Ordered Sequences

class OrderedSequence[A: Order](v: FingerTree[A => Boolean, A]) extends NewType[FingerTree[A => Boolean, A]] {
  val value = v
  def +(a: A) = {
    val spl = v.split(x => x(a))
    new OrderedSequence(spl._1 <++> (a <+: spl._2))
  }
  override def toString = v.toString
}

object OrderedSequence {
  def empty[A: Order] = {
    implicit val r: Reducer[A, A => Boolean] = Reducer((a: A) => (b: A) => a gt b)(new Monoid[A => Boolean] {
      def append(s1: A => Boolean, s2: => (A => Boolean)) = (a: A) => s1(a) || s2.apply(a)
      val zero = (a: A) => false
    })
    new OrderedSequence(FingerTree.empty[A => Boolean, A])
  }
}