(***********************************************************************)
(*                                                                     *)
(*                               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.                                                        *)
(*                                                                     *)
(***********************************************************************)

INCLUDE "utils.ml"
open Format
open Misc
type move = [ `First_child
            | `Next_sibling
            | `Parent
            | `Previous_sibling
            | `Stay ]

module Move =
  struct
    type t = move
    type 'a table = 'a array
    let idx = function
      | `First_child -> 0
      | `Next_sibling -> 1
      | `Parent -> 2
      | `Previous_sibling -> 3
      | `Stay -> 4
    let ridx = function
      | 0 -> `First_child
      | 1 -> `Next_sibling
      | 2 -> `Parent
      | 3 -> `Previous_sibling
      | 4 -> `Stay
      | _ -> assert false

    let create_table a = Array.make 5 a
    let get m k = m.(idx k)
    let set m k v = m.(idx k) <- v
    let iter f m = Array.iteri (fun i v -> f (ridx i) v) m
    let fold f m acc =
      let acc = ref acc in
      iter (fun i v -> acc := f i v !acc) m;
      !acc
    let for_all p m =
      try
        iter (fun i v -> if not (p i v) then raise Exit) m;
        true
      with
        Exit -> false
    let for_all2 p m1 m2 =
      try
        for i = 0 to 4 do
          let v1 = m1.(i)
          and v2 = m2.(i) in
          if not (p (ridx i) v1 v2) then raise Exit
        done;
        true
      with
        Exit -> false

    let exists p m =
      try
        iter (fun i v -> if p i v then raise Exit) m;
        false
      with
        Exit -> true
    let print ppf m =
      match m with
        `First_child -> fprintf ppf "%s" Pretty.down_arrow
      | `Next_sibling -> fprintf ppf "%s" Pretty.right_arrow
      | `Parent -> fprintf ppf "%s" Pretty.up_arrow
      | `Previous_sibling -> fprintf ppf "%s" Pretty.left_arrow
      | `Stay -> fprintf ppf "%s" Pretty.bullet

    let print_table pr_e ppf m =
      iter (fun i v -> fprintf ppf "%a: %a" print i pr_e v;
        if (idx i) < 4 then fprintf ppf ", ") m
  end

type predicate = Move of move * State.t
                 | Is_first_child
                 | Is_next_sibling
                 | Is of Tree.NodeKind.t
                 | Has_first_child
                 | Has_next_sibling

module Atom =
struct

  module Node =
  struct
    type t = predicate
    let equal n1 n2 = n1 = n2
    let hash n = Hashtbl.hash n
  end

  include Hcons.Make(Node)

  let print ppf a =
    match a.node with
    | Move (m, q) ->
      fprintf ppf "%a%a" Move.print m State.print q
    | Is_first_child -> fprintf ppf "%s?" Pretty.up_arrow
    | Is_next_sibling -> fprintf ppf "%s?" Pretty.left_arrow
    | Is k -> fprintf ppf "is-%a?" Tree.NodeKind.print k
    | Has_first_child -> fprintf ppf "%s?" Pretty.down_arrow
    | Has_next_sibling -> fprintf ppf "%s?" Pretty.right_arrow

end


module Formula =
struct
  include Boolean.Make(Atom)
  open Tree.NodeKind
  let mk_atom a = atom_ (Atom.make a)
  let is k = mk_atom (Is k)

  let has_first_child = mk_atom Has_first_child

  let has_next_sibling = mk_atom Has_next_sibling

  let is_first_child = mk_atom Is_first_child

  let is_next_sibling = mk_atom Is_next_sibling

  let is_attribute = mk_atom (Is Attribute)

  let is_element = mk_atom (Is Element)

  let is_processing_instruction = mk_atom (Is ProcessingInstruction)

  let is_comment = mk_atom (Is Comment)

  let mk_move m q = mk_atom (Move(m,q))
  let first_child q =
    and_
      (mk_move `First_child q)
      has_first_child

  let next_sibling q =
  and_
    (mk_move `Next_sibling q)
    has_next_sibling

  let parent q =
  and_
    (mk_move `Parent  q)
    is_first_child

  let previous_sibling q =
  and_
    (mk_move `Previous_sibling q)
    is_next_sibling

  let stay q = mk_move `Stay q

  let get_states_by_move phi =
    let table = Move.create_table StateSet.empty in
    iter (fun phi ->
      match expr phi with
      | Boolean.Atom ({ Atom.node = Move(v,q) ; _ }, _) ->
        let s = Move.get table v in
        Move.set table v (StateSet.add q s)
      | _ -> ()
    ) phi;
    table
  let get_states phi =
    let table = get_states_by_move phi in
    Move.fold (fun _ s acc -> StateSet.union s acc) table StateSet.empty

end

module Transition =
  struct
    include Hcons.Make (struct
  type t = State.t * QNameSet.t * Formula.t
  let equal (a, b, c) (d, e, f) =
    a == d && b == e && c == f
  let hash (a, b, c) =
    HASHINT4 (PRIME1, a, ((QNameSet.uid b) :> int), ((Formula.uid c) :> int))
end)
    let print ppf t =
      let q, l, f = t.node in
      fprintf ppf "%a, %a %s %a"
        State.print q
        QNameSet.print l
        Pretty.double_right_arrow
        Formula.print f
  end


module TransList : sig
  include Hlist.S with type elt = Transition.t
  val print : Format.formatter -> ?sep:string -> t -> unit
end =
  struct
    include Hlist.Make(Transition)
    let print ppf ?(sep="\n") l =
      iter (fun t ->
        let q, lab, f = Transition.node t in
        fprintf ppf "%a, %a → %a%s"
          State.print q
          QNameSet.print lab
          Formula.print f sep) l
  end



type t = {
  id : Uid.t;
  mutable states : StateSet.t;
  mutable starting_states : StateSet.t;
  mutable selecting_states: StateSet.t;
  transitions: (State.t, (QNameSet.t*Formula.t) list) Hashtbl.t;
  mutable ranked_states : StateSet.t array
}

let uid t = t.id

let get_states a = a.states
let get_starting_states a = a.starting_states
let get_selecting_states a = a.selecting_states
let get_states_by_rank a = a.ranked_states
let get_max_rank a = Array.length a.ranked_states - 1

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 =
  let _ = _flush_str_fmt() in
  fprintf fmt
    "Internal UID: %i@\n\
     States: %a@\n\
     Number of states: %i@\n\
     Starting states: %a@\n\
     Selection states: %a@\n\
     Ranked states: %a@\n\
     Alternating transitions:@\n"
    (a.id :> int)
    StateSet.print a.states
    (StateSet.cardinal a.states)
    StateSet.print a.starting_states
    StateSet.print a.selecting_states
    (let r = ref 0 in Pretty.print_array ~sep:", " (fun ppf s ->
      fprintf ppf "%i:%a" !r StateSet.print s; incr r)) a.ranked_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 q2 q1 in if c == 0 then QNameSet.compare s2 s1 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 = Formula.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
  fprintf fmt "%s@\n" line;
  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


let get_trans a tag states =
  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
          TransList.cons (Transition.make (q, labs, phi)) acc1
        else acc1) acc0 trs
    with Not_found -> acc0
  ) states TransList.nil


let get_form a tag q =
  try
    let trs = Hashtbl.find a.transitions q in
    List.fold_left (fun aphi (labs, phi) ->
      if QNameSet.mem tag labs then Formula.or_ aphi phi else aphi
    ) Formula.false_ trs
  with
    Not_found -> Formula.false_

(*
  [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 ->
    if StateSet.mem q a.starting_states then ()
    else
      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, Formula.false_) :: qtrans
      in
      Hashtbl.replace a.transitions q nqtrans
  ) a.states

(* [cleanup_states] remove states that do not lead to a
   selecting states *)

let cleanup_states a =
  let memo = ref StateSet.empty in
  let rec loop q =
    if not (StateSet.mem q !memo) then begin
      memo := StateSet.add q !memo;
      let trs = try Hashtbl.find a.transitions q with Not_found -> [] in
      List.iter (fun (_, phi) ->
        StateSet.iter loop (Formula.get_states phi)) trs
    end
  in
  StateSet.iter loop a.selecting_states;
  let unused = StateSet.diff a.states !memo in
  StateSet.iter (fun q -> Hashtbl.remove a.transitions q) unused;
  a.states <- !memo

(* [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 Formula.expr f with
      Boolean.True | Boolean.False -> if b then f else Formula.not_ f
    | Boolean.Or(f1, f2) ->
      (if b then Formula.or_ else Formula.and_)(flip b f1) (flip b f2)
    | Boolean.And(f1, f2) ->
      (if b then Formula.and_ else Formula.or_)(flip b f1) (flip b f2)
    | Boolean.Atom(a, b') -> begin
      match a.Atom.node with
      | Move (m,  q) ->
          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;
            Formula.mk_atom (Move(m, 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;
                  Hashtbl.add memo_state (q, false) nq;
                  Queue.add (q, false) todo; nq
            in
            Formula.mk_atom (Move (m,not_q))
          end
      | _ -> if b then f else Formula.not_ f
    end
  in
  (* states that are not reachable from a selection stat are not interesting *)
  StateSet.iter (fun q -> Queue.add (q, true) todo) auto.selecting_states;

  while not (Queue.is_empty todo) do
    let (q, b) as key = Queue.pop todo in
    if not (StateSet.mem q auto.starting_states) then
      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;
                nq
            in
            Hashtbl.add memo_state key nq; nq
      in
      let trans = try Hashtbl.find auto.transitions q with Not_found -> [] in
      let trans' = List.map (fun (lab, f) -> lab, flip b f) trans in
      Hashtbl.replace auto.transitions q' trans';
  done;
  cleanup_states auto

(* [compute_dependencies auto] returns a hash table storing for each
   states [q] a Move.table containing the set of states on which [q]
   depends (loosely). [q] depends on [q'] if there is a transition
   [q, {...} -> phi], where [q'] occurs in [phi].
*)
let compute_dependencies auto =
  let edges = Hashtbl.create 17 in
  StateSet.iter
    (fun q -> Hashtbl.add edges q (Move.create_table StateSet.empty))
    auto.starting_states;
  Hashtbl.iter (fun q trans ->
    let moves = try Hashtbl.find edges q with Not_found ->
      let m = Move.create_table StateSet.empty in
      Hashtbl.add edges q m;
      m
    in
    List.iter (fun (_, phi) ->
      let m_phi = Formula.get_states_by_move phi in
      Move.iter (fun m set ->
        Move.set moves m (StateSet.union set (Move.get moves m)))
        m_phi) trans) auto.transitions;

  edges


let compute_rank auto =
  let dependencies = compute_dependencies auto in
  let upward = [ `Stay ; `Parent ; `Previous_sibling ] in
  let downward = [ `Stay; `First_child; `Next_sibling ] in
  let swap dir = if dir == upward then downward else upward in
  let is_satisfied dir q t =
    Move.for_all (fun d set ->
      if List.mem d dir then
        StateSet.(is_empty (remove q set))
      else StateSet.is_empty set) t
  in
  let update_dependencies dir initacc =
    let rec loop acc =
      let new_acc =
        Hashtbl.fold (fun q deps acc ->
          let to_remove = StateSet.union acc initacc in
          List.iter
            (fun m ->
              Move.set deps m (StateSet.diff (Move.get deps m) to_remove)
            )
            dir;
          if is_satisfied dir q deps then StateSet.add q acc else acc
        ) dependencies acc
      in
      if acc == new_acc then new_acc else loop new_acc
    in
    let satisfied = loop StateSet.empty in
    StateSet.iter (fun q ->
      Hashtbl.remove dependencies q) satisfied;
    satisfied
  in
  let current_states = ref StateSet.empty in
  let rank_list = ref [] in
  let rank = ref 0 in
  let current_dir = ref upward in
  let detect_cycle = ref 0 in
  while Hashtbl.length dependencies != 0 do
    let new_sat = update_dependencies !current_dir !current_states in
    if StateSet.is_empty new_sat then incr detect_cycle;
    if !detect_cycle > 2 then assert false;
    rank_list := (!rank, new_sat) :: !rank_list;
    rank := !rank + 1;
    current_dir := swap !current_dir;
    current_states := StateSet.union new_sat !current_states;
  done;
  let by_rank = Hashtbl.create 17 in
  List.iter (fun (r,s) ->
    let set = try Hashtbl.find by_rank r with Not_found -> StateSet.empty in
    Hashtbl.replace by_rank r (StateSet.union s set)) !rank_list;
  auto.ranked_states <-
    Array.init (Hashtbl.length by_rank) (fun i -> Hashtbl.find by_rank i)


module Builder =
  struct
    type auto = t
    type t = auto
    let next = Uid.make_maker ()

    let make () =
      let auto =
        {
          id = next ();
          states = StateSet.empty;
          starting_states = StateSet.empty;
          selecting_states = StateSet.empty;
          transitions = Hashtbl.create MED_H_SIZE;
          ranked_states = [| |]
        }
      in
      auto

    let add_state a ?(starting=false) ?(selecting=false) q =
      a.states <- StateSet.add q a.states;
      if starting then a.starting_states <- StateSet.add q a.starting_states;
      if selecting then a.selecting_states <- StateSet.add q a.selecting_states

    let add_trans a q s f =
      if not (StateSet.mem q a.states) then add_state a q;
      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, Formula.or_ phi f) ]
          in
          let tr2 =
            if QNameSet.is_empty lab2 then []
            else [ (lab2, Formula.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 finalize a =
      complete_transitions a;
      normalize_negations a;
      compute_rank a;
      a
  end


let map_set f s =
  StateSet.fold (fun q a -> StateSet.add (f q) a) s StateSet.empty

let map_hash fk fv h =
  let h' = Hashtbl.create (Hashtbl.length h) in
  let () = Hashtbl.iter (fun k v -> Hashtbl.add h' (fk k) (fv v)) h in
  h'

let rec map_form f phi =
  match Formula.expr phi with
  | Boolean.Or(phi1, phi2) -> Formula.or_ (map_form f phi1) (map_form f phi2)
  | Boolean.And(phi1, phi2) -> Formula.and_ (map_form f phi1) (map_form f phi2)
  | Boolean.Atom({ Atom.node = Move(m,q); _}, b) ->
      let a = Formula.mk_atom (Move (m,f q)) in
      if b then a else Formula.not_ a
  | _ -> phi

let rename_states mapper a =
  let rename q = try Hashtbl.find mapper q with Not_found -> q in
  { Builder.make () with
    states = map_set rename a.states;
    starting_states = map_set rename a.starting_states;
    selecting_states = map_set rename a.selecting_states;
    transitions =
      map_hash
        rename
        (fun l ->
          (List.map (fun (labels, form) -> (labels, map_form rename form)) l))
        a.transitions;
    ranked_states = Array.map (map_set rename) a.ranked_states
  }

let copy a =
  let mapper = Hashtbl.create MED_H_SIZE in
  let () =
    StateSet.iter (fun q -> Hashtbl.add mapper q (State.make())) a.states
  in
  rename_states mapper a


let concat a1 a2 =
  let a1 = copy a1 in
  let a2 = copy a2 in
  let link_phi =
    StateSet.fold
      (fun q phi -> Formula.(or_ (stay q) phi))
      a1.selecting_states Formula.false_
  in
  Hashtbl.iter (fun q trs -> Hashtbl.add a1.transitions q trs)
    a2.transitions;
  StateSet.iter
    (fun q ->
      Hashtbl.replace a1.transitions q [(QNameSet.any, link_phi)])
    a2.starting_states;
  let a = { a1 with
    states = StateSet.union a1.states a2.states;
    selecting_states = a2.selecting_states;
    transitions = a1.transitions;
  }
  in compute_rank a; a

let merge a1 a2 =
  let a1 = copy a1 in
  let a2 = copy a2 in
  let a = { a1 with
    states = StateSet.union a1.states a2.states;
    selecting_states = StateSet.union a1.selecting_states a2.selecting_states;
    starting_states = StateSet.union a1.starting_states a2.starting_states;
    transitions =
      let () =
        Hashtbl.iter (fun k v -> Hashtbl.add a1.transitions k v) a2.transitions
      in
      a1.transitions
  } in
  compute_rank a ; a


let link a1 a2 q link_phi =
  let a = { a1 with
    states = StateSet.union a1.states a2.states;
    selecting_states = StateSet.singleton q;
    starting_states = StateSet.union a1.starting_states a2.starting_states;
    transitions =
      let () =
        Hashtbl.iter (fun k v -> Hashtbl.add a1.transitions k v) a2.transitions
      in
      Hashtbl.add a1.transitions q [(QNameSet.any, link_phi)];
      a1.transitions
  }
  in
  compute_rank a; a

let union a1 a2 =
  let a1 = copy a1 in
  let a2 = copy a2 in
  let q = State.make () in
  let link_phi =
    StateSet.fold
      (fun q phi -> Formula.(or_ (stay q) phi))
      (StateSet.union a1.selecting_states a2.selecting_states)
      Formula.false_
  in
  link a1 a2 q link_phi

let inter a1 a2 =
  let a1 = copy a1 in
  let a2 = copy a2 in
  let q = State.make () in
  let link_phi =
    StateSet.fold
      (fun q phi -> Formula.(and_ (stay q) phi))
      (StateSet.union a1.selecting_states a2.selecting_states)
      Formula.true_
  in
  link a1 a2 q link_phi

let neg a =
  let a = copy a in
  let q = State.make () in
  let link_phi =
    StateSet.fold
      (fun q phi -> Formula.(and_ (not_(stay q)) phi))
      a.selecting_states
      Formula.true_
  in
  let () = Hashtbl.add a.transitions q [(QNameSet.any, link_phi)] in
  let a =
    { a with
      selecting_states = StateSet.singleton q;
    }
  in
  normalize_negations a; compute_rank a; a

let diff a1 a2 = inter a1 (neg a2)