Comments on: Revisiting higher-rank impredicative polymorphism in Scala

By: Vincent Cremet

Vincent Cremet — Thu, 20 Nov 2008 14:10:18 +0000

You wrote: “I think Vincent Cremet was the first person to suggest this sort of encoding, and I vaguely recall reading about it on one of the Scala mailing lists, but I could not find the message after a little bit of time spent searching.”

I found the message you mention (it was in the old list called “scala-lounge”):

http://article.gmane.org/gmane.comp.lang.scala.user/697

The idea of your encoding is the same as mine (except you use the name “Univ” instead of “Forall”). But your blog article is more complete as it also describes how to treat bounds and how to quantify over more than one type variable.

By: washburn

washburn — Wed, 28 May 2008 10:49:17 +0000

@Matt: True. The problem had occurred to me at some point, as well as the problem that this only gives you upper bounds for the quantified types, but I didn't think of it when I wrote up the above. The latter could be fixed as

trait Univ1[UBound1,LBound1<:UBound1,Body[_]] {
   def Apply[T1>:LBound1<:UBound1] : Body[T1]
}

Kind polymorphism could be used to address the problem of requiring n variations of Univ1, but it is something that I do not think is considered critical enough that it would be implemented in the near future. Virtual classes and dependent method types, among other things, are higher priority at the moment.

By: Matt Hellige

Matt Hellige — Tue, 27 May 2008 22:16:35 +0000

One thing that makes this a little more annoying than one would like is that one has to define a new Univ not just for each number of type parameters, but for each different combination of kinds as well:

trait Univ1Again[Bound1,Body[Bound1[_]]] {
def Apply[T1[_] <: Bound1] : Body[T1]
}

and so on… This makes the required family of Univs irritatingly large.

But anyway it’s a very nice trick, and anonymous (and curried) type functions would make it even nicer.