This is literally a "the type system is unsound if we don't consider the required runtime semantics of the type system" paper.
Even ignoring this, the example they give is something the the typesystem correctly rejects, but what they want is a compile time failure that should be possible. I would say the if anything this is a compiler bug.
Is it though? I always thought it was unsound due to, at a minimum, mutable covariant arrays. It's definitely possible to have a type error at runtime without using a cast.
Integer a = 0;
Object c = a;
String b = (String) c;
The problem with the code in the paper is that Java 1.5 introduced generic types, that are in principle meant easy such situations and it appears that there are some corner cases where it does not work as expected (to more general populace).
For example consider this code
static class Upcast {
static <T extends String> String cast(T t) {
return t;
}
}
Integer a = 0;
Object c = a;
String b = Upcast.cast(c);
String b = Upcast.cast((String)c);
The paper demonstrates a more complex indirection to avoid the compiler warning but still produce a runtime exception.
Object[] foo = new String[10] foo[0] = new Integer(1)
which is the type error, even if the reported error is something akin to a "array store error" or something (it's been a long time since i did java programming :D)
Of course the whole generics system in Java is basically just "syntactic sugar" to save your from writing a ton casts, so it will just break at run-time.
(Where by "nonexistent type" I mean "a type for which there cannot be an instance". "imaginary type" might be a better term, since the type itself exists in the type system.)
The problem here lies in the fact that Java lets you create an instance of any type you can write the signature for via `null`. This lies in conflict with the ability to specify nonexistent types (which is a relatively common ability in type systems and might not even be possible to excise without causing significant complexity).
The paper actually explicitly acknowledges this, Section 3 pg. 3, if you read closely. In fact there is an even bigger danger lurking, which is that Java has non-deterministic type inference. It's not even necessarily a "compiler bug" that the first example, Unsound.java, is rejected:
> ... As a consequence, the method type-checks. Furthermore, even though type-argument inference in Java is undecidable, this type argument is identified by javac, version 1.8.0_25, which consequently accepts and compiles the code in Figure 1. However, constraint solving is generally a non-deterministic process, and type-argument inference itself is non-deterministic [35], so the Eclipse Compiler for Java, ecj version 3.11.1.v20150902-1521, and the current compiler for the upcoming Java 9, javac build 108, fail to type-check this code...
Non-determinism means something very specific here: it does not necessarily mean the compiler randomly rejects something based on whether it's a random day of the week or because `rand() % 4 == 0`. It means the compiler has no sound method for inferring the type of a value, given multiple choices, so it "just" picks one, in an ill specified way. It could pick the first one or the second, and whichever type it picks will influence further constraint generation/inference. See this paper, section 7.2:
http://www.cs.cornell.edu/~ross/publications/tamewild/tamewi...
The Eclipse compiler only coincidentally rejects one of these programs due to this type inference problem. Other valid, unsound programs are accepted by it, and these programs are unsound due to the same basic principles the original (rejected one) used. The Unsound9.java example should still work.
The fact a compiler is rejecting a valid program (a bug in the eclipse compiler) is essentially orthogonal to the fact the program it rejects may show the type system is unsound (a bug in the language itself, so to speak).
Furthermore your parent post is still simply wrong. You say:
> Java's type system is _sound_ as it guarantees that you will never use a variable of one type as another incompatible type.
But this is literally the point of the paper. They cast Integer to String, you cannot get this through downcasting alone. It is unsound. They are able to write a function of type "a" to "b" for any types "a" and "b". It's almost the textbook definition of being able to break the type system, from the viewpoint of Java-the-language. This same "cast anything to anything else" is also considered a breaking of the type system in Haskell, too, and being able to write a similar "coerce" function is Very Bad.
In fact, it's very similar in theory to the way you might construct or leverage such a "bug" in Haskell. They are essentially constructing an argument to the compiler -- in the form of a type, which is how the compiler thinks -- that there is an equality between two arbitrary types A and B, so we can coerce between them. The compiler needs some evidence that this equality, this argument that A and B are the same, is legitimate. Otherwise, it rejects the argument, because it's not that gullible (it rejects the program as "this program failed to type check"). Because the argument to the compiler is made in the form of a type, the compiler considers "evidence" for that argument, to be a value of that type. So if your type makes the argument that "Integer and String are equal", then you need to represent that argument as a type, and create evidence for it by creating a value of that type. Then the compiler thinks your argument is legitimate. (This is a core central component to e.g. constructive mathematics/constructive computerized theorem proving)
`null` inhabits every type, so every type contains `null`. Even the type that says "String equals Integer" has `null` as a value. Thus, we can "prove" to the compiler that yes, we can turn an Integer into a String, we have the argument (the type) and the evidence (the value) to prove it! But the evidence is actually bogus.
I honestly suggest you give the original paper and the surrounding references a good reading. It all seems very sound and straightforward to me as an argument (with a bit of PLT background), and frankly I can't make heads or tails of most of your complaints in this thread, though if you're unfamiliar with the field, teasing out the subtle parts is probably a bit difficult.
An explicit downcast is allowed to fail at runtime. But if you can get a runtime cast failure in code that did not contain any cast, that's a soundness bug.
Relevant quote from the paper:
> When executed, a ClassCastException is thrown inside the main method with the message “java.lang.Integer cannot be cast to java.lang.String”. The reason is that the JVM does not directly support generics, implementing them through type erasure and type casts. This is fortunate since it causes the JVM to catch the error before it can directly cause severe problems, such as accessing memory associated with a field that is not actually present (though it might be possible that it can indirectly cause problems).