Scala collection type for filter

Question

Assume you have a List(1,"1") it is typed List[Any], which is of course correct and expected. Now if I map the list like this

scala> List(1, "1") map {
     |   case x: Int => x
     |   case y: String => y.toInt
     | }

the resulting type is List[Int] which is expected as well. My question is if there is an equivalent to map for filter because the following example will result in a List[Any]. Is this possible? I assume this could be solved at compile time and possibly not runtime?

scala> List(1, "1") filter {
     |   case x: Int => true
     |   case _ => false
     | }

Answer 1

Scala 2.9:

scala> List(1, "1") collect {
     |   case x: Int => x
     | }
res0: List[Int] = List(1)

Answer 2

For anyone stumbling across this question wondering why the most-voted answer doesn't work for them, be aware that the partialMap method was renamed collect before Scala 2.8's final release. Try this instead:

scala> List(1, "1") collect {
     |   case x: Int => x
     | }
res0: List[Int] = List(1)

(This should really be a comment on Daniel C. Sobral's otherwise-wonderful answer, but as a new user, I'm not allowed to comment yet.)