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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Chomsky terminology was not originally used in describing Corm. Even though some languages are context-sensitive, context-sensitive grammars are rarely used for describing computer languages. Note that many things such as the format of a first-name, apartment specifier, ZIP-code, and Roman numeral are left unspecified here. Communications of the ACM.

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

Context-sensitivity fogm that terminal symbols may also appear in the left-hand sides of rules. Retrieved April 18, In the natural language we complement the BNF metalanguage by explaining naut the digit sequence can have no white space between the digits.

Each of these names denotes a class of basic symbols. Not to be confused with Boyce—Codd normal form. Others changed it to a programming language. BNF is very similar to canonical-form boolean algebra equations that are, and were at the time, used in logic-circuit design.

The language of languages

As an aside, if you think you’ve invented a new parsing technique, you need to check this book first. For instance, C is slightly context-sensitive because of the way it handles identifiers and type, nsur this context-sensitivity is resolved by a special convention, rather than by introducing context-sensitivity into the grammar. 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.

Studies of boolean algebra is commonly part of a mathematics. From Wikipedia, the free encyclopedia. There are no specifics on white space in the above. As proposed by Backus, the formula defined “classes” whose names are enclosed in angle brackets.


For instance, the Python lexical specification uses them. I’ll discuss grammars beyond context-free at the end. The is used to separate alternative definitions and is interpreted as “or”. Retrieved Jun 3, A class is an abstraction, we can talk about it independent of its formation.

In the committee’s report, Peter Naur called Backus’s notation Backus normal form. Many BNF specifications found online today are intended to be human-readable and are non-formal. Not all of these are strictly a superset, as some change the rule-definition relation:: Natural-language description further supplemented the syntax as well. For more on this, see my article tutirial translating math into code. The first symbol of an alternative may be the class being defined, the repetition, as bacus by Naur, having the function of specifying that the alternative sequence can recursively begin with a previous alternative and can be repeated any number of times.

Backus-Naur Form (BNF)

Each term in this particular rule is a rule-name. The definition of floating point literals in Python is a good example of combining several notations:. 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. While this change appears small, it makes grammars equivalent to Turing machines in terms of the languages they can describe.

Archived from the original on 5 June Retrieved May 11, The grammar for the entire Python language uses a slightly different but still regular notation. He was the first managing editor of the Communications of the ACM. To go beyond the expressive power of context-free grammars, one needs to allow a degree of context-sensitivity in the grammar. Naur changed two of Backus’s symbols to commonly available characters.


In computer scienceBackus—Naur form or Backus normal form BNF is a notation technique for context-free grammars flrm, often used to describe the syntax of languages used in computing, such as computer programming languagesdocument formatsfrom sets and communication protocols.

As an example, consider this possible BNF for a U.

Wikipedia articles needing clarification from April Wikipedia articles needing clarification from May Articles with inconsistent citation formats Pages using RFC magic links. This page was last edited on 6 Decemberat 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. Retrieved 24 September 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 Extended Backus Naur Form”.

In so doing the ability to use a natural najr description, metalinguistic variable, language construct description was lost. Even when grammars backuw not an object of mathematical study themselves, in texts that deal with discrete mathematical structures, grammars appear to define new notations and new structures.

Though yacc is most commonly used as a tutoroal generatorits roots are obviously BNF. For instance, if we were creating a grammar to handle english text, we might add a rule like: But, the reverse is not true: Another common extension is the use of square brackets around optional items. A BNF class describes a language construct formation, with formation defined as a pattern or the action of forming bacus pattern. Context-free grammars have sufficient richness to describe the recursive syntactic structure of many though certainly not all languages.

In EBNF, square brackets around an expansion, [ backuw ]indicates that this expansion is optional.

BNF is a notation for Chomsky’s context-free grammars.