How to represent the set of Integers including - Infinity in Scala-CodePudding

I have just started with Scala, and I'm trying to create a data type, which is a union of Integers and the special values Infinity and -Infinity. I'm trying to figure out how to do this the most idiomatic way in Scala.

One option I've tried so far is by using a trait:

trait MySet
case object Infinity extends MySet 
case object NegInfinity extends MySet 
case class Value(value: Int) extends MySet

This seams to work, but I'm not sure if this is the smartest way of doing it. In the end, I want to use this to model algebraic structures such as Groups, Monoids, etc. with MySet as the carrier set. E.g. doing something like:

trait Monoid[T]:
    val zero: T
    def @ (x: T, y: T): T

Something in that direction.

Thanks for all suggestions!

CodePudding user response：

As Luis said in the comment, make the trait sealed will make it so that the compiler will know what are the possible extentions of MySet

Otherwise, your monoid can be enriched with the following operations :

val mySetMonoid = new Monoid[MySet] {
  // 1) first the associative operation, which I guess would be  
  def op(a1: MySet, a2: MySet) = (a1, a2) match {
    case (Value(x), Value(y)) => x y
    case (Value(_), Infinity) => Infinity
    case (Value(_), NegInfinity) => NegInfinity
    case (Infinity, Value(_)) => Infinity
    case (NegInfinity, Value(_)) => NegInfinity
    case (NegInfinity, Infinity) => throw new UnsupportedOperationException(..) 
        // here you need to be more specific
        // on how you want to handle  infinity 
        // and -infinity being added
  }
  // 2) then the definition of your zero in regard of the associative operation
  val zero = Value(0)
}