XorMonoid.scala

object PdxleifMonoid {
  trait Monoid[A] {
    def op(a1: A, a2: A): A
    def id: A
  }

  def XorMonoid[A]: Monoid[Option[A]] =
    new Monoid[Option[A]] {
      def op(a1: Option[A], a2: Option[A]) =
        (a1, a2) match {
          case (None, None) =>
            None
          case (Some(_), Some(_)) =>
            None
          case (Some(a), None) =>
            Some(a)
          case (None, Some(a)) =>
            Some(a)
        }
      def id =
        None
    }
}