Anatomy of an interpreter: the Lexer

Posts in this series: Lexer, Parser, Evaluator

I have been having a lot of fun recently writing my Scheme interpreter Subs. I have never implemented a full programming language before, so I am learning fast (mostly through mistakes) and wanted to write down some of the stuff I am discovering.

Note: if you want to learn more about what Scheme is I recommend Scheme (Wikipedia) and the book SICP, which is the inspiration for all this.

I am writing everything from scratch, just because it's fun (certainly not because I think it is in any way better to do it that way...). As we will see, that gives me opportunities to do things in different ways from the normal way such things are done. So far, every time I find out I've deviated from the normal way I've quickly discovered why I am wrong, and had to learn the true path.

Text-based programming languages, whether interpreted or compiled, need a lexer. A lexer takes in characters and spits out "tokens", which are groups of characters that represent a single thing, such as a bracket, a variable name or a number. (Those tokens are then passed on to the parser, which I will cover in a different post.)

Scheme (and other Lisp variants) are fairly easy to lex because they don't have much syntax - you just need to be able to understand round brackets, numbers and strings, and a couple of special cases that I won't go into because I haven't actually implemented them yet. (Mind you, I haven't implemented strings yet either...)

When I started Subs I took my normal approach of doing whatever I wanted without any research or even much thought, and wrote something that I called a lexer, but which was really something else. It took in a stream of characters, read it one "word" at a time (using whitespace as separators), broke up the word if it contained bracket characters, and emitted a tree structure with each branch representing a bracketted list. It just seemed sensible, while I was watching the brackets flow by, to understand them and create a tree structure.

However, for a number of reasons, that approach turned out to be wrong.

First, reading a "word" at a time made things much harder than simply stepping through each character. It made my initial implementation slightly faster, but as soon as I realised I cared about white space (e.g. keeping track of what line we are on) it had to go. When it went it also turned out to be easier to deal with unusual code layout - for example "a(b" should be lexed as 3 tokens, but would be handed to us as a single word.

Second, and more importantly, creating a tree structure at this point was a waste of time. Creating tree structures is normally the job of a parser, and mixing these responsibilities gave me some pointless inefficiency: the lexer emitted a tree of tokens, which the parser then translated into another tree (of fully-understood code objects). It turned out that walking the tree of tokens and copying that structure in the parser was at least as hard as just taking in a flat stream of tokens and constructing the tree just once.

So, I re-wrote Lexer into something that is starting to become worthy of the name. The most interesting parts of its signature look like this:

class Lexer
{
public:
    Lexer( std::istream& instream );
    Token NextToken();
};

It takes in a reference to a stream, which will provide the characters, and when NextToken is called, it reads enough characters to determine what the next token will be, and returns it.

Side note: Subs is written using Test-Driven Development. I re-implemented the Lexer and Parser from scratch (naming the new classes NewLexer and NewParser until they were ready), modified the code that used them to use the new interfaces, ran the tests, and immediately knew that the new classes worked as well as the old ones. That level of confidence is incredibly freeing. I can't imagine how I would ever have convinced myself the new classes were ready had I not had that safety net of 100s of tests that ensure the interpreter correctly responds to each type of input.

Currently the Token class it returns is pretty much just a string, with some information attached about where that string was in the original text. In researching this article I realised that most lexers attach more information than that to their tokens - they understand its basic type such as integer, decimal, string, bracket or symbol. At the moment in Subs, this work is done in the parser (so for the lexer each token is just a string), but I can see why it is helpful to do this work in the lexer, because for most types we have the information anyway. For example, in order to recognise that '"foo (bar"' (where the double-quotes are in the real code) is a single token we must understand that it is a string. Since we know it at this stage, we might as well record it in the Token object so we don't have to work it out again later. When Subs supports strings, I will probably add a "type" field to the token and move this work from the parser.

On a more general programming point, following on from comments I made in a previous post, it is worth noting that the structure of the lexer (and, as we will see later, the parser) uses a technique called "streams". What this means is that we write functions like NextToken that process a small part of the total problem, and return their answer. If we chain together functions like that (for example the parser's equivalent function calls NextToken whenever it needs a new token) we can process arbitrarily large input without using lots of memory or slowing down. The lexer is able to process any number of tokens using a very small amount of memory, and will only fall over if it encounters a single token that is ridiculously large.

The stream style can be very useful for some problems, not only because it can be efficient with memory, but also because it can help break problems into neat, small pieces that are easier to implement correctly. It is also useful for writing code in a functional style, because it allows us to avoid having any internal state (e.g. we could easily implement NextToken to take in the stream it should read from and avoid any member variables at all in Lexer), by pushing state out into the input and output, instead of having it in our program. In this case that means instead of reading, storing and then processing a program, our lexer can simply process a few characters and emit a token without knowing anything about the surrounding code or wider context. This makes it much easier to test, and (potentially) easier to do clever things with, like prove mathematically that it is correct (!)

Next time, the parser.