2

Please take this question with a grain of salt. I'm trying to write a very simple layout engine and wanted to formally create a grammar to parse the input. I stayed up all night researching LL(k) parsers - mostly from papers from different colleges. They tend to use the same examples and I've never been a fan of abstracting through notation, so I'm almost positive I have the syntax incorrect.

The input is very trivial: 

header>rows>h-row>a|b

main>rows>m-row>qs|d
qs>qs-row>qa|qu

footer>rows>f-row>a|b

And this is the grammar definition:

S -> aBC
B -> op
C -> a

First:

S: [a]
B: [>, |, /]
C: [a]

Follow:

S: $
C: $
B: C | S
iwannawriteacompiler
  • 205
  • 2
  • 7

1 Answers1

3

It's a perfectly valid grammar, and it's certainly LL(1). But since it only generates three sentences, it's probably not what you are looking for.

The three sentences:

a < a
a | a
a / a

For precision: As written, it's not quite correct. In order to achieve what I imagine you meant by the FIRST sets, you'd actually need to he a bit more precise. Instead of using $op$, you write:

$$\begin{align}B& \to \mathbb{<}\\ B&\to\text{|}\\ B&\to\text{/} \end{align}$$

Alternatively, you could define $op$ as the three possible operators, as above, and leave $B\to op$.

Also: $FOLLOW$ sets (like $FIRST$ sets) are sets of terminals. So $S$ and $C$ are not going to be found in any $FOLLOW$ set. $FOLLOW(B)$ is $\{a\}$.

rici
  • 12,150
  • 22
  • 40