module type NUM = sig
  type t

  val zero : t
  val one : t
  val minus_one : t

  val sign : t -> int

  val of_int : int -> t
  include Sidekick_sigs.EQ with type t := t
  include Sidekick_sigs.ORD with type t := t
  include Sidekick_sigs.HASH with type t := t
  include Sidekick_sigs.PRINT with type t := t

  val (+) : t -> t -> t
  val (-) : t -> t -> t
  val ( * ) : t -> t -> t
  val (~-) : t -> t

  val neg : t -> t
  val min : t -> t -> t
  val max : t -> t -> t

  val (=) : t -> t -> bool
  val (<>) : t -> t -> bool
  val (>) : t -> t -> bool
  val (>=) : t -> t -> bool
  val (<) : t -> t -> bool
  val (<=) : t -> t -> bool
end

module type INT = sig
  include NUM

  val succ : t -> t
end

module type RATIONAL = sig
  include NUM
  type bigint

  val (/) : t -> t -> t
  val num : t -> bigint
  val denum : t -> bigint

  val pp_approx : int -> Format.formatter -> t -> unit
  (** Pretty print rational with given amount of precision
      (for example as a floating point number) *)
end