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Everybody knows there can sometimes be good reasons for violating the principles of normalization good logical reasons, I mean; I m not a fan of denormalizing for performance, which should never be necessary anyway, in a properly architected DBMS (but that s another topic I don t want to get into in detail on here). I described one such reason earlier in this chapter, in the section A Brief Review of Normalization, where I showed there can be a conflict between the objective of full normalization and the objective of dependency preservation; in other words, we might decide it s worth living with some redundancy in order to make certain update procedures simpler,14 and certain constraints easier to state and maintain, than they would otherwise be. There might be other good reasons, too. In the same kind of way, sometimes there ll be good reasons for violating The Principle of Orthogonal Design. In particular, recall from the section Tuples vs. Propositions earlier in this chapter that the very same tuple can represent any number of distinct propositions. One consequence of this fact is that a design that violates orthogonality might sometimes be acceptable. The following simple example is due to Hugh Darwen. Consider the predicates Employee E# is on vacation and Employee E# is awaiting phone number allocation. The obvious design for this situation involves two unary relvars that is, relvars of degree one that look like this (in outline): ON_VACATION { E# } KEY { E# } NEEDS_PHONE { E# } KEY { E# }
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13. I mention this point because the principle has been criticized as having been defined purely to bolster up the view updating mechanism. I reject this criticism. As I ve tried to show, orthogonality would still be a good idea even if view updating weren t an issue at all. 14. I remark in passing that this observation suggests another possible characterization of redundancy (or at least another way to think about it, if only informally): Reducing redundancy makes more single-tuple updates logically acceptable than would otherwise be the case because the presence of redundancy implies that sometimes we have to update several tuples at the same time, as it were, meaning that what would otherwise be single-tuple updates have to become multi-tuple updates instead.
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CHAPTER 12 DATA REDUNDANCY AND DATABASE DESIGN
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Clearly, the very same employee can be represented in both of these relvars at the same time, and the design thus violates orthogonality. But even if the very same tuple t appears in both relvars, those two appearances represent two different propositions, and there s no redundancy involved. Violating orthogonality doesn t necessarily imply redundancy as indeed we already know. (On the other hand, it would be remiss of me not to point out that there is at least a difference in kind between the example just discussed and the examples of light vs. heavy parts LP vs. HP discussed, and illustrated in Figures 12-5 and 12-6, earlier in this chapter. In the LP vs. HP examples, we can write a formal constraint, to the effect that the WEIGHT value has to lie in a certain range, that a given part tuple has to satisfy in order for it to be accepted into LP or HP or both. However, there s no formal constraint we can write that a given E# tuple has to satisfy in order for it to be accepted into ON_VACATION or NEEDS_PHONE or both. If the user asserts that a certain E# tuple is to be inserted into, say, ON_VACATION, then the system simply has to trust the user; there s no check it can perform to ascertain that the tuple does indeed belong in ON_VACATION instead of or as well as NEEDS_PHONE.) Here s another example, also due to Hugh Darwen, that might mistakenly be thought to violate orthogonality15 but in fact doesn t. It s based on an example from his presentation How to Handle Missing Information Without Using Nulls (slides available at http://www. thethirdmanifesto.com, May 9th, 2003). We re given three relvars that look like this (in outline): EARNS { E#, SALARY } KEY { E# }
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SALARY_UNK { E# } KEY { E# } UNSALARIED { E# } KEY { E# } Sample values are shown in Figure 12-9.
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