When trying to use higher kinded existentials in Scala I run into the following problem:
trait A[H[_]]
trait Test {
val l: A[List]
// [error] type mismatch;
// [error] found : A[List]
// [error] required: A[_[_] <: Any]
// [error] Note: List <: Any, but trait A is invariant in type H.
// [error] You may wish to define H as +H instead. (SLS 4.5)
val x: A[B] forSome { type B[_] } = l
}
Adding a covariant annotation to H as the compiler suggests works. Is there a way to work around this if I don't want H to be covariant?
A slight variation of the example gives a more helpful error message:
scala> l: (A[B] forSome { type B[_] })
<console>:10: error: type mismatch;
found : A[List]
required: A[_[_] <: Any]
Note: List <: Any, but trait A is invariant in type H.
You may wish to define H as +H instead. (SLS 4.5)
l: (A[B] forSome { type B[_] })
^
<console>:10: error: can't existentially abstract over parameterized type B
l: (A[B] forSome { type B[_] })
^
Looking for this error brings us to a TODO in the compiler.
Since existential types are going to disappear, per Odersky's email, I don't think this limitation will be fixed. However, Martin Odersky's email also reminds us that existential types are equivalent to abstract types. Hence, the above example can be encoded as follows:
scala> trait A { type H[_] }
defined trait A
scala> val l: A {type H[X] = List[X]} = null
l: A{type H[X] = List[X]} = null
scala> l: A
res0: A = null
Type application is syntactically ugly, but turning a value into an existential becomes trivial (also to implement in a compiler, which is part of Odersky's point).
What's useful to encode existentials is that type members don't have to be instantiated ever. So, to encode A[_] we can write:
scala> class A { type T }
defined class A
scala> new A
res1: A = A@3a7049a6
What's confusing here is that this does not work for objects:
scala> object B { type T }
<console>:8: error: only classes can have declared but undefined members
object B { type T }
^
But I recently got that accepted as a bug — see here for a pull request clarifying the spec (approved by Adriaan Moors), and here for my bug report and one-line fix to the compiler (still waiting for review).