Appendix: Backus-Naur Form

The Backus-Naur form (BNF) (also known as Backus normal form) is a metasyntax used to express context-free grammars: that is, a formal way to describe formal languages.

It is widely used as a notation for the grammars of computer programming languages, command sets and communication protocols; most textbooks for programming language theory and/or semantics document BNF. Some variants, for example ABNF, have their own documentation..

It was originally named after John Backus and later (at the suggestion of Donald Knuth) also after Peter Naur, two pioneers in computer science, namely in the art of compiler design, as part of creating the rules for Algol 60.

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

<symbol> ::= <expression with symbols>

where <symbol> is a nonterminal, and the expression consists of sequences of symbols and/or sequences separated by `|', indicating a choice, the whole being a possible substitution for the symbol on the left. Symbols that never appear on a left side are terminals. Symbols inside brackets [ ] are optional.

Example:

As an example, 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 here. If necessary, they may be described using additional BNF rules, or left as abstractions if irrelevant for the purpose at hand.

Variants

There are many variants and extensions of BNF, possibly containing some or all of the POSIX regular expression wild cards, see Appendix . The Extended Backus-Naur form (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.