class virtual ['a] group :
  object
    method virtual equal : 'a -> 'a -> bool
    method not_equal : 'a -> 'a -> bool
    method virtual zero : 'a
    method virtual plus : 'a -> 'a -> 'a
    method virtual opposite : 'a -> 'a
    method minus : 'a -> 'a -> 'a
  end

class virtual ['a] ring :
  object
    inherit ['a] group
    method virtual one : 'a
    method virtual product : 'a -> 'a -> 'a
  end

class virtual ['a] field :
  object
    inherit ['a] ring
    method virtual inverse : 'a -> 'a
  end

module type Group = sig
  type t

  val meth : t group
end

module type Ring = sig
  include Group

  val meth : t ring
end

type int

module Int : sig
  include Ring with type t = int

  val of_int64 : int64 -> t
end

module type Field = sig
  include Ring

  val meth : t field
  val characteristic : int
end

(*module type Polynomial = functor (_ : Ring) -> Ring*)

module IntMod : functor
  (_ : sig
     val modulus : Int.t
   end)
  -> sig
  include Ring

  val inj : int -> t
  val proj : t -> int
end

module Fp : functor
  (_ : sig
     val modulus : Int.t
   end)
  -> sig
  include Field

  val of_int64 : int64 -> t
end

module EllipticCurve : functor
  (F : Field)
  (_ : sig
     val a1 : F.t
     val a2 : F.t
     val a3 : F.t
     val a4 : F.t
     val a6 : F.t
     val p : F.t
   end)
  -> sig
  include Group
  val meth : 
  object
    inherit ['a] group
    method virtual random : 'a -> 'a
  end
end