In the classic formalization of generative grammars first proposed by Noam Chomsky in the 1950s,^[ grammar G consists of the following components:

• A finite set N of nonterminal symbols, that is disjoint with the strings formed from G.


• A finite set Σ of terminal symbols that is disjoint from N.


• A finite set P of production rules, each rule of the form

(Σ∪�)∗�(Σ∪�)∗→(Σ∪�)∗

where ∗ is the Kleene star operator and ∪ denotes set union. That is, each production rule maps from one string of symbols to another, where the first string (the "head") contains an arbitrary number of symbols provided at least one of them is a nonterminal. In the case that the second string (the "body") consists solely of the empty string—i.e., that it contains no symbols at all—it may be denoted with a special notation (often Λ, e or �) in order to avoid confusion.

• A distinguished symbol �∈� that is the start symbol, also called the sentence symbol.

A grammar is formally defined as the tuple (�,Σ,�,�). Such a formal grammar is often called a rewriting system or a phrase structure grammar in the literature.