Backus-Naur notation (shortly BNF) is a formal mathematical way to describe a language, (to The Backus-Naur Form is a way of defining syntax. It consists of. The standard technique for defining the syntax of a computer language is to use Backus-Naur Form (BNF). The variant used in this tutorial is as follows. A Practical Tutorial on Context Free Grammars. Robert B. . Backus-Naur Form ( BNF) is a notation for expressing a CFG. The notation.

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More important than the minor syntactic differences between the forms of EBNF are the additional operations it allows in expansions. Extended Backus Naur Form”. Studies of boolean algebra is commonly part of a mathematics. The language of languages [ article index ] [] [ mattmight ] [ rss ].

Juxtaposition of marks or variables in a formula signifies juxtaposition of the sequence denoted. Others changed it to a programming language.

BNF and EBNF: What are they and how do they work?

Archived from the original PDF on By using this site, you agree to the Terms of Use and Privacy Policy. As an example, consider this possible BNF for a U. In the natural language we complement the BNF metalanguage by explaining that the digit sequence can have no white naaur between the digits. An example of its use as a metalanguage would be in defining an arithmetic expression:.

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. The other part of that rule aside from a line-end is an expression, which consists of two lists separated by a pipe.


Each term in this particular rule is a rule-name. For more on this, see my article on translating math into code. The natural-language supplement provided specific details of the language class semantics to be used by a compiler implementation and a programmer writing bacuks ALGOL program. Context-free grammars have sufficient richness to describe the recursive syntactic structure of many though certainly not all languages.

BNF is very similar to canonical-form boolean algebra equations that are, and were at the time, used in logic-circuit design. Here’s a definition of a date and time format taken from RFC If necessary, they may be described using additional BNF rules. Retrieved May 11, By restricting the rules so that the the left-hand side has strictly fewer symbols than all expansions on the right, context-sensitive grammars are equivalent to decidable linear-bounded automata.

English is only one of the possible natural nakr.

Backus-Naur Form (BNF)

In the committee’s report, Peter Naur called Backus’s notation Backus normal form. The is used to separate alternative definitions and is interpreted as “or”. Meanwhile, string rewriting rules as formal, abstract systems were introduced and studied by mathematicians such as Axel Thue inEmil Post s—40s and Alan Turing tutoiral As far as the rule states, we could have space between the digits.

There are no specifics on white space in the above. The origin of BNF is not as important as its impact on programming language development.

This assumes that no whitespace is necessary for proper interpretation of the rule. In computer science, the most common type of grammar is the context-free grammar, and these grammars will be the primary focus of this article.


They are applied wherever exact descriptions of languages are needed: Parsing expression grammars build on the BNF and regular expression notations to form an alternative class of formal grammarwhich is essentially analytic rather than generative in character. Wikipedia articles needing clarification from April Wikipedia articles needing clarification from May Articles with inconsistent citation formats Pages using RFC magic links.

Views Read Edit View history. BNF today is one of the oldest computer-related languages still in use.

Backus–Naur form – Wikipedia

Another forn extension is the use of square brackets around optional items. Noam Chomskyteaching linguistics to students of information theory at MIT backud, combined linguistics and mathematics by taking what is essentially Thue’s formalism as the basis for the description of the syntax of natural language.

Archived from the original on 5 June The integer rule is a good example of natural and metalanguage used to describe syntax:. Any mark in a formula, which is not a variable or a connective, denotes itself.

The grammar for the entire Python language uses a slightly different but still regular notation. But, the reverse is not true: These often include many of the following syntax rules and extensions:. Even though some languages are context-sensitive, context-sensitive grammars are rarely used for describing computer languages.

As proposed by Backus, the formula defined “classes” whose names are enclosed in angle brackets. Defining a language A grammar defines a language.

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