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 is to be assignable to, to be assignable to is to be a variable.)
Please note very carefully that it isn’t just simple things like the integer 3 that are legitimate values. On the contrary, values can be arbitrarily complex—for example, a value might be a geometric point; or a polygon; or an X ray; or an XML document; or a fingerprint; or an array; or a stack; or a list; or a relation (and on and on). Analogous remarks apply to variables too, of course. I’ll have more to say about such matters in the next chapter.
Now, you might think it’s hard to imagine people getting confused over a distinction as obvious and fundamental as the one between values and variables. In fact, however, it’s all too easy to fall into traps in this area. By way of illustration, consider the following extract from a tutorial on object databases (the italicized portions in brackets are comments by myself):
We distinguish the declared type of a variable from ... the type of the object that is the current value of the variable [so an object is a value] ... We distinguish objects from values [so an object isn’t a value after all] ... A mutator [is an operator such that it’s] possible to observe its effect on some object [so in fact an object is a variable].
Get SQL and Relational Theory, 2nd Edition now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
