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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In EBNF, square brackets around an expansion, [ expansion ]indicates that this expansion is optional. In some forms of EBNF, theoperator explicitly denotes concatenation, rather than relying on juxtaposition. Context-sensitivity means that terminal symbols may also appear in the left-hand sides of rules.

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

Or, if we were describing a programming language, we could add a rule like: Parsing expression grammars build on the BNF and regular expression notations to form an alternative class of formal grammarmaur is essentially analytic rather than generative in character. Naur changed two of Backus’s symbols to commonly available characters.

This assumes that no whitespace is necessary for proper interpretation of the rule. But, the reverse is not true: From Wikipedia, the free encyclopedia. Not to be confused with Boyce—Codd normal form.

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

When describing languages, Backus-Naur form BNF is a formal notation for encoding grammars intended for human consumption. By equivalence is here meant that any of the three structures shown in the left column may be replaced, in any occurrence outside of strings, by the symbol shown in the same line in the right column without any effect on the action of the program.


Donald Knuth ttorial that BNF should rather be read as Backus—Naur formas it is “not a normal form in the conventional sense”, [9] unlike, for instance, Chomsky normal form.

Noam Chomskyteaching linguistics to students of information theory at MITcombined linguistics and mathematics by taking what is essentially Thue’s formalism as the basis for the description of the syntax of natural language.

We can talk about term, independent of its definition, as being added or subtracted in expr. In computer scienceBackus—Naur form or Backus normal form BNF is a notation technique for context-free grammarsoften used to describe the syntax of languages used in computing, such as computer programming languagesdocument formatsinstruction sets and communication protocols.

As far as the rule states, we could have space between the digits. BNF today is one of the oldest computer-related languages still in use. 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. As an aside, if you think you’ve invented a new parsing technique, you need to check this book first.

Programming Systems and Languages. In the first half of the 20th century, linguists such as Leonard Bloomfield and Zellig Harris started attempts to formalize the description of language, including phrase structure.

Here’s a definition of a date and time format taken from Bsckus Symbols that never appear on a left side are terminals. Backus – “.

Each of these names denotes a class of basic symbols. Archived from the original on 5 June For instance, the Python lexical specification uses them. It’s common to find regular-expression-like operations inside grammars. Context-free grammars have sufficient richness to describe the recursive syntactic structure of many though certainly not all languages.


The natural-language tutroial provided specific details of the language class semantics to be used by a compiler implementation and a programmer writing an ALGOL program. As an example, consider this possible BNF for a U. These changes made that META II and its derivative programming languages able to define and extend their own metalanguage. The definition of floating point literals in Nnaur is a good example of combining several tutrial.

The integer rule is a good example of natural and metalanguage used to describe syntax:. Proceedings of the International Conference on Information Processing.

In the committee’s report, Peter Naur called Backus’s notation Backus normal form. Communications of the ACM. The grammar for the entire Python language uses a slightly different but still regular notation. In so doing the ability to use a natural language description, metalinguistic variable, language construct description was lost.

For describing ordinary natural languages designation like word, verb, noun, are used. Juxtaposition of marks or variables in a formula signifies juxtaposition of the sequence denoted. More important than the minor syntactic differences between the forms of EBNF are the additional operations it allows in expansions.