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The following extract from an article by David Beech ( New Life for SQL, Datamation, February 1st, 1989) is typical of the arguments that are advanced by duplicate row advocates: For example, the row cat food 0.39 could appear three times [on a supermarket checkout receipt] with a significance that would not escape many shoppers ... At the level of abstraction at which it is useful to record the information, there are no value components that distinguish the objects. What the relational model does is force people to lower the level of abstraction, often inventing meaningless values to be inserted in an extra column whose purpose is to show what we knew already, that the cans of cat food are distinct. Apart from the remark regarding lowering the level of abstraction, which I think is just arm waving,2 this seems to me to be exactly the straw man argument I gave in my article Why Duplicate Rows Are Prohibited (in Relational Database Writings 1985 1989, Addison-Wesley, 1990), under the heading Why Duplicates Are Good ( ) to wit: 1. Duplicates occur naturally in practice. 2. Given that this is so, it s a burden on the user to have to invent some artificial identifier in order to distinguish between them. In a subsequent section of that same article, titled Why Duplicates Are Bad: The Fundamental Issue, I went on to refute this argument as follows: 1. Individual objects must be identifiable (that is, distinguishable from all other objects) for if an object is not identifiable, then it s impossible even to talk about it, let alone perform any kind of operation upon it or use it for any sensible purpose. In other words, objects must have identity. Note: Here and throughout this chapter, I use the term object in its ordinary English sense, not in the special rather loaded sense in which it s used in the OO world.
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2. If anything, in fact, the relational representation raises the level of abstraction, because it eliminates irrelevant details details, that is, that have to do merely with the way data is presented to the end user. After all, the checkout receipt is really just a report (it certainly isn t part of the database!), and there s no particular reason why we should have to represent data in the same way in the database and in a report; in fact, there are good reasons not to. (Thanks to Fabian Pascal for these observations, and more generally for his review of and helpful comments on an earlier draft of this chapter.)
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2. In a collection of objects in which there are no duplicates (in other words, a mathematical set), objects obviously do have identity, because they are in fact self-identifying. For example, in the set of integers {3,6,8,11}, there s no ambiguity as to which element of the set is 6 and which is 8 (etc.). However, in the collection (3,6,6,8,8,8,11), which is certainly not a mathematical set (it is a multiset or bag instead), we cannot make an analogous statement; both 6 and 8 are now ambiguous. 3. So what is the identification mechanism in a collection that permits duplicates (in other words, a bag) For example, in the bag just shown, how can we distinguish the two 6 s from one another Note that there must still be an identification mechanism; if we cannot distinguish the two 6 s from one another somehow, we cannot even tell there are two of them (an illustration of what I believe is known in the world of philosophy as The Principle of Identity of Indiscernibles). In other words, we wouldn t even know there were any duplicates in the first place! Now, a common reaction to this argument is But I really don t need to distinguish among the duplicates all I want to do is be able to count them. The point I m trying to make is that you do need to distinguish them, even just to count them (for otherwise how do you know which ones you ve already counted ). This point is crucial, of course, and I really don t know how to make it any more strongly than I already have. How then do we distinguish duplicates such as the two 6 s in the bag shown above The answer, of course, is that we do so by their relative position; we say something like this 6 is here and that 6 is there, or this one is the first 6 and that one is the second. And so we have now introduced a totally new concept, one that is quite deliberately omitted from the relational model: positional addressing. Which means we re now quite beyond the pale! that is, we ve moved quite outside the framework of relational theory. Which means that there s no guarantee whatsoever that any results that hold within that framework still apply. For example, does JOIN still work (As a matter of fact, it doesn t.) What about UNION EXTEND SUMMARIZE Are the theorems of normalization still valid What about the quantifiers EXISTS and FORALL What about the rules for functional dependency inference What about expression transformation and optimization Etc., etc., etc. Furthermore, we now definitely need certain additional operators, such as retrieve the nth row or insert this new row here or move this row from here to there. In my opinion pace Beech these operators constitute a much greater burden on the user than does the occasional need to invent an artificial identifier. The relational model, by contrast, adopts the position that, since objects do have to be identifiable somehow, then we might as well represent their identity in exactly the same way as everything else: namely, by values in columns. (Especially as there will often be a natural identifier that is usable as such a column value anyway, which means that the problem of having to invent an artificial value might not arise all that often in practice.) In this way we can stay securely within the context of relational theory, and all of the desirable properties of that theory will thus still be directly applicable. To return for a moment to the cat food argument, Beech goes on to say: We are not being less than respectable mathematically if we consider collections containing duplicates, because mathematicians deal with such collections, called multisets or ... bags.
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