Attempt to create a higher-rank polymorphic function with type bounds

higher-rank polymorphic function with type bounds.scala

/*
  I want to use a higher-rank polymorphic function when transforming an AST to generalize the
  'traversal' so it can be separated from the actual transformation of each node. 
  
  This snippet of code doesn't quite capture my use case but it provokes the same compile error
  as I get here: https://gist.github.com/1139579
*/

trait ~>[F[_],G[_], -UpperBound] {
  def apply[A <: UpperBound](a: F[A]): G[A]
}

type Id[A] = A

// Just some data so I have something to use for my type bounds 
abstract class AClass { val name: String }
case class BClass(name: String, age: Int) extends AClass
case class CClass(name: String) extends AClass 

// Attempt to create higher-rank polymorphic function with type bounds on the input 
val transform = new (~>[Id,Id,AClass]) {
  def apply[A <: AClass](a: A): A = a match {
    case BClass(n,x) => BClass(n.reverse,x) // Doesn't compile: found BClass, required A
    case CClass(n)   => CClass(n.reverse)   // Doesn't compile: found CClass, required A
  }
}

def apply[B <: AClass](f: ~>[Id,Id,AClass], b: B, c: CClass): (B, CClass) = (f(b), f(c))

println(apply(transform, new BClass("Mads", 21), new CClass("runarorama")))