TLDR: Backus-Naur form (BNF) is a way to describe the structure and syntax of programming languages and other formal languages. It uses symbols and rules to define how the language should be written and understood.

Backus-Naur form (BNF) is a notation that is used to describe the syntax of programming languages, document formats, instruction sets, and communication protocols. It is a way to formally define the rules and structure of a language. BNF consists of symbols and rules that specify how the language should be written and understood.

In BNF, a specification is made up of derivation rules, which are written as " ::= ". The symbols can be either nonterminals (variables) or terminals (specific words or characters). The "::=" symbol means that the symbol on the left must be replaced with the expression on the right. The "|" symbol is used to indicate a choice between different sequences of symbols.

For example, a BNF specification for a U.S. postal address could look like this:

::= ::= | ::= "." | ::= ::= "," ::= "Sr." | "Jr." | | "" ::= | ""

This BNF specification describes the structure of a postal address, with different parts like the name, street address, and zip code. Each part is defined using nonterminals and terminals, and the "|" symbol is used to indicate alternative choices.

BNF has been used for many years to describe the syntax of programming languages and other formal languages. It was first proposed by John Backus, a programming language designer at IBM, and has since been widely adopted in the field of computer science.

In summary, Backus-Naur form (BNF) is a notation used to describe the syntax and structure of programming languages and other formal languages. It consists of symbols and rules that define how the language should be written and understood. BNF is used in official language specifications, manuals, and textbooks on programming language theory.

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• Context-free grammars