Database Design and Relational Theory

Appendix B. Redundancy Revisited

Nothing is certain but the unforeseen

—19th century proverb

In Chapter 13, I discussed a normal form I called RFNF (redundancy free normal form). However, I did also mention in that chapter the fact that that very same name had been used earlier in a paper by Millist W. Vincent to mean something rather different.^[180] In this appendix, I present a brief introduction to Vincent’s RFNF.

Consider our usual suppliers relvar S, with its FD {CITY} → {STATUS} and sample value as shown in Figure 1-1. The tuple for supplier S1 in that relvar has city London and status 20; as a consequence, the tuple for supplier S4, which also has city London, must have status 20, for otherwise the FD {CITY} → {STATUS} would be violated. In a sense, therefore, the occurrence of that status value 20 in the tuple for supplier S4 is redundant, because there’s nothing else it could possibly be—it’s a logical consequence of, and is fully determined by, the values appearing elsewhere in the relation that’s the current value of the relvar at the time in question.

Examples like the foregoing provide the motivation for the following intuitively attractive definition (due to Vincent but considerably paraphrased here):

• Definition: Let relation r be a value of relvar R, let t be a tuple in r, and let v be an attribute value within t. Then that occurrence of v within t is redundant in r, and R is subject to redundancy, if and only if replacing that occurrence of v by an occurrence of v′ ( ...