Rename (relational algebra)
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In relational algebra, a rename is a unary operation written as ρa / b(R) where:
The result is identical to R except that the b field in all tuples is renamed to an a field. For an example, consider the following Employee relation and its renamed version:
| Employee | ρEmployeeName / Name(Employee) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Formally the semantics of the rename operator is defined as follows:
![\rho_{a/b}(R) = \{ \ t[a/b] : t \in R \ \}](http://upload.wikimedia.org/math/d/b/8/db82aa3dcacfb468b1da2e3284254293.png)
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) ) \ \}](http://upload.wikimedia.org/math/5/2/0/5205ffae5f78b98f4db9d944ff5db3e6.png)
The result of the rename is only defined when the attribute a did not appear already in the header of the operand.
