Skip to main content

context-free grammar

context-free grammar A grammar in which the left-hand side of each production is a single nonterminal, i.e. productions have the form A → α

(read as rewrite A as α), where α is a string of terminals and/or nonterminals. These productions apply irrespective of the context of A. For brevity one writes A → α1 | α2 | .. .. | α n

to indicate the separate productions A → α1, A → α2, .., .., A → αn

As an example, the following generates a simple class of arithmetic expressions typified by (a + b) × c:

E → T | T + E | (E)

T → E | E × T | a | b | c

The BNF notation used in defining the syntax of programming languages is simply a context-free grammar.

Context-free grammars are a class of phrase-structure grammar (PSG). GPSG represents the principal attempt at constructing context-free grammars capable of characterizing the grammars of natural language.

Compare context-sensitive grammar.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"context-free grammar." A Dictionary of Computing. . Encyclopedia.com. 17 Oct. 2018 <http://www.encyclopedia.com>.

"context-free grammar." A Dictionary of Computing. . Encyclopedia.com. (October 17, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/context-free-grammar

"context-free grammar." A Dictionary of Computing. . Retrieved October 17, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/context-free-grammar

Learn more about citation styles

Citation styles

Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

http://www.mla.org/style

The Chicago Manual of Style

http://www.chicagomanualofstyle.org/tools_citationguide.html

American Psychological Association

http://apastyle.apa.org/

Notes:
  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.