Fixing type inference for higher kinded type

Question

Ok, so I have this wonderfully simple setup:

trait Sys[S <: Sys[S]]

trait Elem[S <: Sys[S]]

trait AttrElem[S <: Sys[S]] {
  type E <: Elem[S]

  def attributes: Any
  def element: E
}

And a factory:

object Factory {
  def apply[S <: Sys[S], E1 <: Elem[S]](
    elem: E1): AttrElem[S] { type E = E1 } = new Impl(elem)

  private class Impl[S <: Sys[S], E1 <: Elem[S]](val element: E1) 
    extends AttrElem[S] { 

    type E = E1

    def attributes = 1234
  }
}

Now in practice the f*** Scala type inference breaks down:

def test[S <: Sys[S]](elem: Elem[S]): Unit = {
  Factory(elem)
}

<console>:62: error: inferred type arguments [Nothing,Elem[S]] do not conform
  to method apply's type parameter bounds [S <: Sys[S],E1 <: Elem[S]]
             Factory(elem)
             ^

---

So my next attempt is existential types:

object Factory {
  def apply[S <: Sys[S], E1[~] <: Elem[~] forSome { type ~ <: Sys[~] }](
    elem: E1[S]): AttrElem[S] { type E = E1[S] } = new Impl(elem)

  private class Impl[S <: Sys[S], E1[~] <: Elem[~] forSome { type ~ <: Sys[~] }](
    val element: E1[S]) extends AttrElem[S] { 

    type E = E1[S]

    def attributes = 1234
  }
}

This gives me this following lovely message:

<console>:62: error: inferred kinds of the type arguments (S,E1[S]) do not 
  conform to the expected kinds of the type parameters (type S,type E1) in
  class Impl.
E1[S]'s type parameters do not match type E1's expected parameters:
type E1 has one type parameter, but type E1 (in class Impl) has one
               elem: E1[S]): AttrElem[S] { type E = E1[S] } = new Impl(elem)
                                                              ^

"type E1 has one type parameter, but type E1 has one" -- huh?

---

Question: How can I define the factory's apply method to infer the types?

Answer 1

The following "redundancy" seems to satisfy the compiler:

def apply[S <: Sys[S], E1 <: Elem[S]](elem: E1 with Elem[S]): 
  AttrElem[S] { type E = E1 } = ...

That is, adding with Elem[S]. It looks like a needless deficiency of the Scala compiler to not infer S from E1 <: Elem[S] where Elem is invariant in S.

Or am I missing a crucial bit?