Removing left recursion

Question

I am feeling quite nostalgic so I've decided to write an adventure game creator that allows complex sentences to be entered by the user.

I have hand rolled a lexer and parser that uses the visitor pattern and it works quite well, until I encountered a left-recursion issue with one of my BNF (Backus-Naur Form) rules:

object          ::= {adjective} noun 
                  | object AND {adjective} noun

After removing the left-recursion by following this wiki entry does this look right?

object      ::= {adjective} noun object2
object2     ::= AND {adjective noun} 
              | !Empty

Edited:

I am hand rolling the lexer and parser using C# by following the guide given here. I an not using any parser generators for this exercise.

Also, I got the BNF rules for the parser from this website.

It would be helpful if you explained what tools or algorithms you're using for parsing. Since you're having trouble with left recursion, I deduce that you're using recursive descent, which is fine, but it would be helpful to know for sure, and what parser generator (if any) you're using. — rob mayoff, Jul 15 '13 at 08:28

score 2 · Accepted Answer · answered Jul 15 '13 at 08:24

2

Is there any reason to prefer left-recursion over right recursion in this case? Wouldn't this be simpler:

object ::= {adjective} noun |
           {adjective} noun AND object

If you really want to make your solution work, you need to make object2 right-recursive:

object      ::= {adjective} noun object2
object2     ::= AND {adjective noun} object2 |
                !Empty

answered Jul 15 '13 at 08:24

rob mayoff

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Using left-recursion is resulting in a stack overflow error and I had to change the rule to use right-recursion to get around this. The original BNF rule for `object` only allows a single `AND`, that's why I haven't made `object2` right recursive. – Intrepid Jul 15 '13 at 08:31
The first BNF rule in your question allows one or more repetitions. It doesn't limit the input to two repetitions. – rob mayoff Jul 15 '13 at 08:59
Rob: Actually yes, you're quite correct it does allow or or more repetitions. My mistake! I am accepting your second answer after changing my code to follow this rule and it now works. Thanks! – Intrepid Jul 15 '13 at 09:21

score 2 · Answer 2 · answered Jul 15 '13 at 08:32

Usually when I have this rule (yours):

object          ::= {adjective} noun | 
                    object AND {adjective} noun

I apply the following transformations:

Stage 1 (still left recursion) -

object          ::= ad_noun | 
                    object AND ad_noun

ad_noun         ::=  {adjective} noun

Stage 2 (change to right recursion) -

object          ::= ad_noun | 
                    ad_noun AND object

ad_noun         ::=  {adjective} noun

Removing left recursion

2 Answers2