How to define a cyclic type definition?

Question

This is not a valid type definition:

scala>  type Addable = { def +(subject: Addable) }
<console>:4: error: illegal cyclic reference involving type Addable
        type Addable = { def +(subject: Addable) }

Can this be expressed in scala?

Answer 1

Here's what I did in a library I wrote, HTH:

  trait Addable {
    type AddableType <: Addable
    def + (subject: AddableType): AddableType
  }
  trait Rational extends Addable {
    type AddableType = Rational
    override def + (subject: Rational): Rational 
  }

Answer 2

No, it can't.

On page 40 of The Scala Language Specification Version 2.7:

However, it is a static error if a type alias refers recursively to the defined type constructor itself. That is, the type T in a type alias type t[tps] = T may not refer directly or indirectly to the name t.