TraitTest.scala

trait Similarity {
  def isSimilar(x: Any): Boolean
  def isNotSimilar(x: Any): Boolean = !isSimilar(x)
}

class TestClass(val member: Boolean)  extends Similarity {
  // method implementation with cast
  def isSimilar(x: Any) = { x.asInstanceOf[TestClass].member == member }
}

object TraitTest {
   def testSimilarity(arg0: Similarity, arg1: Similarity) {
      println(arg0.isSimilar(arg1))
   }
}
object MainApp extends Application {
   TraitTest.testSimilarity(
     new TestClass(true), new TestClass(false) // false 
   ) 
   TraitTest.testSimilarity(
     new TestClass(true), new TestClass(true) // true
   )
}

A small example to show how traits work as a polymorphic type in scala: