The Universe of Discourse

Subtypes and polymorphism

[ Note: You are cautioned that this article is in the oops section of my blog, and so you should understand it as a description of a mistake that I have made. ]

For more than a year now my day job has involved work on a large project written entirely in Java. I warned my employers that I didn't have any professional experience in Java, but they hired me anyway. So I had to learn Java. Really learn it, I mean. I hadn't looked at it closely since version 1.2 or so.

Java 1.5 has parametrized types, which they call "generics". These looked pretty good to me at first, and a big improvement on the cruddy 1975-style type system Java had had before. But then I made a shocking discovery: If General is a subtype of Soldier, then List<General> is not a subtype of List<Soldier>.

In particular, you cannot:

        List<General> listOfGenerals = ...
        List<Soldier> listOfSoldiers = listOfGenerals;

I was, of course, completely wrong in all respects. The assignment above leads to problems that are obvious if you think about it a bit, and that should have been obvious to me, and would have been, except that I was so busy exulting in my superiority to the entire Java community that I didn't bother to think about it a bit.

You would like to be able to do this:

        Soldier someSoldier = ...;
        listOfSoldiers.add(someSoldier);

        General someGeneral = listOfGenerals.getLast();
        someGeneral.orderAttack(...);

The language designers must forbid one of these operations, and the best choice appears to be to forbid the assignment of the List<General> object to the List<Soldier> variable on line 2. The other choices seem clearly much worse.

The canonical Java generics tutorial has an example just like this one, to explain precisely this feature of Java generics. I would have known this, and I would have saved myself two weeks of grumbling, if I had picked up a damn book or something.

Furthermore, my premise was flawed. The H-M languages (SML, Haskell, Miranda, etc.) have not had this right for twenty years. It is easy to get right in the absence of references. But once you add references the problem becomes notoriously difficult, and SML, for example, has gone through several different strategies for dealing with it, as the years passed and more was gradually learned about the problem.

The naive approach for SML is simple. It says that if α is any type, then there is a type ref α, which is the type of a reference that refers to a storage cell that contains a value of type α. So for example ref int is the type of a reference to an int value. There are three functions for manipulating reference types:

        ref    : α → ref α
        !      : ref α → α
        :=     : (ref α * α) → unit

        val a = "Kitty cat";    (*   a : string       *)
        val r = ref a;          (*   r : ref string   *)
        r := "Puppy dog";
        print !r;

        val a = "Kitty cat";
        val r = ref a;
        r := 37;               (* fails *)

That is the obvious, naive approach. What goes wrong, though? The canonical example is:

        fun id x = x             (*   id : α → α         *)
        val a = ref id;          (*   a : ref (α → α)    *)

        fun not true = false
          | not false = true ;   (*   not: bool → bool   *)
        a := not;

        (!a) 13                  

Then we define a logical negation function, not, which has type bool → bool, that is, it takes a boolean argument and returns a boolean result. Since this is a subtype of α → α, we can store this function in the cell referenced by a.

Then we dereference a, recovering the value it points to, which, since the assignment, is the not function. But since a has type ref (α → α), !a has type α → α, and so should be applicable to any value. So the application of !a to the int value 13 passes the type checker, and SML blithely applies the not function to 13.

I've already talked about SML way longer than I planned to, and I won't belabor you further with explanations of the various schemes that were hatched over the years to try to sort this out. Suffice it to say that the problem is still an open research area.

Java, of course, is all references from top to bottom, so this issue obtrudes. The Java people do not know the answer either.

The big error that I made here was to jump to the conclusion that the Java world must be populated with idiots who know nothing about type theory or Haskell or anything else that would have tipped them off to the error I thought they had committed. Probably most of them know nothing about that stuff, but there are a lot of them, and presumably some of them have a clue, and perhaps some of them even know a thing or two that I don't. I said a while back that people who want to become smarter should get in the habit of assuming that everything is more complex than they imagine. Here I assumed the opposite.

As P.J. Plauger once said in a similar circumstance, there is a name for people who are so stupid that they think everyone else is stupid instead.

Maybe I won't be that person next time.

[ Addendum 20201021: [Here's the original post by Plauger](https://groups.google.com/g/comp.std.c/c/aPENvL9wZFw/m/II24s61rOcoJ), in case I want to find it again, or someone else is interested. ]

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