Recursive grammar

In computer science, a grammar is informally called a recursive grammar if it contains production rules that are recursive, meaning that expanding a non-terminal according to these rules can eventually lead to a string that includes the same non-terminal again. Otherwise it is called a non-recursive grammar.

For example, a grammar for a context-free language is left recursive if there exists a non-terminal symbol A that can be put through the production rules to produce a string with A (as the leftmost symbol). All types of grammars in the Chomsky hierarchy can be recursive and it is recursion that allows the production of infinite sets of words.