Backus–Naur Form

 

A BNF specification is a set of derivation rules, written as

 <symbol> ::= __expression__

where <symbol> is anonterminal, and the__expression__ consists of one or more sequences of symbols; more sequences are separated by thevertical bar, '|', indicating achoice, the whole being a possiblesubstitution for the symbol on the left. Symbols that never appear on a left side areterminals. On the other hand, symbols that appear on a left side arenon-terminals and are always enclosed between the pair <>.

Example

As an example, consider this possible BNF for a U.S. postal address:

 <postal-address> ::= <name-part> <street-address> <zip-part>       <name-part> ::= <personal-part> <last-name> <opt-jr-part> <EOL>                     | <personal-part> <name-part>   <personal-part> ::= <first-name> | <initial> "."   <street-address> ::= <house-num> <street-name> <opt-apt-num> <EOL>        <zip-part> ::= <town-name> "," <state-code> <ZIP-code> <EOL>     <opt-jr-part> ::= "Sr." | "Jr." | <roman-numeral> | ""

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 name-part consists of either: a personal-part followed by a last name followed by an optional suffix (Jr., Sr., or dynastic number) and end-of-line, or a personal part followed by a name part (this rule illustrates the use ofrecursion in BNFs, covering the case of people who use multiple first and middle names and/or initials).
• A personal-part consists of either a first name or an initial followed by a dot.
• A street address consists of a house number, followed by a street name, followed by an optionalapartment specifier, followed by an end-of-line.
• 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.
• A opt-jr-part consists of a suffix, such as "Sr.", "Jr." or a roman-numeral, or an empty string (i.e. nothing).

Note that many things (such as the format of a first-name, apartment specifier, ZIP-code, and Roman numeral) are left unspecified here. If necessary, they may be described using additional BNF rules.

Further examples

BNF's syntax itself may be represented with a BNF like the following:

 <syntax> ::= <rule> | <rule> <syntax> <rule>   ::= <opt-whitespace> "<" <rule-name> ">" <opt-whitespace> "::="                  <opt-whitespace> <expression> <line-end> <opt-whitespace> ::= " " <opt-whitespace> | ""  <!-- "" is empty string, i.e. no whitespace --> <expression>     ::= <list> | <list> "|" <expression> <line-end>       ::= <opt-whitespace> <EOL> | <line-end> <line-end> <list>    ::= <term> | <term> <opt-whitespace> <list> <term>    ::= <literal> | "<" <rule-name> ">" <literal> ::= '"' <text> '"' | "'" <text> "'" <!-- actually, the original BNF did not use quotes -->

This assumes that no whitespace is necessary for proper interpretation of the rule. <EOL> represents the appropriateline-end specifier (inASCII, carriage-return and/or line-feed, depending on theoperating system). <rule-name> and <text> are to be substituted with a declared rule's name/label or literal text, respectively.

In the U.S. postal address example above, the entire block-quote is a syntax. Each line or unbroken grouping of lines is a rule; for example one rule begins with "<name-part> ::=". The other part of that rule (aside from a line-end) is an expression, which consists of two lists separated by a pipe "|". These two lists consists of some terms (three terms and two terms, respectively). Each term in this particular rule is a rule-name.

Variants

There are many variants and extensions of BNF, generally either for the sake of simplicity and succinctness, or to adapt it to a specific application. One common feature of many variants is the use ofregular expression repetition operators such as * and +. TheExtended Backus–Naur Form (EBNF) is a common one. In fact the example above is not the pure form invented for the ALGOL 60 report. The bracket notation "[ ]" was introduced a few years later inIBM's PL/I definition but is now universally recognised.ABNF and RBNF are other extensions commonly used to describe Internet Engineering Task Force (IETF) protocols.

Parsing expression grammars build on the BNF andregular expression notations to form an alternative class of formal grammar, which is essentially analytic rather than generative in character.

Many BNF specifications found online today are intended to be human readable and are non-formal. These often include many of the following syntax rules and extensions:

• Optional items enclosed in square brackets. E.g. [<item-x>]
• Items repeating 0 or more times are enclosed in curly brackets or suffixed with an asterisk. E.g. <word> ::= <letter> {<letter>}
• Items repeating 1 or more times are followed by a '+'
• Terminals may appear in bold and NonTerminals in plain text rather than using italics and angle brackets
• Alternative choices in a production are separated by the ‘|’ symbol. E.g., <alternative-A> | <alternative-B>
• Where items need to be grouped they are enclosed in simple parentheses