type state = int
val mk_state : unit -> state

type formula_expr =
    False
  | True
  | Or of formula * formula
  | And of formula * formula
  | Atom of ([ `Left | `Right | `LLeft | `RRight ] * bool * state)
and formula = { fid : int; fkey : int; pos : formula_expr; neg : formula; st : (Ptset.t*Ptset.t*Ptset.t)*(Ptset.t*Ptset.t*Ptset.t); size: int;}
val true_ : formula
val false_ : formula
val atom_ : [`Left | `Right | `LLeft | `RRight ] -> bool -> state -> formula
val and_ : formula -> formula -> formula
val or_ : formula -> formula -> formula
val not_ : formula -> formula 
(*val equal_form : formula -> formula -> bool *)
val pr_frm : Format.formatter -> formula -> unit


module HTagSet : Hashtbl.S with type key = Ptset.t*Tag.t


type 'a t = { 
  id : int;
  mutable states : Ptset.t;
  init : Ptset.t;
  mutable final : Ptset.t;
  universal : Ptset.t;
  starstate : Ptset.t option;
  (* Transitions of the Alternating automaton *)
  phi : (state,(TagSet.t*(bool*formula*bool)) list) Hashtbl.t;
  sigma : (int,('a t -> Tree.t -> Tree.t -> Ptset.t*'a)) Hashtbl.t;
}

val dump : Format.formatter -> 'a t -> unit
    
module Transitions : sig
type t = state*TagSet.t*bool*formula*bool
(* Doing this avoid the parenthesis *)
val ( ?< ) : state -> state 
val ( >< ) : state -> TagSet.t*bool -> state*(TagSet.t*bool*bool)
val ( ><@ ) : state -> TagSet.t*bool -> state*(TagSet.t*bool*bool)
val ( >=> ) : state*(TagSet.t*bool*bool) -> formula -> t
val ( +| ) : formula -> formula -> formula
val ( *& ) : formula -> formula -> formula
val ( ** ) : [`Left | `Right | `LLeft | `RRight ] -> state -> formula

end
type transition = Transitions.t
val equal_trans : transition -> transition -> bool 


  module type ResultSet = 
  sig
    type t
    val empty : t
    val cons : Tree.t -> t -> t
    val concat : t -> t -> t
    val iter : (Tree.t -> unit) -> t -> unit
    val fold : (Tree.t -> 'a -> 'a) -> t -> 'a -> 'a
    val map : (Tree.t -> Tree.t) -> t -> t
    val length : t -> int
  end

  module IdSet : ResultSet

  val top_down_count : 'a t -> Tree.t -> int
  val top_down : 'a t -> Tree.t -> IdSet.t

  type jump_kind = [ `TAG of Tag.t | `CONTAINS of string | `NOTHING ]
  val bottom_up_count : 'a t -> Tree.t -> jump_kind -> int