How to express type constraints for higher kinded type

Question

I am trying to create a list of some trait, parameterised by a type using the CRTP, and cannot figure out how to express the type constraints. Here is some sample code that illustrates the problem:

trait A[X] { def x: X } trait B[Y <: A[Y]] { def y(i: Int): Y } case class C(i: Int) extends A[C] { def x = C(i) } case class D(i: Int) extends A[D] { def x = D(i) } case class E() extends B[C] { def y(i: Int) = C(i) } case class F() extends B[D] { def y(i: Int) = D(i) } object Program extends App { def emptyList[X[_ <: Z forSome { type Z <: A[Z] } ]]() = collection.mutable.ListBuffer.empty[X[_]] val myList = emptyList[B]() myList += E() myList += F() println(myList.map(_.y(2).x)) }

So here I'm trying to create a list of objects that conform to the B trait. However this code will not compile, and gives the following error:

kinds of the type arguments (B) do not conform to the expected kinds of the type parameters (type X). B's type parameters do not match type X's expected parameters: type Y's bounds >: Nothing <: A[Y] are stricter than type _'s declared bounds >: Nothing <: Z forSome { type Z <: A[Z] } val myList = emptyList[B] ()

To me it seems like _ <: Z forSome { type Z <: A[Z] } is indeed at least as strict as Y <: A[Y] but maybe I'm missing something.

So the question is - what should the constraints be on the emptyList function to correctly handle B?

I think the problem here is that what you really want is to say X[_ <: Z forAll { type Z <: A[Z] } ] - i.e. you want a higher-rank type. I haven't worked out how to achieve this, though! — Submonoid
– Submonoid, Commented Nov 2, 2012 at 17:43

Kipton Barros · Accepted Answer · 2012-11-03 21:07:06Z

After some trial and error, I got it to work. Note: the compiler tells us that type parameters in A[+X] and B[+Y] must be covariant.

trait A[+X] { def x: X } trait B[+Y <: A[Y]] { def y(i: Int): Y } case class C(i: Int) extends A[C] { def x = C(i) } case class D(i: Int) extends A[D] { def x = D(i) } case class E() extends B[C] { def y(i: Int) = C(i) } case class F() extends B[D] { def y(i: Int) = D(i) } object Test extends App { def emptyList[X[Y <: A[Y]]] = collection.mutable.ListBuffer.empty[X[Y forSome {type Y <: A[Y]} ]] val myList = emptyList[B] myList += E() myList += F() println(myList.map(_.y(2).x)) }

I was trying out covariance settings as well, but didn't manage to get the emptyList method correct. Thanks for figuring that out.

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