How can I eliminate left recursion in the following grammar?

Question

Here's the grammar, which is supposed to describe a language of nested braces with commas as delimiters:

L ::= {L} | L,L |

A few more examples of strings I'd expect the grammar to accept and reject:

Accept:

{,{,,{,}},,{,}}
{{{{}}}}
{,{}}

Reject:

{}{}
{,{}{}}
{{},{}

what tooling are you using to get the left recursion error from? — Simeon Pilgrim, Jul 08 '09 at 01:57
Not homework, just trying to work my way through a book on compilers. For fun, I swear! — wkf, Jul 08 '09 at 02:03

John Kugelman · Accepted Answer · 2009-07-08T02:22:50.223

4

Done by hand:

L ::= { L } | { L } , | , L | ε

Or, instead of just winging it we could use a more systematic approach and apply the algorithm from Wikipedia on removing immediate left recursion:

L ::= { L } L₁ | L₁
L₁ ::= ε | , L L₁

edited Jul 08 '09 at 02:22

answered Jul 08 '09 at 01:59

John Kugelman

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Can't think of a way to derive `{{},}` from this grammar – Johannes Schaub - litb Jul 08 '09 at 02:03
@litb: the outer {} is the first rule {L} the {}, is firstly second rule L,L with the first of those {} and the second empty. – Simeon Pilgrim Jul 08 '09 at 02:10
nod, I only just clicked you where meaning JK's grammar vs. wkf's my bad. – Simeon Pilgrim Jul 08 '09 at 02:15

a_m0d · Answer 2 · 2009-07-08T02:27:55.740

0

First of all, that grammar won't accept your first example, since it requires the commas to be after the close brace and before the open brace. I would suggest to re-write it as

L::= {L} | ,L

This won't get rid of the left recursion, but it will at least match your acceptable answers.

edited Jul 08 '09 at 02:27

answered Jul 08 '09 at 02:01

a_m0d

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Not true. His grammar will accept `{,}`, where the ',' is produced by L1=L2,L3 with L2 and L3 being empty. – John Kugelman Jul 08 '09 at 02:04
Your right - I didn't realise that that was the point of the empty rule at the end – a_m0d Jul 08 '09 at 02:27

How can I eliminate left recursion in the following grammar?

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