Entry 005: Functions: take 1

Started 2024-02-18
Published 2024-03-01

Purpose

I proposed in Entry 003 to design the minimal language features required for ProbMod's trait attribution example model. In Entry 004, I added conditionals and the "condition" effect, which was sufficient for the first model, of one student and one test:

Infer(function() {
  var examFair = flip(.8)
  var doesHomework = flip(.8)
  var pass = flip(examFair ?
                  (doesHomework ? 0.9 : 0.4) :
                  (doesHomework ? 0.6 : 0.2))
  condition(!pass)
  return {doesHomework: doesHomework, examFair: examFair}
})

(I should explain that model, but I won't be referring to it again in this entry, so I won't for now. See the link above.)

The next (and final) iteration of this example model makes use of functions, function application, and memoization, so I guess I'll work on those in order starting with function definitions and application.

Experimental plan

Wiring semantics

As usual, the visuals won't be directly executed, but rendered with enough precision to hint at a sensible semantics. Here's what I'm thinking.

A function definition is drawn as a box. The box is analogous to function() { … } in JavaScript. Wires interact with the boundaries of the box in a few ways:

Wire direction Connected outside? Connected inside? Diagram Purpose
Entering ✓ ✓ Diagram of a wire entering a function, connected to nodes on both ends. A captured value. These wires can come from enclosing scopes, but not disjoint ones.

This diagram is like defining a global constant 0.8 and referring to it inside the function as an argument to flip.
Entering ✓ Diagram of a wire entering a function, connected to a node only on the inside. A function parameter, like the x in function (x) { … }. One end of the wire is unplugged until the function is used. Makes sense.

This diagram is like calling flip(x) inside a function with an argument named "x".
Entering ✓ Diagram of a wire entering a function, connected to a node only on the outside. A function application, like f(x), where x is the value carried by the wire. Multiple wires all take part of the same function application, like f(a, b, c).

This diagram is like calling f(flip(), flip()). See the note below about argument ordering.
Exiting ✓ Diagram of a wire exiting a function, connected to a node only on the inside. The value to return. There can be only one of these per box.

This diagram is like writing return flip().
Exiting ✓ Diagram of a wire exiting a function, connected to a node only on the outside. Carries the returned value.

This diagram is like flip(f()).

When you need to refer to the function itself, like to pass it to a map(…) or whatever, you draw a wire starting at the edge of the box itself, as opposed to a wire that crosses over the edge.

I arrived at this design with two use cases in mind:

  1. Anonymous functions used in one place. Like the one in this snippet that evaluates to an array of the results of calling flip() 10 times:

    repeat(10, function() { flip() })

    I wanted using functions like this to be easy: draw a box, put stuff in it, freely pull in wires with values from the surrounding context to capture them, then draw a wire connecting the function box itself to the node that needs a callback. Quick and easy?

  2. Named functions intended for reuse. At the function definition, you don't know where wires connected to the outside go, so you drape them over the edge of the box and they'll be rendered with an end cap like “…” or something to indicate that they go… somewhere. This is consistent with the way other nodes work (like "flip") whose definitions aren't visible: you pull wires into and out of them, without really knowing what they connect to on the inside.

If a function has multiple wires going into it, how does the function decide which one to use for which purpose? In function(a, b) { … }, the arguments have names to tell them apart. We need something like that.

The direction the wire comes from seems important for some functions. For example, there's a strong directional component to the left and right sides to a “<” node.

But in repeat(count, fn)? In textual language, I forget the order of arguments of functions like that all the time. Enforcing an order makes code harder to write, but I don't know if it helps readability very much. (Would there be harm in defining both repeat(count, fn) and repeat(fn, count)?) In the visual language I'm designing, I don't think it would be confusing to see count come from the left sometimes and right in others. You can see the numbers going in.

So there are options. In some cases, it seems reasonable for us to automatically determine which wire is which based on the values coming in ("that's a number—must be the number of times to repeat"). In other cases, maybe we use the location of the wire (“<”). In other cases, maybe we can draw on an RCA cable metaphor and use color, or a cable tag metaphor where you write down what the values on that wire are for. Something to think about later!

Which interesting new model will I implement?

I don't have a particular model in mind. I'll throw together some code that uses functions. Whatever. I just need to see functions defined and applied on the screen.

Observations and data

How I add a new language feature

I've added new language constructs for a few entries in a row, and I noticed that a pattern has emerged in how I do it:

  1. Sketch a new model in my paper notebook, with the same nodes-and-wires representation as I want on the screen.

    (Looking back, starting on paper is why nodes are currently just words floating in space. I don't draw borders or backgrounds on paper, and that translated directly to the screen representation.)

    (Looking back further, I realize I'm drawing on the aesthetics of the Princeton Sound Lab software I worked on, especially sndpeek and TAPESTREA. Not really where I want to stay, but it works for now.)

  2. Delete all remnants of the previous model from the source code, except the pieces that made it into the helper classes that I use for drawing nodes and wires and charts and whatnot. Start with a blank canvas every time.

  3. Translate the model to the screen using Three.js graphics primitives. I even add placeholder charts of fake data everywhere that I'll want a real one later.

  4. Write a rejection sampler for the model in TypeScript. To write a rejection sampler for a model where every setting of random variables is either valid or invalid (i.e. the only likelihoods are 0 and 1), all I have to do is write it like a normal, deterministic program and return early from any execution trace where a condition is false. So this step is easy.

    Rejection sampling is more inefficient the less informative the priors are, because so few of the samples end up satisfying all the conditions. But for the models I've wanted to use so far, JavaScript has been fast enough for this not to be a problem. ¯\_(ツ)_/¯

  5. Hook the charts up to the output of the Sampler.

So that's what I did this time, too.

I don't need to actually load and save models for what I'm trying to learn.

Stage 1: anonymous function, used in one place

I decided to implement this model first:

sum(repeat(3, function() { flip() }))

Its output is the sum of three coin flips, where heads is 1 and tails is 0.

(When I step outside my head, I can see how bizarre that statement is, and yet, I've written so many similar models that it seems like the most natural thing in the world to do. That mismatch is going to cause problems in how I talk about this language with others, and that's is why I'm trying to get as far from coin-flipping as possible as quickly as possible.)

Anyway, I translated that model like this:

Animation of that model implemented in this PPL

Some thoughts:

Stage 2: defining a helper function

I decided to extend the earlier example with a function that clamps the sum to return no value larger than 2:

var clamp = function(num) {
  return num > 2 ? 2 : num
}
clamp(sum(repeat(3, function() { flip() })))

It came out like this:

Animation of that model implemented in this PPL

Yeesh. "clamp" has to be the ugliest function I've ever seen. 😬

Anyway, some other notes:

Discussion of results

The elephant in the room is that I started with this modest WebPPL model:

var clamp = function(num) {
  return num > 2 ? 2 : num
}

and turned it into this:

The clamp function implemented in the PPL

It takes work to read, and I'm not happy about it:

On the other hand, I can live with all of this for now because it meets my criteria: it represents a reasonably unambiguous language semantics that I'm confident that I can edit using commonly-available input devices. All right? So I'll address all this later. Perhaps by improving wire rendering beyond straight lines. Perhaps by being more flexible about the direction wires can enter a node (swap left and right sides of an if by adding those color or text tags?). Later, though.

What worked?

Conclusion

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