSet.empty;
(*                  top_states = StateSet.empty;
                  bottom_states = StateSet.empty; *)
                  selection_states = StateSet.empty;
                  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 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
  Hashtbl.replace a.transitions q ntrs


let print fmt a =
  fprintf fmt
    "Unique ID: %i@\n\
     States %a@\n\
     Selection states: %a@\n\
     Alternating transitions:@\n"
    (a.id :> int)
    StateSet.print a.states
(*    StateSet.print a.top_states
    StateSet.print a.bottom_states *)
    StateSet.print a.selection_states;
  let trs =
    Hashtbl.fold
      (fun q t acc -> List.fold_left (fun acc (s , f) -> (q,s,f)::acc) acc t)
      a.transitions
      []
  in
  let sorted_trs = List.stable_sort (fun (q1, s1, phi1) (q2, s2, phi2) ->
    let c = State.compare q1 q2 in - (if c == 0 then QNameSet.compare s1 s2 else c))
    trs
  in
  let sfmt = str_formatter in
  let _ = flush_str_formatter () in
  let strs_strings, maxs = List.fold_left (fun (accl, accm) (q, s, f) ->
    let s1 = State.print sfmt q; flush_str_formatter () in
    let s2 = QNameSet.print sfmt s; flush_str_formatter () in
    let s3 = SFormula.print sfmt f; flush_str_formatter () in
    ( (s1, s2, s3) :: accl,
      max
        accm (2 + String.length s1 + String.length s2))
  ) ([], 0) sorted_trs
  in
  List.iter (fun (s1, s2, s3) ->
    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.selection_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