Wednesday, August 02, 2017

How important is decidability in programming tools?

Hoisted from the drafts folder because the discovery that TypeScript's system is Turing-complete is making the rounds.

It's a common assumption in the programming language community that practical type systems should be decidable. Or, at least, it used to be: in the early 2000s, I had a grad school colleague who spent a lot of time trying to invent restrictions that made the type system of Cecil decidable, and people seemed to feel that his formalization of Cecil would be unreasonable if he could not solve this problem.

Over a decade later, it's well-known that Java with generics and wildcards was undecidable for years before people even realized it. Furthermore, devising restrictions to the type system that achieve decidability seems to be an open research problem.

Did hundreds of thousands of Java programmers experience an existential crisis when Java with generics was found to be undecidable? Are they waiting with bated breath for researchers to solve this urgent problem? I'm pretty sure 99.99% of them don't know that the problem exists and won't notice if it's ever fixed.

Meanwhile, the PL research community has mostly gotten bored of object-oriented languages and type systems thereof, and moved on to other things. And the functional programming community (or some fraction thereof) has embraced Scala, whose type system is also undecidable.

Conversely, it is well-known that in ML, it is possible to write a program by hand on a single sheet of paper that will take longer than the lifetime of the universe to typecheck, because Hindley-Milner is superexponential in the worst case.

What is the practical difference between a typechecker that can hang until the universe is a cold, featureless void of uniformly distributed entropy and a typechecker that can hang forever? In both cases, you would hit Ctrl-C after a decent interval and rewrite your program. Would it make much difference if ML's type system were undecidable? Probably not.

I remember standing up at an ECOOP talk one year and asking a question along those lines. The researchers had made a big deal about the importance of decidability for the problem they were solving, and I asked why it was so important. The presenters seemed to think the question was ridiculous and I'm pretty sure everyone else in the room thought so too. I probably didn't word my question well — I wasn't a good researcher and I'm not proud of my time in academia — but I still think I was basically right that one time.

The important thing is that tools have tractable runtimes for the programs that people want to write. Unfortunately, "tractable runtime for reasonable programs" is much harder to demonstrate using the formal and empirical tools that exist today than "decidable for all syntactically valid programs". And the gap in available intellectual tools has led a research community to handcuff itself needlessly in hunting for useful results.

No comments:

Post a Comment