Database Design and Relational Theory

Chapter 4. FDs and BCNF (Informal)

It is downright sinful to teach the abstract before the concrete

—Z. A. Melzak: Companion to Concrete Mathematics

As we saw in the previous chapter, Boyce/Codd normal form (BCNF for short) is defined in terms of functional dependencies. In fact, BCNF is really the normal form with respect to functional dependencies (just as—to get ahead of ourselves for a moment—5NF is really the normal form with respect to join dependencies). The overall purpose of the present chapter is to explain this observation; as the chapter title indicates, however, the various explanations and associated definitions are all (intentionally, of course) a little informal at this stage. (Informal, but not inaccurate; I won’t tell any deliberate lies.) A more formal treatment of the material appears in the next chapter.

FIRST NORMAL FORM

To begin at the beginning: Let relation r have attributes A1, ..., An, of types T1, ..., Tn, respectively. By definition, then, if tuple t appears in relation r, then the value of attribute Ai in t is of type Ti (i = 1, ..., n). For example, if r is the current value of the shipments relvar SP (see Figure 1-1 in Chapter 1), then every tuple in r has an SNO value that’s of type CHAR, a PNO value that’s also of type CHAR, and a QTY value that’s of type INTEGER.

Now I can give a precise definition of first normal form:^[34]

• Definition: Let relation r have attributes A1, ..., An, of types T1, ..., Tn, respectively. Then r is in first normal form (1NF) ...