Classifying Grammars

Recall that a grammar G is a quadruple G = (V, T, S, P)
where

V is a finite set of (meta)symbols, or variables.
T is a finite set of terminal symbols.
S V is a distinguished element of V called the start symbol.
P is a finite set of productions.

The above is true for all grammars. We will distinguish among different kinds of grammars based on the form of the productions. If the productions of a grammar all follow a certain pattern, we have one kind of grammar. If the productions all fit a different pattern, we have a different kind of grammar.

Productions have the form:

Different types of grammars can be defined by putting additional restrictions on the left-hand side of productions, the right-hand side of productions, or both.