How to abstract from type of immutable value performing its transformations?

I want to incapsulate real type of immutable Solution object in implementation of Modifier but can’t find a way to avoid downcasts. How can I write Listeners independent on type of Solution without making them have a type parameter?

The following code illustrates that downcasts are unvoidable if Listener is unaware about concrete type of Solution.

 trait Solution {} //Immutable abstact class
 trait Listener(val modifier: Modifier) {
   开发者_StackOverflow def onChange(iSolution: Solution): Solution
 }
 trait Modifier { //Implementations use different descendants of Solution
    def addListener(listener: Listener)
    def emptySolution: Solution
    def transfrom1(iSolution: Solution): Solution //Downcast of argument can’t be avoided in implementations of these
    def transfrom2(iSolution: Solution): Solution
 }
 class Listener1 extends Listener { //Should be independent from Solution concrete type. Current implentation meets this requirement by introducing downcasts in Modifier.
    val modifier: Modifier
    def onChange(iSolution: Solution) = modifier.transform1(modifier.transform2(iSolution)) // Some action involving solution transformations with modifier
 }

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One possible answer is already in your question - you can use abstract types.

Here is an example that may help you:

trait Solution {}
trait Listener {
  val modifier: Modifier
  def onChange(iSolution: modifier.solType): modifier.solType
}
trait Modifier {
  type solType <: Solution
  def addListener(listener: Listener)
  def emptySolution: Solution
  def transform1(iSolution: solType): solType
  def transform2(iSolution: solType): solType
}
trait Listener1 extends Listener {
  val modifier: Modifier
  def onChange(iSolution: modifier.solType) = modifier.transform1(modifier.transform2(iSolution))
}