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Fourth, it might be argued that if 1NF and normalized mean the same thing, and if all tables are therefore normalized (as indeed they are), then the terms unnormalized and denormalized aren t very useful. Again, however, I think they do still have a role to play: They can be used with reference to higher levels of normalization. For example, we might replace two 3NF tables by a single 2NF table (obtained by joining the two 3NF tables together) and thereby carry out an act of denormalization from 3NF to 2NF. Fifth, I ve now taken many pages to explain what 1NF is, but you might have noticed there s one question I haven t raised at all, let alone answered: namely, why is 1NF a good idea I justify the omission as follows. Given that (as we ve seen) all relations are 1NF relations, the question is logically equivalent to this one: Why are relations a good idea Or, more generally, why is the relational model a good idea And while it might be a useful exercise to write something that answers this latter question at length, such is not the purpose of the present chapter. Sixth, the point is worth spelling out explicitly that all of the tables shown in this chapter (including the ones with RVAs in particular) aren t just in 1NF in fact, they re all in the highest possible normal form.14 RVAs do not in and of themselves constitute a violation of any particular level of normalization. Seventh, there s a term I ve deliberately avoided in this chapter so far: predicate. However, I hope you re aware that every table corresponds to some predicate, which is (loosely) what the table means. For example, consider tables T1 and T3 from earlier in this chapter. The predicate for T1 is Supplier S# supplies part P#, while the (more complicated!) predicate for T3 is Supplier S# supplies exactly that set of parts whose part number is mentioned in relation P#_REL, no more and no less. Observe that the parameters of a given predicate correspond to the columns of the corresponding table. And since so far as I know nothing in logic limits the kinds of parameters that can appear in a predicate, so nothing in the relational model limits the kinds of columns that can appear in a table. It follows that RVAs in particular must be legitimate. Eighth, my own research recently has concerned temporal databases, and it would be very remiss of me not to mention that RVAs are actually required (at least conceptually) as a basis for temporal database support. See the book mentioned in passing earlier in this chapter Temporal Data and the Relational Model, by Hugh Darwen, Nikos Lorentzos, and myself (Morgan Kaufmann, 2003), for further explanation.
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14. Except for those in Figures 8-5 and 8-13, neither of which directly and faithfully represented a relation at all. In fact, you might have noticed that I deliberately never called those particular examples tables, since the only tables I m really interested in are normalized ones.
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My last point is this: Supporting RVAs involves comparatively little in the way of additional learning on the part of the user!15 We need tables anyway on the outside (as it were); and if we need them on the outside, we have to understand them anyway, and we have to know how to carry out relational algebra operations, and relational comparisons, and relational assignments (and so on) on them anyway. By contrast, if we were to introduce, say, arrays on the inside, then users would necessarily have to understand arrays, and a whole set of array operations, in addition to the relational ones. Thus, if we need any kind of collection data type at all on the inside as well as on the outside, then surely tables are the one requiring the minimum of extra learning; and the minimum amount of extra syntax in the query language; and the minimum number of extra pages in the documentation; and so on. I ll close with an exercise (due to Hugh Darwen) that might help you appreciate the occasional usefulness of RVAs, even in base tables: I decided to throw a party, so I drew up a list of people I wanted to invite and made some preliminary soundings. The response was good, but several people made their acceptance conditional on the acceptance of certain other invitees. For example, Bob and Cal both said they would come if Amy came; Hal said he would come if either Don and Eve both came or Fay came; Guy said he would come anyway; Ian said he would come if Bob and Amy both came; and so on. Design a table to show whose acceptance is based on whose.
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