(***********************************************************************)
(*                                                                     *)
(*                               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 2013-03-08 16:24:41 CET by Kim Nguyen>
*)

INCLUDE "utils.ml"
open Format
open Utils

type move = [ `Left | `Right | `Up1 | `Up2 | `Epsilon |`Is1 |`Is2 ]
type state_ctx = { mutable left : StateSet.t;
             mutable right : StateSet.t;
             mutable up1 : StateSet.t;
             mutable up2 : StateSet.t;
             mutable epsilon : StateSet.t;
             mutable is_left : bool;
             mutable is_root : bool}

type pred_ = move * bool * State.t
let make_ctx a b c d e f g =
  { left = a; right = b; up1 = c; up2 = d; epsilon = e; is_left = f; is_root = g }

let print_ctx fmt c = fprintf fmt "{ left : %a; right : %a; up1: %a ; up2 : %a; epsilon : %a ; is_left : %b; is_root : %b }"
  StateSet.print c.left StateSet.print c.right StateSet.print c.up1 StateSet.print c.up2
  StateSet.print c.epsilon
  c.is_left c.is_root

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


  include Hcons.Make(Node)
  let _pr_buff = Buffer.create 10
  let _str_fmt = formatter_of_buffer _pr_buff
  let _flush_str_fmt () = pp_print_flush _str_fmt ();
    let s = Buffer.contents _pr_buff in
    Buffer.clear _pr_buff; s

  let print ppf a =
    let _ = _flush_str_fmt () 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
      | `Is1 -> "?", Pretty.subscript 1
      | `Is2 -> "?", Pretty.subscript 2
    in
    fprintf _str_fmt "%s%s" dir num;
    if s != State.dummy then State.print _str_fmt s;
    let str = _flush_str_fmt () in
    fprintf ppf "%s%s" (if b then "" else Pretty.lnot) 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 s == State.dummy then
      let dir =
        match l with
          | `Is1 -> ctx.is_left
          | _ -> not ctx.is_left
      in
      let res = dir && not ctx.is_root in
      res && b || (not (b || res))
    else begin
      if not 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
          | _ -> StateSet.empty
      end
    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;
 }


let get_trans a states tag =
  StateSet.fold (fun q acc0 ->
    try
      let trs = Hashtbl.find a.transitions q in
      List.fold_left (fun acc1 (labs, phi) ->
        if QNameSet.mem tag labs then (q,phi)::acc1 else acc1) acc0 trs
    with Not_found -> acc0
  ) states []

(*
  [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 _pr_buff = Buffer.create 50
let _str_fmt = formatter_of_buffer _pr_buff
let _flush_str_fmt () = pp_print_flush _str_fmt ();
  let s = Buffer.contents _pr_buff in
  Buffer.clear _pr_buff; s

let print fmt a =
  fprintf fmt
    "\nInternal UID: %i@\n\
     States: %a@\n\
     Top states: %a@\n\
     Bottom 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, _) (q2, s2, _) ->
    let c = State.compare q1 q2 in - (if c == 0 then QNameSet.compare s1 s2 else c))
    trs
  in
  let _ = _flush_str_fmt () in
  let strs_strings, max_pre, max_all = List.fold_left (fun (accl, accp, acca) (q, s, f) ->
    let s1 = State.print _str_fmt q; _flush_str_fmt () in
    let s2 = QNameSet.print _str_fmt s;  _flush_str_fmt () in
    let s3 = SFormula.print _str_fmt f;  _flush_str_fmt () in
    let pre = Pretty.length s1 + Pretty.length s2 in
    let all = Pretty.length s3 in
    ( (q, s1, s2, s3) :: accl, max accp pre, max acca all)
  ) ([], 0, 0) sorted_trs
  in
  let line = Pretty.line (max_all + max_pre + 6) in
  let prev_q = ref State.dummy in
  List.iter (fun (q, s1, s2, s3) ->
    if !prev_q != q && !prev_q != State.dummy then fprintf fmt " %s\n%!"  line;
    prev_q := q;
    fprintf fmt " %s, %s" s1 s2;
    fprintf fmt "%s" (Pretty.padding (max_pre - Pretty.length s1 - Pretty.length s2));
    fprintf fmt " %s  %s@\n%!" Pretty.right_arrow s3;
  ) strs_strings;
  fprintf fmt " %s\n%!" line

(*
  [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 auto =
  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 q == State.dummy then if b then f else SFormula.not_ f
      else
        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 enclosing 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
              auto.states <- StateSet.add nq auto.states;
              if not (StateSet.mem q auto.bottom_states) then
                auto.bottom_states <- StateSet.add nq auto.bottom_states;
              if not (StateSet.mem q auto.top_states) then
                auto.top_states <- StateSet.add nq auto.top_states;
              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
  (* states that are not reachable from a selection stat are not interesting *)
  StateSet.iter (fun q -> Queue.add (q, true) todo) auto.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
              let nq = State.make () in
              auto.states <- StateSet.add nq auto.states;
              if not (StateSet.mem q auto.bottom_states) then
                auto.bottom_states <- StateSet.add nq auto.bottom_states;
              if not (StateSet.mem q auto.top_states) then
                auto.top_states <- StateSet.add nq auto.top_states;
              nq
          in
          Hashtbl.add memo_state key nq; nq
    in
    let trans = Hashtbl.find auto.transitions q in
    let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
    Hashtbl.replace auto.transitions q' trans'
  done