(BNF, originally "Backus Normal Form") A formal metasyntax used to express context-free grammars. Backus Normal Form was renamed Backus-Naur Form at the suggestion of Donald Knuth.

BNF is one of the most commonly used metasyntactic notations for specifying the syntax of programming languages, command sets, and the like. It is widely used for language descriptions but seldom documented anywhere (how do you document a metasyntax?), so that it must usually be learned by osmosis (but see RFC 2234).

Consider this BNF for a US postal address:

 <postal-address> ::= <name-part> <street-address> <zip-part>
 <personal-part> ::= <name> | <initial> "."
 <name-part> ::= <personal-part> <last-name> [<jr-part>] <EOL>
               | <personal-part> <name-part>
 <street-address> ::= [<apt>] <house-num> <street-name> <EOL>
 <zip-part> ::= <town-name> "," <state-code> <ZIP-code> <EOL>

This translates into English as: "A postal-address consists of a name-part, followed by a street-address part, followed by a zip-code part. A personal-part consists of either a first name or an initial followed by a dot. A name-part consists of either: a personal-part followed by a last name followed by an optional "jr-part" (Jr., Sr., or dynastic number) and end-of-line, or a personal part followed by a name part (this rule illustrates the use of recursion in BNFs, covering the case of people who use multiple first and middle names and/or initials). A street address consists of an optional apartment specifier, followed by a street number, followed by a street name. A zip-part consists of a town-name, followed by a comma, followed by a state code, followed by a ZIP-code followed by an end-of-line."

Note that many things (such as the format of a personal-part, apartment specifier, or ZIP-code) are left unspecified. These lexical details are presumed to be obvious from context or specified somewhere nearby.

There are many variants and extensions of BNF, possibly containing some or all of the regexp wild cards such as "*" or "+". EBNF is a common one. In fact the example above isn't the pure form invented for the ALGOL 60 report. "[]" was introduced a few years later in IBM's PL/I definition but is now universally recognised. ABNF is another extension.