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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Symbols that never appear on a left side are terminals. Or even reordering an expression to group data types and evaluation results of mixed types. Many spin-off metalanguages were inspired by BNF.

Backus-Naur Form (BNF)

In the committee’s report, Peter Naur called Backus’s notation Backus normal form. Regular expressions sit just beneath context-free grammars in descriptive power: The grammar for the entire Python language uses a slightly different but still regular notation.

We can talk about a term being a specific data type and how an expr is to be evaluated having specific combinations of data types. In the natural language we complement the BNF metalanguage by explaining that the digit sequence can have no white space between the digits.

The name of a class of literals is usually defined by other means, such as a regular expression or even prose. Anything other than the metasymbols:: 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. Apparently, Backus was familiar with Chomsky’s work.


The language of languages

Backus – “. ABNF also provides the ability to specify specific byte values exactly — detail which matters in protocols. Defining a language A grammar defines a language.

These often include many of the following syntax rules and extensions:. But, the reverse is not true: Context-sensitivity means that terminal symbols may also appear in the left-hand sides of rules.

Here’s a definition of a date and time format taken from RFC The other part of that rule aside from a line-end is an expression, which consists of two lists separated by a pipe. As far as the rule states, we could have space between the digits.

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

After reading this article, you will be able to identify and interpret all commonly used notation for grammars. In some forms of EBNF, theoperator explicitly denotes concatenation, rather than relying on juxtaposition. Not all of these are strictly a superset, as some change the rule-definition relation:: While this change appears small, it makes grammars equivalent nair Turing machines in terms of the languages they can describe.

Even when grammars are not fomr object of mathematical study themselves, in texts that deal with discrete mathematical structures, grammars appear to define new notations and new structures. It’s common to find regular-expression-like operations inside grammars. 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.


For an comprehensive treatment of parsing techniques, I recommend Grune and Jacobs, Tutorila Techniques: Extended Backus Naur Form”.

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

This assumes that no whitespace is necessary for proper interpretation of the rule. Proceedings of the International Conference on Information Processing.

Another common extension is the use of square brackets around optional items. Association for Computing Machinery.

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. More important than the minor tutogial differences between the forms of EBNF are the additional operations it allows in expansions.

The Schorre Metacompilers made it a programming language with only a few changes.