language-agnosticcomputer-sciencebnfebnfrecursive-descent

Converting EBNF to BNF

It's been a few years since my computer-language class and so I've forgotten the finer points of BNF's and EBNF's and I don't have a textbook next to me. Specifically, I've forgotten how to convert an EBNF into BNF.

From what little I remember, I know that one of the main points is to convert

{ term }

into

<term> | <many-terms>

But I don't remember the other rules. I've tried to look this up online but I can only find links to either homework questions, or a small comment about converting terms with curly braces. I can't find an exhaustive list of rules that define the translation.

Solution

  • See this page.🕗 It contains instructions for each production that needs to be converted:

    From EBNF to BNF

    For building parsers (especially bottom-up) a BNF grammar is often better, than EBNF. But it's easy to convert an EBNF Grammar to BNF:

    • Convert every repetition { E } to a fresh non-terminal X and add

      X = ε | X E.

    • Convert every option [ E ] to a fresh non-terminal X and add

      X = ε | E.

      (We can convert X = A [ E ] B. to X = A E B | A B.)

    • Convert every group ( E ) to a fresh non-terminal X and add

      X = E.

    • We can even do away with alternatives by having several productions with the same non-terminal.

      X = E | E'. becomes X = E. X = E'.