2020-01-19, 0900h

Introduction Enclosing variables

Manipulating Enclosed Variables

Passing Lambdas Around

Things

Introduction

In this post I'd like to explain how things (in-game objects) work. (This will also, incidentally, be a short tutorial on lambda calculus and closures.)

In the language of game design, Racket-MUD uses a type “entity component system,” more or less. I call it quality of things, and developed it mostly in the isolation of solitary hacking, so there are some differences.

Everything a user interacts with inside Racket-MUD is a thing, and every thing has qualities, which define its capabilities.

From the user's perspective, a thing is a loaf of bread, a field, a starship, or even abstract things like jealousy: it all depends on the sort of MUD being implemented.

From the engine's perspective, a thing is a function, into which functions are thrown, and out of which comes a function.

Enclosing variables

Let's forget about things for a moment and look at some more generic code.

(define alef 7)

What's this do? It defines alef as 7. Simple enough.

(define bet (λ () 7))

What does this one do? It defines bet as a function, that returns 7. ((λ () 7) breaks down to “make a function (λ) that takes zero arguments (()) and returns 7.“)

By-the-by, that λ symbol? That's the lowercase “lambda” character from the Greek alphabet; it's used in a few programming languages (and branches of mathematics) to mean “a function.”

alef ; -> 7 bet ; -> <#procedure:bet> (bet) ; -> 7

Calling alef returns 7, but calling bet returns a procedure – so, we have to call that procedure, by doing (bet): and now we get our 7.

Pretty simple. Let's build on this.

(define gimel (λ () (define num 7) (λ () num)))

Less simple: there are two of those λ things. We know that calling gimel will return a function: let's look at what that function actually would contain:

(define num 7) (λ () num)

So, first, it's defining num as 7 and then… it returns a function, that we can see, takes no arguments, and returns num. So how do we use gimel?

gimel ; -> <#procedure:gimel> (gimel) ; -> <#procedure> ((gimel)) ; -> 7

Well, we've certainly added complexity, but there hasn't been any new capabilities added.

(define dalet (λ () (define num 7) (λ () (+ 1 num))))

Here, we've replaced returning num with returning (+ 1 num).

So, running these we get:

dalet ; <#procedure:dalet> (dalet) ; <#procedure> ((dalet)) ; 8

Manipulating Enclosed Variables

Now we're getting somewhere. Let's add some more capabilities. Here, we're going to make it so that the procedure returned by the outer-function is capable of taking an argument; that'll be added (+) to num.

(define he (λ () (define num 7) (λ (x) (+ x num))))

So now we can do:

he ; <#procedure:he> (he) ; <#procedure> ((he) 1) ; 8 ((he) 10) ; 17

Now that's something! Let's rename the function we've been working on to make what it does more clear.

(define add-to-seven (λ () (define seven 7) (λ (x) (+ x seven))))

Maybe now the point of why I've done this will be a little more clear: we've created a bit of data, seven, and it's held inside the function. Basically, all we can do is ask the function, “what would happen if we added x to 7?”

Let's make it a bit more general.

Passing Lambdas Around

(define do-to-seven (λ () (define seven 7) (λ (f) (f seven))))

We've changed the returned function here: now it doesn't take x and return the result of (+ x seven). It takes f and returns the result of (f seven).

You might be able to infer that f is intended to be a function, not a number, and that it needs to take one argument, and that argument will be seven. Let's play around with this.

do-to-seven ; <#procedure:do-to-seven> (do-to-seven) ; <#procedure>

Y'know these nested parantheses aren't always that easy to read. Let's switch up the style a bit.

(define seven-doer (do-to-seven)) seven-doer ; <#procedure>

Alright – now we can directly access the enclosed function, (λ (f) (f seven)), with seven-doer. Let's move on.

(seven-doer (λ (S) S)) ; -> 7

What does this do? It calls seven-doer, passing it a lambda function that takes one argument, S, and returns S. This returns 7. Let's see how, by looking how the statement expands. First, the code above turns into, more-or-less:

((λ (f) (f seven)) (λ (S) S))

Ew. Hard to read, but try to follow the parantheses. The whole thing is one statement, with two parts: the first is a lambda function that takes f and returns (f seven), and the second is a lambda function that takes S and returns S.

The first part of the statement is treated as a function, and the second part is its argument, so the next step from here is to pass the second part into the first part. We get to

((λ (S) S) seven)

(That is, (f seven) when f is (λ (S) S).)

So, from here, we pass seven into the lambda function, which just returns whatever seven is, in this case, 7.

Phew! That was a lot. The point is, now, we have a function that we can ask, “Hey, show me what would happen if I do the following to 7…“

…and “the following” can be just about anything you think of. Like, say, doubling it.

(define double (λ (x) (* x 2))) ; -> <#procedure:double> (do-to-seven double) ; -> 14

Now, this is a lot of semantic overhead for what is essentially (* 7 2). but let's see how this relates to Racket-MUD's things.

Things

(define thing-maker (λ (name) (let ([thing (make-hash (list (cons 'name name)))]) (λ (f) (f thing)))))

(This isn't actually the code for making a thing, just a simple version for explaining the concepts.)

Let's pull this apart:

thing-maker is a function that takes one argument, name, creates a hash-table called thing to store the name, and returns a function that takes one argument, f, and returns the result of (f thing).

(define bob (thing-maker "Bob")) ; <#procedure> (bob (λ (thing) (hash-ref thing 'name))) ; "Bob"

So this defines bob as the result of (thing-maker "Bob"): a procedure, (λ (f) (thing f), where thing is a a hash-table of the key 'name to the value "Bob".

Essentially, bob, the variable, is something into which we can throw queries about Bob, the thing.

So if we give the function (λ (thing) (hash-ref thing 'name))) to bob – or any thing – we're basically asking that thing, “Hey, what's your name?”

And the thing will look at itself, and say what it's name is – "Bob".

In this way, we're able to arbitrarily define new qualities for the thing (by adding them to its hash-table), or manipulate them in new wyas, without having to extend the core functionality of the thing, which is, essentially, just making a hash-table and returning (λ (f) (f hash-table)).

And that's how things work!