In relational algebra, a rename is a unary operation written as ${\displaystyle \rho _{a/b}(R)}$ 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.^[1] For an example, consider the following invocation of ρ on an Employee relation and the result of that invocation:

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

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

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

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

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

References