Database Reference
In-Depth Information
Example 7:
We could rewrite the solution to example 4 as follows:
8.3 Quantifiers, Free and Bound Variables
Carrying on, we need to introduce two quantifiers, and clarify what is meant by
free
and
bound
variables. The mathematical notations will be introduced, followed by the
relational calculus notations. The mathematical notations are indicated in Figure
8-1
:
Figure 8-1.
Quantifiers
Additionally, if P(x) is a condition in tuple variable x, then
• $x) (P(x)) means $x satisfying P(x)
(
• "x) (P(x)) means all variables in range of x satisfies
the condition P(x)
(
As expressed in the previous section, the relational calculus notations for the
universal and existential quantifiers as follows:
8.3.1 Well-Formed Formula
Based on the notation given in the previous section, a WFF may be clarified as follows:
a.
A simple comparison (condition) is a WFF
b.
If F is a WFF, so are NOT (F) and (F)
c.
If F1, F2 are WFF then so are (F1 AND F2), (F1 OR F2) and (If
F1 THEN F2)
