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’m so pleased with my progress on the Ca compiler, I’ve decided to provide an ad hoc link to it in its current state. I’m not confident enough to give proper instructions for it though, as it is for hardcore haxx0rz only.

I’ve made the switch from make to ant for the build system. There are a number of things which are bizarre about ant. For instance, failonerror should default to true in every case. Perhaps there are some cases where silent failure can be acceptable, which can be made explicit in those cases with a failonerror="false", but in a build system, I have a hard time believing that an error should, by default, be considered a success. Also there is no convenient built-in way to copy a file while retaining permissions.

Aside from that, I like the ant model of things. Java is not such a horrible way to describe how to build something.

As for the compiler itself, there are a number of bug fixes still in the queue, such that it still can’t be used for useful work. For useless work, however, it is quite fabulous, if I say so myself.

Even more exciting is I’ve run into a theoretical problem which is proving very difficult to prove. Research is one of the few vocations where your very metric of “success” is the number of problems you create. I’m off for a camping trip over the next few days which will give me some time to mull it over.

Next month I’ll be taking a trip back to my alma mater. I’ve been invited by my undergraduate supervisor to help him and his post-doctoral student on a new project he’s starting up. It’s a programming language based on co-inductive types where each program is guaranteed to halt in polynomial time. My job is to come up with, ideally, some clever ways of implementing it efficiently. I don’t know many more details than that, but it sounds like a dream project for me.

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.

I’ve been thinking about the compiler again and how best to implement higher-order functions, once time comes to do that. Currently the compiler uses a lambda lifter. I.e., there are no closures. Every function is lifted out of any scope to the top-level, collecting extra parameters along the way. This is fine for first-order programs, since you can change every call to a nested function into a call with extra arguments. However, in first order programs, this causes problems because the arities have to match. For instance:

f x = let g y = x + y; in
  g (x + 4);

Gets transformed into:

f_g x y = x + y;
f x = f_g x (x + 4);

Every function is now at the global level and g has all the variables it needs. This causes problems with higher-order functions though:

f x zs = let addX y = x + y; in
  map addX zs;

Naïvely this is:

f_addX x y = x + y;
f x zs = map (f_addX x) zs;

Ahh, but the first argument to map is a closure, not a function! We should properly implement closures as lambda lifted functions, so we can’t very well implement lambda lifted functions are closures! There are myriad other problems with this approach, but suffice it to say it won’t work.

Anyway, I was contemplating abandoning lambda lifting entirely and just leaving closures implemented as closures in C. The GNU C Compiler has a little-known and little-used, sadly, feature usually called nested functions. They’re half-closures in a way. They’re closures up until their lexical scope disappears. Well, such is the C way. But they would do what I needed.

I was reading the original 1988 Usenix paper which describes the technique, usually called “trampolining,” to implement nested functions quite smartly in C. As I was reading, I discovered that the author had originally intended to implement unnamed functions in C!

He gives two suggestions for syntax. I like the first one he suggests, which looks something like (int (*)(int x) { return x + 2; }). For instance, you could do something like (int (*)(int x) { return x + 2; })(3), which would evaluate to 5. Perhaps not the most useful example, but you get the idea.

These unnamed functions are really no more of a bother to implement than named functions, once you allow nested functions, but it appears this feature was never implemented in GCC! I suppose to get good use out of them you’d need a less bulky syntax. Type inference could help there.

Anyway, the point of this post was to register my dismay at GCC never implementing unnamed functions, despite there being no technical reason for not doing so. They can be quite handy, those unnamed functions.

For what it’s worth, I think I’ve decided against relying on GCC’s trampolining to do higher-order functions and lambda abstractions in Ca. It is very clever and very efficient, but the semantics are a bit hairy for the 21st century. For example, I just looked at some SPARC assembler that GCC produced for it, and it involves a system call to make to the stack executable. In today’s security conscious kernels, executing the stack, as trampolining necessarily requires, is less practical than it once was. Maybe one day we can get rid of these blunt MMUs, but that’s a rant for another time. In any case, MMU concerns aside, executing the stack mucks with the instruction cache on architectures with separate caches. As I said, hairy semantics.

In Breuel’s paper, he sets up other simpler solutions for implementing closures as being impractical due to their changing calling conventions. Well, I’m making my own language and I can make my own calling conventions. I expect that higher-order functions will simply be passed as two pointers instead of one. It saves everyone a lot of headaches.

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