BNF

Backus–Naur Form (BNF) is a notation for describing the syntax of programming languages and data formats. It expresses context-free grammars through a set of production rules that define how valid strings in a language are formed. A rule typically has the form a nonterminal symbol, followed by a mapping symbol, and then a sequence of terminals and/or other nonterminals. Terminals are literal tokens, while nonterminals refer to other rules. The starting nonterminal designates the language’s syntax to be described.

BNF was developed in the 1960s in connection with the ALGOL language, with John Backus and Peter Naur credited in the Backus–Naur form. The notation gained wide adoption as a precise, machine-readable way to specify language syntax, enabling compiler writers and language designers to share formal descriptions.

Notation and variants: In classic BNF, production rules use symbols such as ::= or : = and may rely on angle-bracket conventions for nonterminals, for example, <expression> ::= <term> | <expression> "+" <term>. Extended BNF (EBNF) adds shorthand for optional, repeated, and grouped constructs, and ABNF (augmented BNF) is used in IETF specifications. Many language specifications and parser generators rely on BNF or its variants.

Applications and limitations: BNF serves as a foundation for documenting syntax and for generating parsers and compiler components. It is typically complemented by lexical specifications that describe tokens. While powerful for syntax, BNF itself does not define semantics, and some languages require unambiguous grammars or transformations to suitable parsing strategies.