Re: eliminating left-recursion

"aegis" <aegis@mad.scientist.com> wrote
> Given the following production:
>
> d-declarator: ID | d-declarator '[' constant ']' | '(' d-declarator ')'
> ;
>
> How can I eliminate left-recursion here? The method sketched
> out in 'Compilers, Principles, Techniques and Tools' only
> presents a very simple case...


The method in ASU is fully general -- given a production of the form:


        X ::= X A | B


Trnsforiming it into


        X ::= B X'
        X' ::= A X' | epsilon


is equivalent, but right recursive instead of left recursive. The intuition
behind this is that the original rule is equivalent to (EBNF):


        X ::= B A*


The recursive part of the original rule will expand to zero or more 'A'
components, but you eventually have to expand a B, which will go on the
beginning of the rule.


For your example:


        X == d-declarator
        A == '[' constant ']'
        B == ID | '(' d-declarator ')'


so the replacement expansion is


        d-declarator: ( ID | '(' d-declarator ')' ) d-declarator-tail
        d-declarator-tail: '[' constant ']' d-declarator-tail


for which you might need to expand the first rule as


        d-declarator: ID d-declarator-tail | '(' d-declarator ')' d-declarator-
tail


Chris Dodd
cdodd@acm.org

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