In computer science, a production or production rule is a rewrite rule that replaces some symbols with other symbols. A finite set of productions ${\displaystyle P}$ is the main component in the specification of a formal grammar (specifically a generative grammar).

In such grammars, a set of productions is a special case of relation on the set of strings ${\displaystyle V^{*}}$ (where ${\displaystyle {}^{*}}$ is the Kleene star operator) over a finite set of symbols ${\displaystyle V}$ called a vocabulary that defines which non-empty strings can be substituted with others. The set of productions is thus a special kind subset

and productions are then written in the form ${\displaystyle u\to v}$ to mean that ${\displaystyle (u,v)\in P}$ (not to be confused with ${\displaystyle \to }$ being used as function notation, since there may be multiple rules for the same ${\displaystyle u}$). Given two subsets ${\displaystyle A,B\subset V^{*}}$, productions can be restricted to satisfy ${\displaystyle P\subset A\times B}$, in which case productions are said "to be of the form ${\displaystyle A\to B}$. Different choices and constructions of ${\displaystyle A,B}$ lead to different types of grammars. In general, any production of the form

where ${\displaystyle \epsilon }$ is the empty string (sometimes also denoted ${\displaystyle \lambda }$), is called an erasing rule, while productions that would produce strings out of nowhere, namely of the form

are never allowed.

In order to allow the production rules to create meaningful sentences, the vocabulary is partitioned into (disjoint) sets ${\displaystyle \Sigma }$ and ${\displaystyle N}$ providing two different roles:

In the most general case of an unrestricted grammar, a production ${\displaystyle u\to v}$, is allowed to map arbitrary strings ${\displaystyle u}$ and ${\displaystyle v}$ in ${\displaystyle V}$ (terminals and nonterminals), as long as ${\displaystyle u}$ is not empty. So unrestricted grammars have productions of the form

or if we want to disallow changing finished sentences