SQL and Relational Theory, 2nd Edition

RELATIONS vs. TYPES

Chapter 2 discussed types and relations, among other things. However, I wasn’t in a position in that chapter to explain the most important logical difference between those two concepts—but now I am, and I will.

I’ve shown that the database at any given time can be thought of as a collection of true propositions: for example, the proposition Supplier S1 is under contract, is named Smith, has status 20, and is located in city London. More specifically, I’ve shown that the argument values appearing in such a proposition (S1, Smith, 20, and London, in the example) are, precisely, the attribute values from the corresponding tuple, where each such attribute value is a value of the associated type. It follows that:

Types are sets of things we can talk about; relations are (true) statements we make about those things.

In other words, types give us our vocabulary—the things we can talk about—and relations give us the ability to say things about the things we can talk about. For example, if we limit our attention to suppliers only, for simplicity, we see that:

• The things we can talk about are character strings and integers—and nothing else. (In a real database, of course, our vocabulary will usually be much more extensive than this, especially if any user defined types are involved.)

• The things we can say are things of the form “The supplier with the supplier number denoted by the specified character string is under contract; has the name denoted by another specified character ...