# Crash course on parsers

If you've never worked with a parser generator before, or aren't really familiar with context-free grammars, this section is just a very brief introduction into the basic idea. Basically a grammar is a nice way of writing out what kinds of inputs are legal. In our example, we want to support parenthesized numbers, so things like 123, (123), etc. We can express this with a simple grammar like:

Term = Num | "(" Term ")"


Here we say we are trying to parse a term, and a term can either be a number (Num) or some other term enclosing in parentheses (here I did not define what a number is, but in the real LALRPOP example we'll do that with a regular expression). Now imagine a potential input like ((123)). We can show how this would be parsed by writing out something called a "parse tree":

(  (  1  2  3  )  )
|  |  |     |  |  |
|  |  +-Num-+  |  |
|  |     |     |  |
|  |   Term    |  |
|  |     |     |  |
|  +---Term----+  |
|        |        |
+------Term-------+


Here you can see that we parsed ((123)) by finding a Num in the middle, calling that Num a Term, and matching up the parentheses to form two more terms on top of that.

Note that this parse tree is not a data structure but more a visualization of the parse. I mean, you can build up a parse tree as a data structure, but typically you don't want to: it is more detailed than you need. For example, you may not be that interested in the no-op conversion from a Num to a Term. The other weird thing about a parse tree is that it is intimately tied to your grammar, but often you have some existing data structures you would like to parse into -- so if you built up a parse tree, you'd then have to convert from the parse tree into those data structures, and that might be annoying.

Therefore, what a parser generator usually does, is instead let you choose how to represent each node in the parse tree, and how to do the conversions. You give each nonterminal a type, which can be any Rust type, and you write code that will execute each time a new node in the parse tree would have been constructed. In fact, in the examples that follow, we'll eventually build up something like a parse tree, but in the beginning, we won't do that at all. Instead, we'll represent each number and term as an i32, and we'll propagate this value around.

To make this a bit more concrete, here's a version of the grammar above written in LALRPOP notation (we'll revisit this again in more detail of course). You can see that the Term nonterminal has been given the type i32, and that each of the definitions has some code that follows a => symbol. This is the code that will execute to convert from the thing that was matched (like a number, or a parenthesized term) into an i32:

Term: i32 = {
Num => /* ... number code ... */,
"(" Term ")" => /* ... parenthesized code ... */,
};


OK, that's enough background, let's do this for real!