Rename Operation (9/9)
• Allows us to name, and therefore to refer to, the results of relational-algebra expressions.
• Allows us to refer to a relation by more than one name.
• Example:
ρ
x
(E)
returns the expression E under the name X
• If a relational-algebra expression E has arity n, then
returns the result of expression E under the name X, and with the
attributes renamed to A
1
, A
2
, …., A
n
.
Union
• Notation: r ∪ s
• Defined as:
r ∪ s = {t | t ∈ r or t ∈ s}
• For r ∪ s to be valid. (type compatibility)
1. r, s must have the same arity (same number of attributes)
2. The attribute domains must be compatible (example: 2
nd
column
of r deals with the same type of values as does the 2
nd
column of s)
• Example: to find all customers with either an account or a loan
∏
customer_name
(depositor) ∪ ∏
customer_name
(borrower)
• Key constraints can be violated when the union is processed if both have the same attribute as a
key before union.
)(
),...,,(
21
E
n
AAAx
ρ
