When I get the opportunity to do research these days, it’s mostly focused on trying to formalize the abstract syntax, typing and operational semantics from the programming language’s point-of-view, not the logic’s point-of-view, once and for all. Once of the major problems is that the typing for Pola is complicated, much more complicated than typing systems I’ve done in the past. On the one hand this makes me very pleased with myself that I was able to get type inference going as well as I have, but on the other hand it’s a huge obstacle to getting other people interested in what we’re doing.

I apologize for the sloppy prose, but this is from a rough draft of notes I’m keeping for myself. The notation used in this typing rule is actually much simpler than what I’d had previously.

It’s horrendously confusing and yet, through many revisions, it’s the simplest and most straight-forward I’ve been able to come up with to describe what’s happening at the type level. Sometimes I think it would be easier to just show people the code instead of the sequents, ha!

Anyway, I shall keep at trying to simplify this stuff. It’s further emboldened the motivation I have for prettying of the “face” of this language for mortal users.


I always feel bad about not updating here, but I never have much to say. Or, perhaps equivalently, I have too much to say. The nature of Pola, the polynomial-time programming language I’m working on, is constantly changing and I wouldn’t really want to explain all the details here anyway. Suffice it to say that the spirit of the language remains essentially the same and the details of the language change day-to-day, a slight exaggeration.

I’m newly committed to better balancing my research and my teaching. Teaching had taken over my time completely this term and research had fallen by the way-side, which is really a shame. I’ve changed that this week, though, and have got a lot of good work done.

I gave a short talk about my research at the Western Research Forum, an annual mini-conference here at UWO for graduate students of all disciplines. I’m pleased to announce that I won second place for the natural sciences session. First place went to someone dealing with meteorites: it was also my choice for first place, so I have no problems losing to that. After my presentation I got a lot of good question which, if nothing else, shows I could keep people’s interest. The questions didn’t come exclusively from computer scientists, either, but from other physical scientists curious about how this might relate to all the FORTRAN code they have to work through. It was good to see.

The highlight of the conference was seeing Jorge Cham, author of Piled Higher and Deeper. I very highly recommend going to see him talk if you get the chance. It’s a funny talk, of course, but carries a lot of insight with it, too. I’ve uploaded one picture from the talk which made a big impression on me.

Talking with people about my research, I always go back and forth between my motivations and where I want to focus my research. When talking with people in theory or in programming languages, they seem to be most interested in proving theoretical properties of the language and making sure that’s all very solid. When talking with everyone else, the prevailing opinion is “yes, but no one would ever use it”, reinforcing that the “face” of the language, the syntax and the typing system, is most important. I need to get a good balance between the two.

The paper we submitted to PLDI (Programming Language Design and Implementation), sadly, was not accepted. It’s not a huge surprise: our paper wasn’t a perfect fit for PLDI; further, our work was in a mild state of flux and the paper reflected that. We’ve submitted a paper to TLCA (Typed Lambda Calculi and Applications) and are anxious to get feedback there.

In just over two hours, I’ll be on a plane to Calgary to do more research there. I’m going to be doing some work at the airport and on the plane trying to get the implementation into a good state so we can start doing research right away. Particularly I want to seriously talk about inferring bounds.

Naïve bounds inference is theoretically done, though not implemented yet. Naïve bounds inference is too, well, naïve, however. We need to tighten up the bounds a lot for it to be practical. I’m hoping we can get some time to discuss how bounds inference affects the memory model as well.

So, what we have now is: a functional language allowing inductive and coinductive types—and now even mutually recursive types!—such that every well-typed program halts in polynomial time; an implementation, complete with type inference; inference of time and space bounds.

At the end of this week things should be in really good shape! I’ll post an update, as I’ve been neglecting this blog for too long.

We got a paper submitted to PLDI—Programming Language Design and Implementation—if just. The acceptance rate of late has been around 20% it seems. I think the paper was good, but I have no idea of it was that good. Since PLDI has a double-blind refereeing system, I’ll try not to give too many specifics in this post: specific enough that I can talk about things, but vague enough that a referee won’t inadvertently stumble here from Google.

I’m fairly sure that this language marks the direction my research should be going in during my Ph.D. It has the possibility of being a very nice language. Of course I’ll wait to see what the referees say. It may be unlikely, but there’s always the chance of a “this research is a dead-end because of [reason you’ve never thought of]” which is why it’s nice to get feedback from fresh eyes.

There are issue for the front-end. I think this is the biggest fault of the language as it stands right now. Considering what the language is intended to do—give automatic guarantees on polynomial time complexity—a lot of the complexity is justifiable, but still it can be improved. The typing system is a bore to get around. After becoming familiar with the language for a few weeks or so one starts to get a bit of intuition about how to structure things to “beat” the typing system. Still, it would be nice to add a bit more in the way of inference so the typing system can help you out. The syntax is perhaps more cumbersome, in the sense that there are too many constructs, than is totally necessary.

Changes to the front-end wouldn’t be purely cosmetic, either. The way we have the language right now is nice since everything that’s in there serves a purpose and everything is proved to work correctly. In a language such as this, removing something or changing something is a very delicate matter and it’s easy to destroy the guarantee mentioned above of guaranteeing time complexity. But work and cleverness aside, I’m sure it can be done.

On the back end of things, there aren’t problems so much as there are opportunities. As it stands, the implementation—which needs a lot of work yet—is just a very naïve interpreter. Making a compiler for a language such as this brings up myriad issues which one wouldn’t find in any other language. Memory management is the big one. Garbage collection is likely not necessary at all, so it will be interesting to see exactly what nice—and efficient—memory management schemes it would offer.

I apologize for not posting more often to this blog. It is, of course, the usual excuse—I always find more important things to do. In fact I’m still terribly busy, but I thought I was overdue.

I got back from working with Robin Cockett and Brian Redmond in Calgary. They’re working on a new programming language which uses type theory to enforce that each well-typed program halts in polynomial time. It’s been done before, but nowhere near as nicely as this. The implementation is just a proof-of-concept, nowhere near fit for consumption of a general computer science audience. It was this fact that it’s built on a terribly recondite foundation mixed with discussions over the minutiæ of the syntax got me thinking more about the face of a programming language, the dreaded “front end.”

Syntax in the programming languages world has, to a large extent, been considered a solved problem for the past couple decades, and for good reason. The technology behind parsing has, so far as I’m concerned, been solved. There have been enough languages created, and segregated into successes and failures, that people have a general idea of what a decent programming language should look like. Yet the process is still not formalized. When creating a new language, people—or myself at least—look at existing successful languages, fudge them to fit whatever new characteristics their language will contain, and use common sense to reason it out.

I think I’ve stated on here before my fondness for literate programming. I think code should be primarily documentation and, further, that that documentation should look gorgeous and be easy to read. As I was mulling over programming language syntaxes, I hit an epiphany when I realized that the primary goal in the syntax of a language should be how readable it is when typeset. As we move towards higher-level languages and rely on smarter compilers to do what we want to do, the purpose of a language is no longer to describe exactly which bits gets pushed where, but rather to, in the most elegant way possible, describe the essence of the solution to the problem.

I like the off-side rule—the “significant whitespace” present in Python and Haskell—for exactly this reason. When displaying code that’s meant to be read, it’s imperative that the code be indented nicely anyway. Why not have the language enforce that the program’s structure be identical to how it’s presented?

This got me thinking about syntax highlighting. Highlighting is nearly as important to indentation when understanding the structure of code, in my view. Further, when typesetting literate code, that code should properly be highlighted in the typeset document. So why not make highlighting part of the language? One could distinguish between the highlighted keyword let and the variable name let. It poses some practical problems, namely that you potentially have to abandon straight ASCII as an input format in favour of annotated ASCII such as LaTeX or Rich Text.

The other thing I started thinking about is syntax in the context of information theory. This got in my head as we were discussing the role of keywords such as of in the new language. Should the syntax dictate that you write case x of … or should it leave out the entirely unnecessary keyword of there?

In the interest of maintainable code, there’s value in redundancy. As two extremes: one can write 50 characters of C++ code and, due to the noisiness of C++’s template syntax, relay only 50 bits of actual information; however, 50 characters of Lisp code might relay 200 bits of information. In this case I like Lisp’s syntax better than C++’s, but there’s a huge danger in having a syntax which is too concise: one parenthesis in the wrong spot and the semantics of your program can be completely different from what you intended. And that difference might not be obvious to the reader.

I had this conversation years ago with someone about the operator—used both in programming and English—”not.” Note that whenever someone feels they must get across the point that they are not something, they will emphasize—using italics or boldface or uppercase letters or anything at their disposal—the word “not” and often only the word “not.” Programmers typically don’t have such luxury, and an errant ! symbol can sometimes get lost in the mix. Yet it is one of the most powerful constructs in computer science: that you want to do exactly the opposite of what you’re going to describe next. From the point-of-view of information theory, A and not A are syntactically almost identical.

So that is a clear example of where it would be nice for the language to enforce some redundancy. Don’t just throw a ! in there, but redundantly make other changes to the code that make it clear that something’s going on.

The obvious question is: so how would a language do that? An even better question is: how can a language require redundant information without being complete torture to write in? I’ve no idea, but it would be nice if someone would look at it formally, ha!

I apologize for the long delays between posts. Rest assured no news is good news, and it’s just business as usual.

One bit of exciting news, though, is that I’ve received an email from my old supervisor, Robin Cockett, at the University of Calgary. He has a project for a pretty cool sounding programming language based on Martin Hofmann’s work—where programs are restricted to polynomial time—and needs someone to worry about the implementation details. I’m pretty excited about the prospects.

Also I’ve decided to turn my idle attention to my Zipit, borrowed from my friend Albert. It’s kind of a fun little thing, if annoying to type on, but sports a 60MHz ARMv4 chip in it. I’m toying with the idea of having my compiler target not just C, but also ARM. I’ve got an ARM cross-assembler installed, so it’s just a matter of working out the networking details.

ARM is a surprisingly beautiful ISA. Everyone knows it for its pervasive use of conditional instructions, of course, but its addressing modes are quite nice as well. My only other exposure to pre- and post-index addressing was with the PDP-11, but ARM does it in a much cleaner way.

Last week, my co-supervisor gave me the Steam Boiler Problem. It’s a classical problem for specifications languages. You have a computer monitoring a steam boiler: a giant tank of water with a heat source and a steam pipe at the top. There are water pumps to control—to add more water into the tank—and a series of sensors. Essentially, given complex specifications, you have to get the steam boiler into a functioning state and keep it that way. Sensors can start malfunctioning, too, to make it more difficult.

It’s a good problem because it forced me to look at how Ca is to work with in the flesh, in a complex example. Even though I’m not done, the conclusion is that it needs a lot of syntactic sugar built on top of it.

Some of them are rather superficial, if time-consuming. For example, currently patterns cannot overlap at all in Ca, so something like:

l {
  Cons 5 xs -> ...;
  Cons x xs -> ...;
  _ -> ...;

Is not allowed, though it really should be. I had no idea before now how irritating it is not having that feature. There are other minor syntax features like that that need to be addressed.

The more interesting case is what to do with the catamorphisms. Theoretically they work fine, almost. In practice, they’re a bit cumbersome. When I said “almost” before, I meant they worked fine up to Loïc Colson’s famous inférieur (“minimum”) problem. It pertains to primitive recursive schemes like the one I’m working with, were writing the “minimum function”—finding the minimum of two values—has greater time complexity than in an unrestricted computational model.

What this boils down to in my mind is the inability to perform a catamorphism over two objects simultaneously. Or stated in a more Haskell-ish way, there’s no efficient way to write the zip function.

One solution floating in my mind is to make the catamorphism construct explicitly allow zipping. It’s not too bad adding it in. The syntax would be something like so:

(l, n) {
  (Cons x xs, p+1) -> ...;
  (Nil, 0) -> ...;

Where l is a list and n is a natural number.

Another possible solution, which I quite like, is the idea of making catamorphisms parametric. So you could do something like so:

{ i ->
  Cons x xs -> i * x + @xs x;
  Nil -> i - 2;
} l 0;

The variable i is a parameter over the catamorphism, initially 0. I like this is as it makes a lot of things more natural and doesn’t add any computational power. The syntax for the catamorphism has to change, but I think this is for the best anyway.

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