Backus-Naur Form (BNF) Notation: Defining the Syntax of Formal Languages

Learn about Backus-Naur Form (BNF), a notation for describing context-free grammars used in specifying programming language syntax. This guide explains BNF's syntax, its use in defining production rules, and its importance in compiler design and language specification.

Backus-Naur Form (BNF) Notation

What is BNF?

Backus-Naur Form (BNF) is a notation for describing the syntax of context-free grammars, which are used to specify the structure of programming languages and other formal languages. BNF provides a clear and concise way to define the rules that govern how valid strings in a language are constructed. Each rule in a BNF grammar is expressed as a production, and productions make it easier for both compilers and developers to understand and manage the grammar and the language it defines.

BNF Production Rules

In BNF, a production rule has this general form:

Left-hand side → Definition

Where:

  • Left-hand side is a single non-terminal symbol (a variable representing a grammatical construct).
  • Definition is a sequence of terminal and/or non-terminal symbols.

Terminal symbols are the actual characters or tokens in the language, and non-terminal symbols are variables that represent higher level grammatical constructs.

Example BNF Grammar

Let's create a simple grammar in BNF that generates palindromes (strings that read the same forwards and backwards) using the characters "a", "b", and "c":

BNF Grammar for Palindromes

S → aSa | bSb | c

This single line of BNF defines three rules:

  • S → aSa: The start symbol (S) can be replaced by "a", followed by S, followed by "a".
  • S → bSb: S can be replaced by "b", followed by S, followed by "b".
  • S → c: S can be replaced by "c".

This allows the generation of palindromes like "aba", "bab", "ccc", "aabbaa", etc.

Conclusion

BNF notation provides a powerful and efficient way to define the syntax of programming languages and other formal grammars. It enhances code clarity and is a very important tool in compiler design, providing a formal structure for language specification that helps in creating parsers, compilers, and other language processing tools.