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CHAPTER 13 DATA REDUNDANCY AND DATABASE DESIGN: FURTHER THOUGHTS NUMBER ONE
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With regard to this latter example, I m assuming relvar S has been decomposed into its projections SC and ST on {S#,CITY} and {S#,STATUS}, respectively. If this decomposition isn t done, the constraint is just a simple FD: CONSTRAINT CITY_DETERMINES_STATUS ( S { CITY, STATUS } ) KEY { CITY } ; As this example suggests, the proposed KEY syntax provides a simple way of stating FDs. Of course, the usual A B syntax is simpler still; it might thus profitably be considered as a basis for extending the syntax of Tutorial D constraint definitions still further. If the proposed KEY syntax is accepted, then (as ADR goes on to point out in his comments) dependency loss doesn t mean the dependency in question is actually lost it just means it applies to some different relvar (possibly a virtual relvar or view, more generally what The Third Manifesto calls a pseudovariable).
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Orthogonality Revisited
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I ve left the biggest issue till last. ADR took exception to The Principle of Orthogonal Design, or at least to my formulation thereof; to be specific, he found it too strong, in the sense that it regarded certain situations as violating orthogonality that he didn t. His comments read in part: One of your definitions appears to single out precisely those cases of the same tuple appearing in more than one place that do indeed represent redundancy, thus addressing my complaints ... But later in the chapter you appear to return to [a] version I object to ... If you revised the principle in line with [the definition referenced in the first sentence of this extract], then my complaints would disappear; effectively, the principle would advise against duplicate appearances of a tuple representing the same proposition rather than mere repetition of tuples. Clearly, then, ADR and I agree on wanting to prevent the existence of any constraint that requires a tuple representing some given proposition to appear in more than one place. Here then is my attempt to state this requirement more precisely: The Principle of Orthogonal Design: Let A and B be distinct relvars. Replace A and B by nonloss decompositions into projections A1, A2, ..., Am and B1, B2, ..., Bn, respectively, such that every Ai (i = 1, 2, ..., m) and every Bj (j = 1, 2, ..., n) is in 6NF. Let some i and j be such that there exists a sequence of zero or more attribute renamings with the property that (a) when applied to Ai, it produces Ak, and (b) Ak and Bj are of the same type.6 Then there must not exist a constraint to the effect that, at all times, Ak' = Bj' (where Ak' and Bj' are specified nonempty restrictions of Ak and Bj, respectively). In other words, if there s a constraint to the effect that some such Ak' and Bj' do exist, then that fact constitutes a violation of the principle. Note: Perhaps I should say explicitly that the projections and restrictions referred to in the definition might very well be identity projections and restrictions, respectively.
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6. R1 and R2 are of the same type if and only if they have the same headings (i.e., if and only if they have the same attribute names, and attributes of the same name are defined over the same type in turn).
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CHAPTER 13 DATA REDUNDANCY AND DATABASE DESIGN: FURTHER THOUGHTS NUMBER ONE
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What s the difference between the principle as just defined and the version I gave in the previous chapter Well, here s the definition from that chapter: The Principle of Orthogonal Design (previous version): Let A and B be distinct relvars. Then there should not exist nonloss decompositions of A and B into projections A1, A2, ..., Am and B1, B2, ..., Bn, respectively, such that the relvar constraints for some Ai (i = 1, 2, ..., m) and some Bj (j = 1, 2, ..., n) are such as to permit the same tuple to appear in both. Observe that any database that satisfies the new version of the principle certainly satisfies the old version, but the converse is not true; a database could satisfy the old version and not the new one. In other words, the old version was strictly stronger than the new one and that was the problem; as I observed earlier, the old version was too strong, and regarded as violations certain designs that were in fact perfectly reasonable. Note in particular that simply having the same tuple t appear in two distinct relvars could constitute a violation of the old version; in the new version, by contrast, having tuple t appear in two distinct relvars is a violation only if that tuple is not allowed to appear in one and not the other (in other words, only if there s a constraint to the effect that a certain degree of redundancy must exist). By way of example, consider relvars LP and HP once again, with predicates (to repeat) as follows: LP: Part P# is used in the enterprise, is named PNAME, has color COLOR and weight WEIGHT (which is less than or equal to 17 pounds), and is stored in city CITY. HP: Part P# is used in the enterprise, is named PNAME, has color COLOR and weight WEIGHT (which is greater than or equal to 17 pounds), and is stored in city CITY. This database violates the new version of the principle because the following constraint clearly applies to it: CONSTRAINT LP_AND_HP_OVERLAP ( LP WHERE WEIGHT = WEIGHT ( 17.0 ) ) = ( HP WHERE WEIGHT = WEIGHT ( 17.0 ) ) ; By way of another example (also repeated from the previous chapter), consider the predicates Employee E# is on vacation and Employee E# is awaiting phone number allocation. The obvious design for this situation involves two relvars: ON_VACATION { E# } KEY { E# } NEEDS_PHONE { E# } KEY { E# } Clearly, the very same employee can be represented in both of these relvars at the same time and in the previous chapter I claimed that this state of affairs constituted a violation of The Principle of Orthogonal Design (and so it did, given the definition I was appealing to in that chapter). But I also pointed out that even if the very same tuple appeared in both relvars, those two appearances represented two different propositions, and there wasn t any redundancy involved. And I tried to finesse the situation by claiming that there were occasions on which it was acceptable to violate the principle. Note clearly, however, that the example under discussion doesn t violate the new version of the principle! That s because there s no formal constraint we
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