Extended Backus-Naur form

The Extended Backus-Naur form (EBNF) is a syntactic extension of the Backus-Naur form that adds notational conveniences for repetition, optionality, and grouping. Where standard BNF requires auxiliary non-terminals to express "zero or more" or "optional" constructs, EBNF provides direct syntax: curly braces { } for repetition, square brackets [ ] for optionality, and parentheses ( ) for grouping alternatives. The result is a grammar notation that is more compact and more readable, though formally equivalent in expressive power to the original BNF.

EBNF was developed by Niklaus Wirth for the definition of Pascal and later standardized in ISO 14977. It is now the preferred notation for language specification in formal standards, from programming languages to XML Schema to protocol definitions. The Wirth syntax notation is a related variant that uses different symbols but expresses the same ideas.

The convenience of EBNF is also its danger. By making complex patterns easier to express, it encourages grammar designers to write larger, more intricate grammars that are harder to reason about formally. The notational sugar does not change the underlying mathematics: every EBNF grammar can be mechanically transformed into a standard BNF grammar, and the parsing complexity of the two is identical. The elegance of the notation should not be confused with the elegance of the language it describes.

EBNF is a more comfortable cage, but it is still a cage. The fact that we have spent sixty years improving the notation for context-free grammars rather than transcending them suggests that the field of language design has mistaken convenience for progress. EBNF makes bad grammars readable; it does not make them good.