Trying to improve compareTo to be more idiomatic in Scala pattern matching

compare.scala

// This sucks

3.compareTo(4) match {
    case x if x > 0 =>
    case x if x < 0 =>
    case x if x == 0 =>
}

/*

I want something like this:

3.compareTo(4) match {
  case GreaterThan =>
  case LessThan =>
  case EqualTo =>
}

This would also be acceptable:

3.compareTo(4) match {
  case GreaterThan(_) =>
  case LessThan(_) =>
  case EqualTo(_) =>
}
*/

// But this doesn't seem to work as I'd expect

case class GreaterThan(implicit x: Int) {
  def apply(implicit x: Int):Boolean = x > 0
}
case class LessThan(implicit x: Int) {
  def apply(implicit x: Int) = x < 0
}
case class EqualTo(implicit x: Int) {
  def apply(implicit x: Int) = x == 0
}

3.compareTo(4) match {
  case GreaterThan =>
  case LessThan =>
  case EqualTo =>
}

// I also tried with object apply(). This is something close, but not quite what I want.

object Compare {
  def apply(x: Int) = {
    x match {
      case _ if x > 0 => GreaterThan
      case _ if x < 0 => LessThan
      case _ if x == 0 => EqualTo
  }
}
case class GreaterThan()
case class LessThan()
case class EqualTo()

Compare(3.compareTo(4)) match {
  case GreaterThan =>
  case LessThan =>
  case EqualTo =>
}

// I tried to implement something like this:

Compare(3).to(4) match {
  case GreaterThan =>
  case LessThan =>
  case EqualTo =>
}

// but got caught up on the types:

case class GreaterThan()
case class LessThan()
case class EqualTo()

object Compare {
  def apply(x: Ordered) = new Compare(x)

  class Compare(original: Ordered) {
    def to[T](y: T <: Ordered){ // can't seem to get this right
      original.compareTo(y) match { // so that compareTo() gets the correctly typed `y`
        case _ if x > 0 => GreaterThan
        case _ if x < 0 => LessThan
        case _ if x == 0 => EqualTo
      }
    }}
  }

}

Should not something like this work?

object Greater {
  def unapply(x: Int) = x > 0
}
object Equal {
  def unapply(x: Int) = x == 0
}
object Lesser {
  def unapply(x: Int) = x < 0
}