Database Reference
In-Depth Information
d.
If the tuple variable x occurs
freely
in a WFF F then $x (F) and
"x (F) are WFFs
e.
Nothing else
In layman's terms, a WFF is a simple or complex comparison involving attributes and
scalar values. As can be confirmed from the forgoing sections and examples, WFFs are
necessary for constructing appropriate data retrieval statements from the database.
8.3.2 Free and Bound Variables
A tuple variable is bounded if it occurs with either an existential or universal quantifier.
Consider the scenario below:
This is an example of a bound occurrence of tuple variable
p
. The condition on
p
is
either true or false, even if a particular value of
p
is not substituted. Note also that
p
can
be replaced by
q
. Now consider the following:
This is an example of a free occurrence of variable
p
. The variable occurs in a simple
condition (comparison) — when a particular value of
p
is substituted we can have a
difference. Note that
p
cannot be replaced by
q
.
The following are some rules for free and bound variables:
a.
All occurrences of variables in a simple condition
(comparison) are free.
b.
Any free/bound occurrence in WFF F is also free/bound in
NOT F, (F).
c.
Any free/bound occurrence in WFF F1, F2 is free/bound in
(F1) AND (F2) as well as (F1) OR (F2).
d.
Every free occurrence of x in F is bound in $x (F) or "x (F); the
occurrence of other variables are not affected.
e.
A tuple variable cannot be both free and bound in the same
statement.
