从外部访问抽象类型成员

使用抽象类型成员时，如果不使用asInstanceOf，则无法从外部使用该类型，还有其他选择吗？为什么抽象类型不让自己被“覆盖”，所以它知道它是Int还是String？

scala> trait Param { type A
 | val x:A
 | def get:A = x
 | }

scala> case class IParam(override val x:Int) extends Param {type A = Int}
defined class IParam

scala> case class SParam(override val x:String) extends Param {type A = String}
defined class SParam

scala> val s = Set[Param](IParam(1), SParam("s"))
s: scala.collection.immutable.Set[Param] = Set(IParam(1), SParam(s))

scala> val y:Int = s.head.get
<console>:26: error: type mismatch;
 found   : Param#A
 required: Int
       val y:Int = s.head.get