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. For an example, consider the following invocation of ρ on an Employee relation and the result of that invocation:
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))\ \}.}
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