Case class constructor argument type depending on the previous argument value

I am trying to do the following

trait Stateful {
  type State
}

case class SystemState(system: Stateful, state: system.State) // does not compile

That is, the type of statedepends on (the value of) system. That, however, is not supported:

illegal dependent method type: parameter appears in the type of another parameter in the same section or an earlier one

With function arguments, I could split the arguments into two argument lists, which is not possible with a case class constructor:

def f(system: Stateful)(state: system.State): Unit = {} // compiles

The best I can do is:

case class SystemState[S](system: Stateful { type State = S }, state: S) // compiles

but I was thinking that it should be possible without a type parameter, since in dotty, I suppose type parameters are desugared to type members.

My question then is, can this be expressed without type parameters?

In a more general context, I'm exploring to what extent type parameters can be replaced by type members, and when is it a good idea to do so.

The multiple parameter list approach for dependent types unfortunately is not supported for constructors, so no, you will have to introduce a type parameter.

You could hide that fact if it becomes bothering, though

trait Stateful {
  type State
}

object SystemState {
  def apply(system: Stateful)(state: system.State): SystemState = 
    new Impl[system.State](system, state)

  private case class Impl[S](val system: Stateful { type State = S }, 
                             val state: S)
    extends SystemState {
    override def productPrefix = "SystemState"
  }
}
trait SystemState {
  val system: Stateful
  val state: system.State
}

case object Test extends Stateful { type State = Int }
val x = SystemState(Test)(1234)