4 Extended BNF

Although the original BNF is expressive enough for all formal languages, it is quite cumbersome. The extended BNF (XBNF) uses additional symbols to make syntax notation more concise for human readers. The following symbols are introduced.

• [] to mean whatever is enclosed is optional.
• | to mean alternatives
• * to mean any number of the previous thing.
• {} to create a single group so other operators can apply to the entire group.
• + to mean at least one.

Using this notation, then we can simplify the syntax of an integer as follows:

• S ::= ["+"|"-"]D+
• D ::= "0"|"1"|"2"|"3"|"4"|"5"|"6"|"7"|"8"|"9"

Note that the use of XBNF makes it possible to eliminate the use of the nonterminals I and J!