Formal Grammars in Compiler Design: Defining Programming Language Syntax

Explore the role of formal grammars in specifying the syntax of programming languages within compiler design. This guide explains the components of a formal grammar, different grammar types, and their use in creating unambiguous language specifications for reliable parsing and code generation.

Formal Grammars in Compiler Design

Understanding Formal Grammars

A formal grammar is a set of rules that define the structure of a language. In compiler design, formal grammars are used to specify the syntax of programming languages. The grammar defines which sequences of tokens (the basic units of a programming language) are considered syntactically correct. This is crucial for the compiler to parse (analyze) and interpret the source code accurately.

Components of a Formal Grammar

A formal grammar (often denoted as G) is defined by four components:

• N: A finite set of non-terminal symbols (variables representing grammatical constructs).
• T: A finite set of terminal symbols (actual characters or tokens in the language).
• P: A finite set of production rules (rules defining how non-terminals can be replaced by other symbols).
• S: The start symbol (a non-terminal that begins the derivation of a valid string).

Example Formal Grammar

Let's consider a simple grammar:

• N = {S, R, B} (Non-terminal symbols)
• T = {a, b} (Terminal symbols)
• Production rules:
• S → bR
• R → aR
• R → aB
• B → b

This grammar generates strings of the form banb (where n ≥ 1).