Minimal framework in Scala for collections with inheriting return type

Question

Suppose one wants to build a novel generic class, Novel[A]. This class will contain lots of useful methods--perhaps it is a type of collection--and therefore you want to subclass it. But you want the methods to return the type of the subclass, not the original type. In Scala 2.8, what is the minimal amount of work one has to do so that methods of that class will return the relevant subclass, not the original? For example,

class Novel[A] /* What goes here? */ {
  /* Must you have stuff here? */
  def reverse/* What goes here instead of :Novel[A]? */ = //...
  def revrev/*?*/ = reverse.reverse
}
class ShortStory[A] extends Novel[A] /* What goes here? */ {
  override def reverse: /*?*/ = //...
}
val ss = new ShortStory[String]
val ss2 = ss.revrev  // Type had better be ShortStory[String], not Novel[String]

Does this minimal amount change if you want Novel to be covariant?

(The 2.8 collections do this among other things, but they also play with return types in more fancy (and useful) ways--the question is how little framework one can get away with if one only wants this subtypes-always-return-subtypes feature.)

Edit: Assume in the code above that reverse makes a copy. If one does in-place modification and then returns oneself, one can use this.type, but that doesn't work because the copy is not this.

Arjan linked to another question that suggests the following solution:

def reverse: this.type = {
  /*creation of new object*/.asInstanceOf[this.type]
}

which basically lies to the type system in order to get what we want. But this isn't really a solution, because now that we've lied to the type system, the compiler can't help us make sure that we really do get a ShortStory back when we think we do. (For example, we wouldn't have to override reverse in the example above to make the compiler happy, but our types wouldn't be what we wanted.)

Answer 1

I haven't thought this through fully, but it type checks:

object invariant {
  trait Novel[A] {
    type Repr[X] <: Novel[X]

    def reverse: Repr[A]

    def revrev: Repr[A]#Repr[A]
       = reverse.reverse
  }
  class ShortStory[A] extends Novel[A] {
    type Repr[X] = ShortStory[X]

    def reverse = this
  }

  val ss = new ShortStory[String]
  val ss2: ShortStory[String] = ss.revrev
}

object covariant {
  trait Novel[+A] {
    type Repr[X] <: Novel[_ <: X]

    def reverse: Repr[_ <: A]

    def revrev: Repr[_ <: A]#Repr[_ <: A] = reverse.reverse
  }

  class ShortStory[+A] extends Novel[A] {
    type Repr[X] = ShortStory[X]

    def reverse = this
  }

  val ss = new ShortStory[String]
  val ss2: ShortStory[String] = ss.revrev
}

EDIT

The co-variant version can be much nicer:

object covariant2 {
  trait Novel[+A] {
    type Repr[+X] <: Novel[X]

    def reverse: Repr[A]

    def revrev: Repr[A]#Repr[A] = reverse.reverse
  }

  class ShortStory[+A] extends Novel[A] {
    type Repr[+X] = ShortStory[X]

    def reverse = this
  }

  val ss = new ShortStory[String]
  val ss2: ShortStory[String] = ss.revrev
}