John Graham Backus (April 29, 1911 – October 28, 1988) was a Lithuanian American physicist and acoustician.

In computer science, Backus–Naur form () or Backus normal form (BNF) is a metasyntax notation for context-free grammars, often used to describe the syntax of languages used in computing, such as computer programming languages, document formats, instruction sets and communication protocols. It is applied wherever exact descriptions of languages are needed: for instance, in official language specifications, in manuals, and in textbooks on programming language theory.

Backus-Naur Form

<language, grammar> (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. (1997-11-23)

Frederick Fanning Backus (June 15, 1794 Bethlehem, Litchfield County, Connecticut – November 4, 1858 Rochester, Monroe County, New York) was an American physician and politician from New York.

<language> Extended Backus-Naur Form.

In computer science, extended Backus–Naur form (EBNF) is a family of metasyntax notations, any of which can be used to express a context-free grammar. EBNF is used to make a formal description of a formal language such as a computer programming language.

<language> Any variation on the basic Backus-Naur Form (BNF) meta-syntax notation with (some of) the following additional constructs: square brackets "[..]" surrounding optional items, suffix "*" for Kleene closure (a sequence of zero or more of an item), suffix "+" for one or more of an item, curly brackets enclosing a list of alternatives, and super/subscripts indicating between n and m occurrences. All these constructs can be expressed in plain BNF using extra productions and have been added for readability and succinctness. (1995-04-28)

Extended Backus-Naur Form

Extended Backus-Naur-Form