Swift: Test class type in switch statement

In Swift you can check the class type of an object using 'is'. How can I incorporate this into a 'switch' block?

I think it's not possible, so I'm wondering what is the best way around this.

You absolutely can use is in a switch block. See "Type Casting for Any and AnyObject" in the Swift Programming Language (though it's not limited to Any of course). They have an extensive example:

for thing in things {
    switch thing {
    case 0 as Int:
        println("zero as an Int")
    case 0 as Double:
        println("zero as a Double")
    case let someInt as Int:
        println("an integer value of \(someInt)")
    case let someDouble as Double where someDouble > 0:
        println("a positive double value of \(someDouble)")
// here it comes:
    case is Double:
        println("some other double value that I don't want to print")
    case let someString as String:
        println("a string value of \"\(someString)\"")
    case let (x, y) as (Double, Double):
        println("an (x, y) point at \(x), \(y)")
    case let movie as Movie:
        println("a movie called '\(movie.name)', dir. \(movie.director)")
    default:
        println("something else")
    }
}