Backus-Naur form (BNF) is a notation used to formally describe the syntax of programming languages. It ensures that the language's rules are clearly defined so that a computer can easily parse the source code.

Additionally, regular expressions are not always sufficient for defining certain languages. Therefore, Backus-Naur form serves as a robust metalanguage.

Example 1

<DIGIT> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6

This definition specifies that a digit can be any value from 0 to 6.

Example 2

<LETTER> ::= A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

This definition specifies that a letter can be any character from A to Z.

<WORD> ::= <LETTER><LETTER>

This rule defines a word as two letters. For instance, "W" and "WE" are valid words, while "GOING" is not, as it consists of more than two letters.

Instead of defining new rules for each letter, recursion allows us to generalize rules. Here’s how recursion is used:

This recursive definition means that a word can be a single letter or a letter followed by another word.

This process of analyzing a statement using these rules is known as parsing.