SQL and Relational Theory, 2nd Edition

VALUES vs. VARIABLES

The logical difference between relations and relvars is actually a special case of the logical difference between values and variables in general, and I’d like to take a few moments to look at the more general case. (It’s a bit of a digression, but I think it’s worth taking the time here because clear thinking in this area can be such a great help, in so many ways.) Here then are some definitions:

Definition: A value is what the logicians call an “individual constant,” such as the integer 3. A value has no location in time or space. However, values can be represented in memory by means of some encoding, and those representations or encodings do have location in time and space. Indeed, distinct representations of the same value can appear at any number of distinct locations in time and space—meaning, loosely, that any number of different variables (see the next definition) can have the same value, at the same time or different times. Observe in particular that, by definition, a value can’t be updated; for if it could, then after such an update it wouldn’t be that value any longer.

Definition: A variable is a holder for a representation of a value. A variable does have location in time and space. Also, variables, unlike values, can be updated; that is, the current value of the variable can be replaced by another value. (After all, that’s what “variable” means—to be a variable is to be updatable and to be updatable is to be a variable; equivalently, to be a variable ...