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:

Employee

\rho_{EmployeeName/Name}(Employee)

Name	EmployeeId
Harry	3415
Sally	2241

EmployeeName	EmployeeId
Harry	3415
Sally	2241

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) ) \ \}

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