BackusNaur

Backus–Naur Form, commonly abbreviated as BNF, is a notation for describing the syntax of programming languages and other formal languages. It expresses a context-free grammar as a set of production rules, each replacing a nonterminal with a sequence of terminals and nonterminals. A typical rule is written as A ::= α, where A is a nonterminal and α is a string of symbols. Alternatives are separated by a vertical bar, as in A ::= B | C. Terminals are the literal symbols of the language; nonterminals denote syntactic categories.

The notation emerged in the 1960s to describe the syntax of programming languages such as ALGOL 60. John Backus introduced the form, and Peter Naur helped popularize and formalize it, leading to the combined name Backus–Naur Form. Since then, BNF has become a standard method for documenting language grammars and other formal languages.

Example grammar in BNF can be shown as:

expression ::= term | expression "+" term

term ::= factor | term "*" factor

factor ::= number | "(" expression ")"

Extensions known as Extended Backus–Naur Form (EBNF) add convenient constructs for optional elements, repetitions, and groupings, using symbols for optionality and repetition, which can make grammars more compact and readable. BNF remains foundational in compiler design and language documentation, and is used by parser generators and language standards. While it effectively conveys syntax, BNF itself does not specify semantics and must be complemented by lexical analysis and disambiguation when necessary.