Rename (relational algebra)

In relational algebra, a rename is a unary operation written as  ρ a / b ( R ) {\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:

Employee {\displaystyle {\text{Employee}}} |  ρ EmployeeName/Name ( 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:

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

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

## References

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1. ^ Introduction to Database Systems. Pearson Education India. 2010. pp. 103–105. ISBN 978-81-317-3192-5.