Thursday, February 07, 2008

What's the right quality metric?

Since I'm spending so much time beating on Paul Graham I thought I should balance that by pointing out what I think Paul is doing right, particularly in light of this recent posting:

"The reason I'm focusing on the region between axioms and libraries is that, from the programmer's point of view, these operators are the language. These are what your programs are made of. If Lisp were a house, these operators would be the front door, the living room sofa, the kitchen table. Small variations in their design can greatly affect how well the language works.

I've taken a lot of heat for focusing on this"

For the record, I think focusing on this is absolutely the right thing to do, and I applaud Paul for standing up to criticism and doing it. The only thing I disagree with him on is this:

By definition, there is some optimal path from axioms up to a complete language.

This is true only with respect to a particular quality metric, and I think that the quality metric Paul has chosen is brkn.

What do I suggest instead? Glad you asked.

First, let's go back and revisit briefly the question of what programming languages are for. Paul takes as an axiom that programming languages are for making programs shorter but I say they are for making programs easier to create and maintain, which may or may not be the same thing as making them shorter. Certainly, all else being equal, shorter is better, but all else is rarely equal. Sometimes adding length buys you something, and you have to make the tough call about whether the benefit is worth the cost.

It is ironic that Paul would choose such a simplistic metric after going to such great lengths to make the point that programming is like painting. I think this is a great insight, but one of the conclusions is that assessing the quality of a program, just like assessing the quality of a painting, is not such an easy thing to do. Paul's quality metric for programs is analogous to assessing the quality of a painting by counting the number of brushstrokes, and just as absurd. It is a genuine puzzle that Paul of all people needs to be convinced of this.

Programming is all about translating thoughts in people's brains into bits. There is a huge impedance mismatch between brains and bits, and programming languages help to bridge the gap. But there is no more a one-size-fits-all quality metric for programming languages than there is for paintings, or anything else that involves thoughts. There will always be different strokes for different folks.

That is not to say that we need to descend into the black hole of postmodern relativism and say that it's all just a matter of opinion and interpretation. I think there is a criterion that can be used to effectively compare one language against another, but it is very tricky to state. Here's the intuition:

If language A can do everything that language B can do, and language A can do something than language B cannot do, then language A is superior to language B.

(Note that this criterion can produce only a partial-ordering of language quality, but I think that is both inevitable and OK.)

The problem with this as stated is that all languages are Turing-equivalent, so from a strictly mathematical point of view all programming languages are the same. What I mean by "cannot do" is what cannot be done without transcending the framework of the language. Here are some examples:

1. C cannot throw exceptions.

2. Common Lisp cannot support Arc's composition operator (both because the interpretation of an unescaped colon within a symbol name is hard-coded in the standard to have a particular meaning, and because the semantics of function calls are defined within the standard in such a way that calling a composed function would be a syntax error).

3. Arc cannot (as it currently stands) dereference an array in constant time.

4. You can't add new control constructs to Python.

The obvious drawback to my criterion as stated is that it prefers large, unwieldly, kitchen-sink languages to small, elegant languages. So I'll adopt a version of Paul's minimalist metric as a secondary criterion:

If two languages support essentially the same feature set, but language A is in some sense "smaller" than language B, then language A is superior to language B.

In other words, parsimony is desirable, but only secondarily to features (or, more precisely, a lack of constraints). On this view, it is clear why macros are such a big win: macros are a sort of "meta-feature" that let you add new features, and so any language with macros has a huge leg up (in terms of my quality metric) over any language that doesn't.

So why am I so reticent about Arc? After all, Arc is pretty small, but it has macros, so it should be able to subsume other languages. And because it will subsume other languages in a minimalist way it will be the best language. Right?

Well, maybe. There are a couple of problems.

First, not all macro systems are created equal, and Arc's macro system has some known problems. How serious those problems are in practice is, perhaps, an open issue, but my quality metric doesn't take such things into account. A language that solves a problem is in my view better than a language that leaves it up to the user to solve that problem, even if that problem doesn't arise very often. (I dislike Python's syntactically-significant whitespace for the same reason, and despite the fact that it mostly works in practice.)

Second, there is more than one kind of macro. Common Lisp, for example, has symbol macros, which turn out to be tremendously useful for implementing things like module systems, and reader macros which let you change the lexical surface syntax of the language if you want to, and compiler macros which let you give the compiler hints about how to make your code more efficient without having to change the code itself.

Finally, there are language features like type systems which, I am told by people who claim to understand them (I'm not one of them), are quite spiffy and let you do all manner of cool things.

That's the real challenge of designing the 100-year language. In order to make sure that you're not designing yet another Blub you may need to be able to support features that you don't actually understand, or maybe have never even heard of (or maybe haven't even been invented yet). To think otherwise is, IMO, to deny the vast richness of programming, indeed of mathematics itself.

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