Rename (relational algebra)

In relational algebra, a rename is a unary operation written as $$\rho_{a/b}(R)$$ where:


 * $R$ is a relation
 * $a$ and $b$ are attribute names
 * $b$ is an attribute of $R$

The result is identical to $R$ except that the $b$ attribute in all tuples is renamed to $a$. For an example, consider the following invocation of $&rho;$ on an $Employee$ relation and the result of that invocation:

Formally, the semantics of the rename operator is defined as follows:


 * $$\rho_{a/b}(R) = \{ \ t[a/b] : t \in R \ \},$$

where $$t[a/b]$$ is defined as the tuple $t$, with the $b$ attribute renamed to $a$, so that:


 * $$t[a/b] = \{ \ (c, v) \ | \ ( c, v ) \in t, \ c \ne b \ \} \cup \{ \ (a, \ t(b) ) \ \}.$$