You can't do exactly what you want, as pointed out by other answer, but one approach is to use a factory:
trait Foo {
// methods you need
}
trait FooCompanion[T <: Foo] {
// these methods replace constructors in your example
def apply(s: String): T
def apply(i: Int): T
...
}
Implementation:
class Bar(s: String) extends Foo {
...
}
object Bar extends FooCompanion[Bar] {
def apply(s: String) = new Bar(s)
...
}
and you can have methods taking FooCompanion
. This pattern is used e.g. in the Scala collections library.