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parsinggrammarbnf

Issues understanding BNF grammar form

I am learning how BNF grammar works and I have been given the following example of some BNF grammar rules. I'm just trying to understand what this means and I'm having trouble:

  <S> ::=  ‘(‘ <A> ‘)’     
  <A> ::=  ‘[‘ <A> ‘]’              
      | <S> ‘{‘ <A> ‘}’
      | a | … | z

I don't understand what the brackets in quotations mean. And as far as I understood it this expression should be saying something like 

S expanded = '(' <A> ')'.
A expanded = ‘[‘ <A> ‘]’              
          or <S> ‘{‘ <A> ‘}’
          or a or … or z

but I do not understand why A's expansion would have A inside of it.

Solution

  • The brackets in quotes in the A production here call for literal brackets in the input.

    So a valid example of an A construct could be [ z ].

    As for your second point, the A rule is recursive, meaning that angle brackets may be infinitely nested in an A construct.