Scala: cross (cartesian) product with multiple sou

I'm trying to construct multiple cross products of traversables of different (but each homogeneous) types. The desired return type is a traversable of a tuple with the type matching the types in the input traversables. For example:

List(1, 2, 3) cross Seq("a", "b") cross Set(0.5, 7.3)

This should give a Traversable[(Int, String, Double)] with all possible combinations from the three sources. The case of combining only two sources was nicely answered here. The given idea is:

implicit class Crossable[X](xs: Traversable[X]) {
  def cross[A](ys: Traversable[A]) = for { x <- xs; y <- ys } yield (x, y)
}

The comments there briefly mention the problem of more sources, but I'm looking to find a solution that does not depend on either shapeless or scalaz (on the other hand, I don't mind having some boilerplate to scale up to Tuple22). What I would like to do is something like the following:

implicit class Crossable[X](xs: Traversable[X]) {
  def cross[A](ys: Traversable[A]) = for { x <- xs; y <- ys } yield (x, y)
  def cross[A,B](ys: Traversable[(A,B)]) = // ... extend all Tuple2's in ys with x in xs to Tuple3's
  def cross[A,B,C](ys: Traversable[(A,B,C)]) = // ...
  // ...
}

This obviously does not work due to type erasure (and, unfortunately, would probably require to use parenthesis in the example above, because cross would be right associative).

My question is: Is it somehow possible to exploit Scala 2.10's reflection features to solve the problem? In general, matching both A and X to the various tuple types (and their type parameters, which seems challenging) and merging them to larger tuples should provide a solution satisfying the associative law, right?

I had a go at it and came up with this:

trait Crosser[A,B,C] {
  def cross( as: Traversable[A], bs: Traversable[B] ): Traversable[C]
}

trait LowPriorityCrosserImplicits {
  private type T[X] = Traversable[X]

  implicit def crosser2[A,B] = new Crosser[A,B,(A,B)] {
    def cross( as: T[A], bs: T[B] ): T[(A,B)] = for { a <- as; b <- bs } yield (a, b)
  }
}

object Crosser extends LowPriorityCrosserImplicits {
  private type T[X] = Traversable[X]

  implicit def crosser3[A,B,C] = new Crosser[(A,B),C,(A,B,C)] {
    def cross( abs: T[(A,B)], cs: T[C] ): T[(A,B,C)] = for { (a,b) <- abs; c <- cs } yield (a, b, c)
  }

  implicit def crosser4[A,B,C,D] = new Crosser[(A,B,C),D,(A,B,C,D)] {
    def cross( abcs: T[(A,B,C)], ds: T[D] ): T[(A,B,C,D)] = for { (a,b,c) <- abcs; d <- ds } yield (a, b, c, d)
  }

  // and so on ...
}

implicit class Crossable[A](xs: Traversable[A]) {
  def cross[B,C](ys: Traversable[B])(implicit crosser: Crosser[A,B,C]): Traversable[C] = crosser.cross( xs, ys )
}

The main idea is to defer the work to a type class (Crosser) and implement all the different arities simply by specialising for Traversables of tuples with the corresponding arity minus one. Some test in the REPL:

scala> List(1, 2, 3) cross Seq("a", "b") cross Set(0.5, 7.3)
res10: Traversable[(Int, String, Double)] = List((1,a,0.5), (1,a,7.3), (1,b,0.5), (1,b,7.3), (2,a,0.5), (2,a,7.3), (2,b,0.5), (2,b,7.3), (3,a,0.5), (3,a,7.3), (3,b,0.5), (3,b,7.3))