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In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules can be applied to a nonterminal symbol regardless of its context. In particular, in a context-free grammar, each production rule is of the form. with a single nonterminal symbol, and a string of terminals and/or nonterminals ( can be empty).
Syntax can be divided into context-free syntax and context-sensitive syntax. [7] Context-free syntax are rules directed by the metalanguage of the programming language. These would not be constrained by the context surrounding or referring that part of the syntax, whereas context-sensitive syntax would.
Python syntax and semantics. A snippet of Python code with keywords highlighted in bold yellow font. The syntax of the Python programming language is the set of rules that defines how a Python program will be written and interpreted (by both the runtime system and by human readers). The Python language has many similarities to Perl, C, and Java ...
The general idea of a hierarchy of grammars was first described by Noam Chomsky in "Three models for the description of language". [1] Marcel-Paul Schützenberger also played a role in the development of the theory of formal languages; the paper "The algebraic theory of context free languages" [2] describes the modern hierarchy, including context-free grammars.
In fact, the language defined by a grammar is precisely the set of terminal strings that can be so derived. Context-free grammars are those grammars in which the left-hand side of each production rule consists of only a single nonterminal symbol. This restriction is non-trivial; not all languages can be generated by context-free grammars.
Extended Backus–Naur form. In computer science, extended Backus–Naur form (EBNF) is a family of metasyntax notations, any of which can be used to express a context-free grammar. EBNF is used to make a formal description of a formal language such as a computer programming language. They are extensions of the basic Backus–Naur form (BNF ...
Backus–Naur form. In computer science, Backus–Naur form (/ ˌbækəs ˈnaʊər /) (BNF or Backus normal form) is a notation used to describe the syntax of programming languages or other formal languages. It was developed by John Backus and Peter Naur. BNF can be described as a metasyntax notation for context-free grammars.
The set of all context-free languages is identical to the set of languages accepted by pushdown automata, which makes these languages amenable to parsing.Further, for a given CFG, there is a direct way to produce a pushdown automaton for the grammar (and thereby the corresponding language), though going the other way (producing a grammar given an automaton) is not as direct.