(* This file is free software, part of containers. See file "license" for more details. *)

(** {1 Multiset} *)

type 'a sequence = ('a -> unit) -> unit

module type S = sig
  type elt
  type t

  val empty : t

  val is_empty : t -> bool

  val mem : t -> elt -> bool

  val count : t -> elt -> int

  val singleton : elt -> t

  val add : t -> elt -> t

  val remove : t -> elt -> t

  val add_mult : t -> elt -> int -> t
  (** [add_mult set x n] adds [n] occurrences of [x] to [set]
      @raise Invalid_argument if [n < 0]
      @since 0.6 *)

  val remove_mult : t -> elt -> int -> t
  (** [remove_mult set x n] removes at most [n] occurrences of [x] from [set]
      @raise Invalid_argument if [n < 0]
      @since 0.6 *)

  val update : t -> elt -> (int -> int) -> t
  (** [update set x f] calls [f n] where [n] is the current multiplicity
      of [x] in [set] ([0] to indicate its absence); the result of [f n]
      is the new multiplicity of [x].
      @raise Invalid_argument if [f n < 0]
      @since 0.6 *)

  val min : t -> elt
  (** Minimal element w.r.t the total ordering on elements *)

  val max : t -> elt
  (** Maximal element w.r.t the total ordering on elements *)

  val union : t -> t -> t
  (** [union a b] contains as many occurrences of an element [x]
      as [count a x + count b x]. *)

  val meet : t -> t -> t
  (** [meet a b] is a multiset such that
      [count (meet a b) x = max (count a x) (count b x)] *)

  val intersection : t -> t -> t
  (** [intersection a b] is a multiset such that
      [count (intersection a b) x = min (count a x) (count b x)] *)

  val diff : t -> t -> t
  (** MultiSet difference.
      [count (diff a b) x = max (count a x - count b x) 0] *)

  val contains : t -> t -> bool
  (** [contains a x = (count m x > 0)] *)

  val compare : t -> t -> int

  val equal : t -> t -> bool

  val cardinal : t -> int
  (** Number of distinct elements *)

  val iter : t -> (int -> elt -> unit) -> unit

  val fold : t -> 'b -> ('b -> int -> elt -> 'b) -> 'b

  val of_list : elt list -> t

  val to_list : t -> elt list

  val to_seq : t -> elt sequence

  val of_seq : elt sequence -> t

  val of_list_mult : (elt * int) list -> t
  (** @since 0.19 *)

  val to_list_mult : t -> (elt * int) list
  (** @since 0.19 *)

  val to_seq_mult : t -> (elt * int) sequence
  (** @since 0.19 *)

  val of_seq_mult : (elt * int) sequence -> t
  (** @since 0.19 *)
end

module Make(O : Set.OrderedType) : S with type elt = O.t