I'd like to be able to do something like this:

trait A {
  def f(): ???_THE_EXTENDING CLASS
}
class C extends A {
  def f() = self
}
class D extends A {
  def f() = new D
}
class Z extends D {
  def f() = new Z
}

And the following would not compile, given the above code

class Bad1 extends A {
  def f() = "unrelated string"
}
class Bad2 extends A {
  def f() = new C // this means that you can't just define a type parameter on
                  // A like A[T <: A] with f() defined as f: T
}
class Bad3 extends D // f() now doesn't return the correct type

Is there a name for this kind of relationship? And how is it annotated/implemented in Scala?

Edit

The following sort of works, as you can see:

scala> trait A {
     | def f: this.type 
     | }
defined trait A

scala> class C extends A {
     | def f = this 
     | }
defined class C

scala> class D extends A {
     | def f = new D
     | }
<console>:7: error: type mismatch;
 found   : D
 required: D.this.type
       def f = new D
               ^

Is there a way to get around that?

Edit 2

Using the second system, I can do this, which is good up to the definition of class D:

scala> trait A[T <: A[T]] { def f(): T }
defined trait A
// OR
scala> trait A[T <: A[T]] { self: T =>
     | def f(): T
     | }

scala> class C extends A[C] { def f() = new C }
defined class C

scala> class D extends C
defined class D

scala> (new D).f
res0: C = C@465fadce