What is Context Free Grammar ?

As we know that grammar is a set of rules, similarly context-free grammar has some set of recursive rules through which a pattern is generated. Which describes context-free languages. This Grammar is called context-free grammar because in this production rules are independent of context.

In general, a context-free grammar G is a quadruple(4-tuple) (V, Σ(T), R(P), S) where,

V is a set of variables,

Σ set of terminal symbols and subset of V,

R is a set of rules called as production rules (V − Σ) × V^*,

S is a start symbol V − Σ.

(Nonterminals are usually represented by capital letters and terminals by lower case letters.) 

Every CFG production rule can be written as S→a, where S is a unique nonterminal symbol and a is some combination of non-terminals or production rules.

For example, the following is context-free grammar, as is any combination of the rules in isolation.

Rule 1: S→aSa

Rule 2: S→bSb

Rule 3: S→ϵ

(Epsilon is the empty string.)

The following are examples of strings that may be constructed by this grammar: that is, members of the CFL, L, described by this CFG, and the corresponding derivations.

aa: Rule 1, followed by Rule 3

aabb: Rule 1, followed by Rule 2, followed by Rule 3.

The empty string (Rule 3)

The grammar G, with productions

S → abB,

A → aaBb,

B → bbAa,

A → λ,

is context-free. We leave it to the reader to show that

L (G) = {ab (b b a a) n b b a (b a) n : n ≥ 0}

Context-free grammars are used in compilers and in particular for parsing, taking a string-based program, and figuring out what it means. Typically, CFGs are used to define the high-level structure of a programming language.

Click here to have Examples based on Context-Free Grammar

What are the applications of context-free grammar?

• A context-free grammar is used as the basis for compiler design and implementation. 
• Context-free grammars are used as specification mechanisms for programming languages 
• Designers of compilers use such grammars to implement compiler’s components, such as scanners, parsers, code generators, code synthesizers.
• The implementation of almost any programming language is preceded by a context-free grammar that specifies it.

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