Typing rules for assigning non-wildcards to wildcards

Question

Hi all,
I have the following code:
public class A<T extends Number> {
     T t;
     public void foo() {
          Number number = null;
          Integer integer = null;
          A<? extends Integer> a1 = null;
          A<? super Integer> a2 = null;
          a1.t = null; // OK
          a1.t = integer; // Error
          a2.t = number; // Error
          a2.t = integer; // OK
}The code contains four assignments of a non-wildcard type to a wildcard type. Two of them are correct, two are wrong. Now, intuitively, the following rules seem to hold for such assignments to upper/lower bounded wildcards:
- Only the null-type can be assigned to an upper bounded (or unbounded) wildcard.
- A non-wildcard type can be assigned to a lower bounded wildcard iff it can be assigned to the wildcard's lower bound.
I think that the rules are quite intuitive but I would be interested in finding the formal typing rules for such assignments in the JLS. Can anyone provide a reference into the
JLS which which cover the semantics of the above assignments?
Any help would be really appreciated. Thanks a lot in advance!

Answer 1

kablair & dannyyates,
first of all, thanks a lot for taking you the time to explain the things to me that clearly! Sorry also for the somewhat confusing example by having chosen the final class Integer which is some kind of a special and limiting case.
In any case, I have gone through the JLS yesterday as I was particularly interested in the role of capture conversion to formally explain the correctness of the above code and here are my conclusions I want to share with you: Actually, there seem to be no subtyping rules for wildcards because you always apply capture conversion (JLS3 5.1.10) to wildcards before looking for their subtype relationship to other types. Capture conversion converts each wildcard to a new fresh synthetic type variable which has appropriate upper bounds and also a lower bound. Now, in the very last sentence of section 4.10.2 of the JLS3, it is stated that a type variable is a direct supertype of its lower bound which I think is the key point. This means that you can assign something to a type variable iff you can assign it to its lower bound.
Now, capture conversion converts every unbounded or lower bounded wildcard into a type variable which has the null type as its lower bound. This formally shows that you can really just assign null to them as in the code above. Contrary, every lower bounded wildcard is capture converted to a type variable whose lower bound is the lower bound of the wildcard. So, again, you can assign it every type you can assign to that lower bound. This is also reflected in the above code.
So, that's maybe the formal explanation for something which is intuitively clear anyway...