Boomerang is a bidirectional programming language over strings: it maps input strings to output strings, and then it maps outputs back to inputs. This is perfect for translation, synchronization, and other tasks: think of them as update-able views in a database. Check it out!

I have to say, I can breathe a sigh of relief now that the expression problem has been solved in JavaScript. All of the interpreters and compilers I’d written in JavaScript were so inextensible!

Download the solution to “Correspondence, of a sort”

How far did everyone get? Tips? I realize this was way, way too hard. I’ll make another one in a week or two (ha!), when my current Real Work crunch subsides a little.

Download “Correspondence, of a sort”

First, a disclaimer. I’ve never done this before, and it’s not a good crossword in its construction. Additionally, I might have made a mistake — the tool support for crossword construction on Linux sucks. So don’t get upset. If you have a problem, feel free to e-mail. I’ll post the answers in a new post next Thursday, January 25th. I’d love to .

I’ve thrown a few easy clues in there so people can get a foothold. (I recommend the northeast and southwest.) Frankly, I feel terrible about 53D. I’m sorry. If you e-mail me, I’ll give you the answer, but it’s easier if you just search the Internet, and we can both pretend like it never happened. 45D is weak, but on par with a crappy Friday clue.

That said: wow, is it hard to construct a crossword! First, you pick a theme and some theme clues. Then you fill in some solid squares so that you have a good mix of short and long words. (”Good” is relative. I have too many three letter words. I think going for two whole-board theme clues — 16A and 59A — on my first attempt was over-ambitious.) Then you fill in the boxes. (Ha!) It’s easy to get in a mental rut and see only way to fill in a section. I tend to go for the longer words first, since there’s less of an opportunity for fudging (stock symbols, etc.). The published puzzle is the second iteration — the first 15×15 didn’t pan out, though I came up with a delightfully (?) offensive clue thanks to Joel Weinberger, Sarah Zukowski, and Yaniv Zimet: “AIDS buddy”, 6. I’ll give the answer by e-mail to those who want it.

What are some examples of good writing in computer science research? Functional pearls tend to be well written, but I’m more interested in research writing. I’m looking for papers that not only introduce a new idea, but do so clearly and effectively. Bonus points if it’s a good idea, but I’d just like to see something worth emulating.

Examples are clearly a starting point, but it seems to me that the only way to improve is practicing with aware, concerted effort.

Then again, I’m not sure I’ll ever get the chance. It’s interesting that PL — and many other fields — is often more defined by the tools it happens to use (or happened to use at some point in the past) rather than problems of interest. What circumstances determine the used features of a programming language? How can feature use be encouraged (or discouraged)?

Worrying about memory leaks in JavaScript is a losing battle — the browsers have different collectors. But given functional reactive programming in other settings (e.g., Java/C#), how can we solve this kind of problem? We looked at deletion briefly, but never had time to address the issue in detail. The complexity in our case is that the event registration encodes the entire application — how do you decide that a certain code path is dead? It may be helpful to view a functional-reactive program as a super-graph of data producing, splitting, merging, and consuming nodes; the application state is the subgraph induced by the active nodes reaching the consumers. Then there’s a certain static overhead for the program, plus the dynamic overhead of its active components.

Most of the Flapjax code I’ve written has been for the user interface, so binding and unbinding isn’t much of an issue: if the interface changes temporarily (e.g., tabs), the older behavior is usually recoverable and shouldn’t be collected. When working with more complex models with longer lived state, a deletion policy is more important. Shriram has been working on larger Flapjax applications with application logic as well as presentation — I wonder if he’s run into serious GC issues.

I consider the (excellent) Flapjax tutorial prerequisite reading, so it will be hard to follow along if you’re not vaguely familiar with Flapjax.

The following code is all working JavaScript (in Firefox, at least), so feel free to follow along.

We’ll define a few functions and classes:

1. timer_e, the simplest event stream
2. Event, the class defining event streams
3. showStream, a way to show event streams on the page
4. lift_e, our focus, a way to apply standard operations to event streams
5. hold_e, a lead in to behaviors
6. Behavior, event streams that continuously have a value
7. lift_b, lift_e extended to Behavior

It really will help to follow along, typing in the code: it helped me when I wrote all of this back in March! I could post the collated code from this, but I don’t see the point: it’s all here. If you’d like to see it, just .

Our first event stream: timer_e

We’ll jump right in and define timer_e. timer_e is a timer that fires events at a given interval. JavaScript veterans will ask: how does timer_e differ from window.setInterval? The DOM API function window.setInterval registers a callback: it takes a function and an interval i, and calls the function every i milliseconds. timer_e takes an interval i and returns an event stream; every i milliseconds a new value (the time in milliseconds since the Epoch) will come down the event stream.

The key difference is that window.setInterval doesn’t return anything: you give it a callback, your callback gets called. timer_e gives you a handle to a value that encapsulates the timer itself. This is useful because the timer can be passed around as a value, allowing you to abstract out that part of your program.

Every time the interval — a repeated timer — triggers, the current milliseconds-since-epoch will be sent as a new value on the event stream.

The core event-stream structure: Event

We can make this more concrete by defining Event.

That is, an event stream is just a callback manager, support structure for the observer pattern. Callbacks can be registered on an event stream by running e.listeners.push(…);. To send a new value on the event stream, you can call newValue to notify the listeners. This is how timer_e hooked setInterval up to the Event class: every time the interval called its callback, an event’s newValue method is called with the time since the epoch. (As an aside, Event is called Node in Flapjax, since it represents a node in the callback graph.)

Output: showStream

A function like timer_e is a constructor for integer-valued event streams; that is, Event objects with integer values. For event streams to be useful, we also need a deconstructor for event streams. Since JavaScript runs in browsers, it makes sense to have event stream deconstructors that affect the HTML page through the DOM. In Flapjax, insertDomE is a deconstructor for events with printable values (e.g., strings and numbers, not objects and lists). Given a hook into the HTML page — a unique id, for example — and an event stream, insertDomE will update the HTML page with new values as they appear on the stream.

We’ll write our own, simple version of insertDomE. We’ll call it showStream, since it will do just that: it’ll just write each value out to the DOM.

If you’re running the code, the code below assumes that there’s an HTML block tag (div, say) with id “log” in the document. Alternatively,you could use FireBug and its console.log feature. (It’s a must for JavaScript, anyway.) In this simple example, I just dump out every new value without removing any of the old ones. If you’re following along, why not change the code as an exercise?

If we go ahead and run it, it’ll spit out the time in milliseconds since the epoch once every 100 milliseconds:

You’ll need to run that code in a function called from body.onload, since showStream will only work once the whole page is loaded.

Lifting

The above is enough to see the beginning of a functional reactive system, even though all we’re doing is playing with callbacks. The real payoff of functional reactivity is the ability to manipulate and combine event streams using ordinary operations. The process of applying a standard operator (like + on numbers) is called lifting, and it’s what you came here for.

What is the type of this function? The first argument is a function. The second is an event e. The function listens to the event that its passed, and returns a new event. For every value v that appears on e, the new, f(v) appears on the stream of the new, ‘lifted’ event. Note that this definition of lift_e can’t use time-varying functions (i.e., function-valued event streams) or functions with more than one argument. This is to clarify the core idea of lifting; in Flapjax, lifting works for time-varying functions of arbitrary arity. If you’re following along, try it as an exercise — it’s not too difficult, but it’s not trivial. If you do it without looking at what Flapjax does and reimplementing it, I’d be curious to see what you, dear reader, come up with.

In any case, let’s see this in action! We’ll run a lifted function. (This example is ‘lifted’ from the Flapjax website’s second “time” demo.)

If you’ve been following along, you’ll notice a problem. Redundant values keep getting spit out! The setInterval call in timer_e regularly sends events down the stream, and the lift_e call will happen every time an event occurs. The division and truncation occur ten times a second (or so) with the same result!

Avoiding redundant events: hold_e and Behavior

How can we avoid these redundant events? We need a function to ‘hold onto’ the last value and not propagate identical values. This is quickly and easily written:

We keep the last value seen in valueNow, only propagating new values. (We should probably use a more robust version of equality than === and !==, but that’s irrelevant in this tutorial, where we’ll only use integer-valued events.) If we change the last example to:

Success! Only one message per second appears in the log. In Flapjax, this isn’t exactly the way hold_e is defined. In fact, this definition has a small problem that doesn’t come up with timer_e, but can with other event sources. What happens in lift_e and showStream if no value has come along on a held stream yet?

The first observation is that we have in valueNow a ‘current’ value, a way to track the most recent value sent on an event stream. In fact, even though we don’t give it an initial value syntactically, valueNow has one — undefined! If we turn valueNow into a member variable of a class, rather than a scope variable in a closure, we could use it in functions in place of a default value. The Flapjax solution is to create a subtype of Event, called Behavior. (Actually, it’s to create a subtype of Node called Behaviour. Oy.) Defining this new class isn’t difficult, but it does showcase JavaScript’s funniness.

To paraphrase, a Behavior is an Event with an additional member valueNow; it only propagates events that are different from this value. Basically, we’ve woven together hold_e and Event.

To demonstrate the new form of propagation:

Our (trusty?) old lift_e will work on this structure: it is an event, after all! But we still don’t do anything with valueNow. Fortunately, we can reuse lift_e in writing a new lifting form for Behavior:

Note the subtype-punning with the nested lift_e. Readers familiar with functional-programming will see that we’ve simply threaded the lifting through the new (underlying) datatype.

Using lift_b, we can extend our old example cleanly:

But we can also show that valueNow is propagated correctly:

If we so chose, we could extend showStream to work with valueNow. If you’re following along, try it as an exercise! (I love saying that, particularly since I don’t have to do it!)

Now that we have a solid understanding of lifting, we can finally understand what the difference is between just using Flapjax and using the Flapjax language, via the compiler. Using Flapjax as a language, you have to manually lift operations on Flapjax’s time-varying values. When you use compiled Flapjax, this lifting happens automatically. How? Stay tuned!

• Benjamin Pierce
• Rajeev Alur
• Stephanie Weirich
• Steve Zdancewic
• Val Tannen
• Ben Taskar
• Fernando Pereira

I’m really excited!