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the position that duplicates are a good idea needs to provide a good, convincing answer to this question.5
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Bag Theory
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Recall that, loosely speaking, a bag in mathematics is a set that permits duplicates. Duplicate advocates thus sometimes claim that their approach is just as respectable as the relational approach because it too is based on solid theory (bag theory instead of set theory). Earlier in this chapter, however, I claimed that mathematical bag theory treatments usually start by assuming there s a way to count duplicates! I further claimed that that assumption effectively means that bags are defined in terms of sets. Alps replied by constructing an outline bag theory that he claimed didn t start with such an assumption. But I think it does! One of the three primitives of his theory is an expression of the form count xA which (to quote) is intended to denote the number of times the [object] x occurs in the bag A. Now, this quote might have been meant only as an informal, intuitive remark, not as part of the theory as such, but I m still suspicious. In any case, the question of whether such an assumption is necessary is perhaps a red herring (and I was perhaps wrong to raise it in the first place). The point rather is that bag theory: Is necessarily more complex than set theory Includes set theory as a proper subset (perhaps I should say subbag ) Is reducible to set theory Occam s Razor would thus clearly suggest that we stay with sets and not get into the unnecessary complexities of bags. (As so often in a database context, Occam s Razor is peculiarly apt here. One simple way of stating it is: Entities should not be multiplied beyond necessity. A simpler way still is just: No unnecessary entities. )
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The Performance Issue
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I also recommended earlier in this chapter that users should always ensure that query results contain no duplicates for instance, by always specifying DISTINCT at appropriate points in the query and thus simply forget about the whole problem. However, I also pointed out that SELECT DISTINCT might take longer to execute than SELECT ALL, even if the DISTINCT is effectively a no op. Alps commented that the performance problem doesn t go away if the system is (re)defined to eliminate duplicates automatically: Imagine an address table containing street, city, state, and zip data. If a query is performed selecting city from the table under a system that [eliminates duplicates automatically], the system is going to have to go through all the same checking for duplicates that would be required if [it didn t eliminate duplicates automatically but] the query asked for DISTINCT cities.
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5. It s now been many years since I first issued this challenge, and nobody has yet come up with a cogent response to it. See Appendix B ( More on Counting Pennies ), later.
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Here I think Alps missed my point slightly. What I meant was that, because it appears that always eliminating duplicates implies performance problems, there was a strong motivation for the SQL language designers to make not eliminating duplicates the default. (In fact, I very specifically pointed out that support for duplicates can actually have a negative impact on performance, and my reason for doing so was precisely to provide a counterbalance to this familiar argument.) But the full implications, psychological and otherwise, of this very bad language design decision weren t thought through at the time. It s my belief that the occasional overhead that might be incurred (in a well-implemented system) in always eliminating duplicates would be vastly outweighed by the benefits including performance benefits that such a system would provide. Of course I understand that checking for duplicates is required regardless of whether (a) the system prohibits them or (b) the system permits them but the user specifies DISTINCT. But note that if the language is defined always to eliminate duplicates, at least conceptually, then the system will sometimes be able not to eliminate them for intermediate results, at least, though not of course for final results as an optimization, where appropriate.
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