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 ρ on an Employee relation and the result of that invocation:

$\text{Employee}$	${\rho }_{\text{EmployeeName/Name}}(\text{Employee})$
Name EmployeeId Harry 3415 Sally 2241	EmployeeName EmployeeId Harry 3415 Sally 2241

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

$$\begin{gathered} {\rho }_{a/b}(R)=\{ \\ t[a/b]:t\in R \\ \}, \end{gathered}$$

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

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