Applications of Context Free Grammar

In this article, we have explained the applications of Context Free Grammar in real life applications like designing Compilers, Programming Languages, Generating English sentences and much more.

To learn about the basics of Context Free Grammar, go through this article.

Applications of Context Free Grammar (CFG) are:

• Context Free Grammars are used in Compilers (like GCC) for parsing. In this step, it takes a program (a set of strings).

• Context Free Grammars are used to define the High Level Structure of a Programming Languages.

• Every Context Free Grammars can be converted to a Parser which is a component of a Compiler that identifies the structure of a Program and converts the Program into a Tree.

• Document Type Definition in XML is a Context Free Grammars which describes the HTML tags and the rules to use the tags in a nested fashion.

Following is the Context Free Grammar for HTML (with limited tags):

• Char -? a | A | . . .

• Text -> λ | Char Text

• Doc -> λ | Element Doc

• Element -> Text | < EM > Doc < /EM >|< P > Doc |< OL > List < /OL >

• List -> λ | ListItem List

• ListItem -> < li > Doc

• All finite set of strings are Regular Languages. All Regular Language is a Context Free Language. Hence, all Programming Languages are Context Free Languages / can be represented by a Context Free Grammar.

• Algebraic Expressions can be represented using Context Free Grammar. For example, this is the rules of a Context Free Grammar for syntactically correct Infix expression using 3 variables (x, y, z):

• S -> empty

• S -> (S)

• S -> x

• S -> y

• S -> z

• S -> S + S

• S -> S – S

• S -> S * S

• S -> S / S

Following is the Context Free Grammar for an Imperative Programming Language Brainfuck:

G = (V, Σ, R, S)

where:

V = {Program, Instr}
Σ = {+, -, >, <, , , ., [, ]}
S = Program

R =

• Program -> ε
• Program -> Instr Program
• Instr -> '+'
• Instr -> '-'
• Instr -> '>'
• Instr -> '<'
• Instr -> ','
• Instr -> '.'
• Instr -> '[' Program ']'

There are syntax features that cannot be represented with a Context Free Grammar such as:

• Indentation
• Whitespace
• Typedef in C and C++ Programming Languages
• Macro and Templates in Programming Languages like Lisp, C++, Haskell, Nim and others.

Therefore, Programming Languages / Real life programs are not represented purely by Context Free Grammar.

• Complete Sentences in English Language can be generated using Context Free Grammar. For example:

G is a Context Free Grammer

V = {S, < Noun phrase >, < V erb phrase >, < Adjective phrase >,
< Noun >, < V erb >, < Adjective >}

Start variable = S

Σ = {big, stout, Kiao, bought, white, car, Henry, cheese, ate, green}

Rules:

• S -> < Noun phrase > < Verb phrase >
• < Noun phrase > -> < Noun >|< Adjective phrase >< Noun > | λ
• < V erb phrase > -> < V erb >< Noun phrase >
• < Adjective phrase > -> < Adjective phrase >< Adjective > | λ
• < Noun > -> Kiao | car | Henry | cheese
• < V erb > -> bought | ate
• < Adjective > -> big | stout | white | green

Example of sentences generated using it are:

• Kiao bought car
• Henry ate cheese
• Kiao bought big car

It also generates some invalid sentences:

• big cheese ate Henry

• First Order Logic: Terms and formulas of Formal Logic are Context Free Grammar with the exception of the set of variables which can be infinite along with multiple start variables.

With this article at OpenGenus, you must have a strong idea of how Context Free Grammars are applied in Real Life applications.