The production rules specify how the grammar transforms one string to another. Given a string , we say that the production rule is applicable to this string, since it is possible to use the rule to rewrite the (in ) to obtaining a new string . We say that derives and is denoted as

Successive strings are dervied by applying the productions rules of the grammar in any arbitrary order. A particular rule can be used if it is applicable, and it can be applied as many times as described.

We write if the string can be derived from the string in zero or more steps; if can be derived from in one or more steps.

By applying the production rules in arbitrary order, any given grammar can generate many strings of terminal symbols starting with the special start symbol, S, of the grammar. The set of all such terminal strings is called the language generated (or defined) by the grammar.