SQL and Relational Theory, 2nd Edition

RELATIONS AND THEIR BODIES

The first point I want to discuss is this: Every subset of a body is a body—or, loosely, every subset of a relation is a relation. (Once again I mentioned this fact in Chapter 1, but now I want to say a little more about it.) In particular, since the empty set is a subset of every set, a relation can have a body that consists of an empty set of tuples (and we call such a relation an empty relation). For example, suppose there are no shipments right now. Then relvar SP will have as its current value the empty shipments relation, which we might draw like this (and now I revert to the convention by which we omit the type names from a heading in informal contexts; throughout the rest of the book, in fact, I’ll feel free to regard headings as either including or excluding type names—whichever best suits my purpose at the time):

SNO	PNO	QTY

Note that, given any particular relation type, there’s exactly one empty relation of that type—but empty relations of different types aren’t the same thing, precisely because they’re of different types. For example, the empty suppliers relation isn’t equal to the empty parts relation (their bodies are equal but their headings aren’t).

Consider now the relation depicted here:

SNO	PNO	QTY
S1	P1	300

This relation contains just one tuple (equivalently, it’s of cardinality one). If we want to access the single tuple it contains, then we’ll have to extract it somehow from its containing relation. Tutorial D uses syntax of the form TUPLE ...