# What is a programmable programming language?

When I was still researching this fabled obscure language called Lisp one thing people kept saying about it is that “Lisp is a programmable programming language”, but I could never figure out what they meant by that. It sounds like a smug buzzword or like a gimmick from an academic toy language. Lisp programmers have gotten so used to metaprogramming in Lisp that they seem to forget that it is either an entirely alien concept to people, or something people have been burned by too often (like every C programmer).

When I talk about “Lisp” I mean the Lisp language family in general, not a particular language from that family. There are differences in how macros are written in each one, but the general underlying ideas are the same.

## Domain-specific languages

The English language has a vocabulary and a grammar. The vocabulary is open to extension, we can add to it by assigning a definition to a new term. However, the grammar is fixed, every sentence needs at least a subject and a predicate. The phrase “Alice loves Bob” is a correct sentence, while “Unfair bullet difference night” is impossible to make sense of, even though all the words have meaning. This is so ingrained in our mind that I had to pick the words randomly from a dictionary because my brain would always try to form a meaningful sentence.

However, even though we cannot change the grammar we can define new languages with their own grammar that deviates from English grammar. Take the expression “$2+3=5$”; this is not English, yet you can read it easily. It is a domain-specific language for specifying mathematical expressions. In your mind you can translate it back to English as “The numeric value of the sum of the numbers 2 and 3 is the same as the numeric value of the number 5”, but the message can get lost in all this fluff. The domain-specific language of mathematical notation allows us to express facts in a more concise, clear and less ambiguous way.

Here is where it gets interesting: how is this new language implemented? It was not magically beamed into your brain, you did not teach it to yourself through trial and error, it is not something you instinctively understand. It was taught to you at a young age in English. Someone explained to you in plain English what the symbols mean and the rules for how to combine them. (This is not to be take for granted, there are also languages one can learn in another way, such as body language or the language of facial expressions. Human communication is very complex)

The key point here is that we can extend a spoken language not only by adding to its vocabulary, but also by introducing new constructs which do not necessarily follow the grammar of the host language. These extensions are implemented in the host language itself.

## Metaprogramming in C

What does any of this have to do with programming? The technical analogue to the vocabulary of a spoken language is the set of values in a program. We can always define new values, new functions, classes, operators, and so on. But they always have to follow the “grammar” of the programming language. What we are looking for is a way of changing these rules themselves.

The C preprocessor is a widely know way of metaprogramming. We define little snippets which can then be spliced into the source code. Here is an example:

``````#define FOO(x, y) (x)
int x = FOO(bar(), kill_all_humans());``````

If `FOO` was a function it would have evaluated its arguments first, which would have killed all humans as a side effect. However, the fact that that it is a macro means that the code has been rewritten to a harmless call of `bar()` instead. Macros in C are a very naive text-substitution and notoriously hard for getting right. They are not written in C, but in another language, and the substitution used to be done by a different process than the compilation. C++ has added features like templates precisely to avoid the preprocessor, but doing so comes at the expense of a more complex language. How much more convenient would it be if we could have written our macros in C instead and used all of C's features to generate our code instead?

## Metaprogramming in Lisp

Lisp allows us to do just that, we can write macros in a safe and structured way in Lisp itself. This is possible because of the syntax, or rather non-syntax of Lisp. Take the following expression:

``````(/ (+ (- b)
(sqrt (- (* b b)
(* 4 a c))))
(* 2 a))``````

This is the formula which solves the quadratic equation (the first solution the be precise). If you squint your eyes you can make out a tree structure. In Lisp we write our program by writing the abstract syntax tree (AST) directly instead of hiding the AST behind some unrelated syntax. The AST is what the compiler will operate on to generate machine code. And since the AST is just a tree structure we can manipulate it like any other tree structure. After all, there is nothing sacred about the AST, it is just another data structure which will be manipulated by the compiler, so we can hook into the compiler and manipulate the data ourselves.

### Implementing local bindings

Let us for the sake of argument assume that Lisp did not have any way of creating local bindings. If we want to bind a value to a variable we instead have to create an anonymous function, which has the bindings we want as parameters, and immediately apply it to the values we want to bind.

Assume we want to get the current time from a clock and the current temperature from a thermometer. We then want to log those two values before doing some sort of calculation. We cannot fetch a new value every time we need it because the value might be different, we need to get the values once and bind them.

``````((lambda (t θ)
(log-temperature θ)
(log-time t)
(do-something t θ)) (get-current-time)
(get-current-temperature))``````

This is just awful! It is easy to get a detail like the order of arguments wrong, it is ugly, things that belong together conceptually are separate, and if we had not been told the reason for this convoluted construct we would have to guess the intention behind it.

We can invent a special form for this case. First we need to give it an idiomatic name like `let`, then we group the bindings together and put them at the beginning and enclosed in a pair of parentheses to make them separate form the body of the form.

``````(let ((t (get-current-time))
(θ (get-current-temperature)))
(log-temperature θ)
(log-time t)
(do-something t θ))``````

This is much better. Of course such a useful form is built into pretty much every Lisp, but if it wasn't we could have simply retrofitted it to the language, made it into a library and sent it out to other people to use. I admit, this example is rather trivial, but it still serves as a good illustration: `let` could not have been implemented as a function because it completely breaks how Lisp evaluates s-expressions.

### Lisp in Lisp

The implication of this simple example is that most of the “features” Lisp has are implemented in Lisp itself and can be reduced down to a small set of core features. Structures, object-oriented programming or loops can be simply added to Lisp.

Compare this to other languages: if there is feature you want you first have to convince the standards committee that it is a good idea, then wait for the committee to agree upon an implementation and publish a new standard (and most likely you will have to wait for the committee to schedule a meeting in the first place), then you have to wait for implementations to adopt the new feature, then you have to wait for other people to transition to the new version, and then finally you can use your new feature in production. This is of course assuming that your feature is considered general enough by the committee and not too specific to your use-case.

In Lisp none of this is an issue. Individuals can simply write their own implementations and publish a library. The community can then adopt the library and through common consensus the library gains popularity until it becomes as popular as if it was in the standard.

## OK, but why?

It is easy to see why being able to create big additions like object-oriented programming would be valuable, but most of the times you will never need to create anything as large as CLOS (Common Lisp Object System). Does this level of metaprogramming offer any advantages to the average user or would we be better off just picking a language that already has all those big features? After all, it doesn't really matter how a language feature is implemented, only that you can use it.

This line of thinking assumes that creating new features is hard any only worth the effort for big features. Who in their right mind would want change a language just for a one-off deal? But the truth is that in Lisp writing small one-off macros is actually very easy and low-effort, so you can reap the benefits at a low cost

Enough talk, let's see some actual code. In my guile-msgpack project I need to test whether objects have been correctly serialised into bytes. A full test case looks like this:

``````;; test-bytevector= is a regular function defined only once somewhere else
(test-begin "Single precision floating point numbers")
(test-bytevector= (pack -0.0)
#vu8(#xCA #b10000000 #b00000000 #b00000000 #b00000000))
;; more test-cases here...
(test-end "Single precision floating point numbers")``````

This is not that bad, but there is still a lot of boilerplate code that drowns out the actual content to test. When we think about it, there is really only two pieces of information that matter: the object we want to pack and the bytes we want to compare the result to. Everything else is just fluff meant for for the machine. There is no reason a human should ever have to see or write this fluff. Instead we would much rather write down a specification as to what our tests entail, and have the compiler write the actual computer code for us. Here is what the end result looks like:

``````(test-cases "Single precision floating point numbers"
(+0.0                (#xCA #b00000000 #b00000000 #b00000000 #b00000000))
(-0.0                (#xCA #b10000000 #b00000000 #b00000000 #b00000000))
(+inf.0              (#xCA #b01111111 #b10000000 #b00000000 #b00000000))
(-inf.0              (#xCA #b11111111 #b10000000 #b00000000 #b00000000))
(+nan.0              (#xCA #b01111111 #b11000000 #b00000000 #b00000000))
(-nan.0              (#xCA #b01111111 #b11000000 #b00000000 #b00000000))
(+3.1415927410125732 (#xCA #b01000000 #b01001001 #b00001111 #b11011011))
(-3.1415927410125732 (#xCA #b11000000 #b01001001 #b00001111 #b11011011)))``````

This is much more concise, everything that is irrelevant vanishes from view. We could hand the code to a person who has never programmed in their life and that person would still be able to read and write test cases.

I don't want to bore you with the implementation details, you can read the source code yourself if you want to. The final test specification language allows for slightly more complex specifications for repeating bytes, but even then it comes down to about 20 lines of code while being very generous with whitespace.

## Conclusion

Metaprogramming allows us to extend a language with new features by defining how the written source code is to be transformed into a more low-level code. The user of a macro writes a specificationof the problem, which the macro then translates into Lisp code.

These extensions can be big new language feature like support for object-oriented programming, or small domain-specific extension which would be too specific to be included in the standard. These domain-specific languages can be used by domain experts who might not be Lisp programmers to formulate their computations.

The mathematical notation allows me as a mathematician to express very complex facts clearly and precisely without having to become a linguist. In the same way Lisp can help non-programmers write complex programs in their own domain. And even as a programmer I appreciate being able to think on a higher level, rather than constantly being on the low level of gluing together APIs