Generics compiler error explanation required

Question

Can someone help explain why the following doesn't compile/isn't allowed:
interface Bar<V> {
interface Foo<V> {
     void addAll(Set<Bar<? extends V>> theBar);
Foo<String> foo = null;
Set<Bar<String>> bars = null;
foo.addAll(bars);The compiler gives something like
addAll(java.util.Set<Bar<? extends java.lang.String>>) in Foo<java.lang.String> cannot be applied to (java.util.Set<Bar<java.lang.String>>)
I'm using java 1.6.0_18-b07 for Windows x64
The real life example is taking a Set of Map.Entry from the Map.entrySet method; I am stumped as to why this isn't allowed by the compiler, I have a workaround but I'd like to understand why this isn't valid.

Answer 1

ejp wrote:
'Subtyping does not extend through generic types: T <: U does not imply that C<T> <: C<U>.'
[JLS #4.10|http://java.sun.com/docs/books/jls/third_edition/html/typesValues.html#4.10]
Now I am thoroughly confused. That is supposed to convey that List<Integer> is not a subtype of List<Number> even though Integer is a subtype of Number. In other words Java generics are invariant.
The relevant sections are [4.10|http://java.sun.com/docs/books/jls/third_edition/html/typesValues.html#4.10], [4.10.2|http://java.sun.com/docs/books/jls/third_edition/html/typesValues.html#4.10.2] and [4.5.1.1|http://java.sun.com/docs/books/jls/third_edition/html/typesValues.html#4.5.1.1]. Specifically:
The direct supertypes of the type C<T1,...,Tn> , where Ti,1&#8804;i&#8804;n, is a type, are
- D<U1 theta, ..., Uk theta>, where D<U1,...,Uk> is a direct supertype of C<F1,...,Fn>, and theta is the substitution [F1 := T1, ..., Fn := Tn]
- C<S1,...,Sn> where Si contains (§4.5.1.1) Ti for 1&#8804;i&#8804;n.
Granted, there is an error in the spec, but unless you believe "[...] are D<U1 theta, ..., Uk theta>, where C<S1,...,Sn> where Si contains [...]" is not gibberish, it's an obvious error.
In our case C = Set, T1 = String, n = 1 and one of the direct supertypes is C<S1> where S1 = "? extends String". This is true because String is contained by (<=) "? extends String" as defined by 4.5.1.1:
T <= ? extends TNow we have determined that Set<? extends String> is a direct supertype of Set<String>, the rest can be found in the preface to 4.10:
The supertypes of a type are obtained by reflexive and transitive closure over the direct supertype relation [...]and
The subtypes of a type T are all types U such that T is a supertype of U [...]With kind regards
Ben