Rename (relational algebra)

In relational algebra, a rename is a unary operation written as $ho\_\{a/b\}(R)$ where:

* $a$ and $b$ are attribute names
* $R$ is a relation

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:

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

: $ho\_\{a/b\}(R)\; =\; \{\; t\; [a/b]\; :\; t\; in\; R\; \}$

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

: $t\; [a/b]\; =\; \{\; (c,\; v)\; |\; (\; c,\; v\; )\; in\; t,\; c\; e\; b\; \}\; cup\; \{\; (a,\; t(b)\; )\; \}$

The result of the rename is only defined when the attribute $a$ did not appear already in the
header of the operand.