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Set Operations
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ne of the great strengths of relational database theory is that the tables (or more formally, the relations) are made up of distinct rows and so can be considered a set. You can then use all the power of mathematical set theory to help you with combining and extracting specific information. Don t be alarmed by the words mathematical and theory, as the ideas presented are both simple and elegant. The algebra notation introduced in s 1 and 2 is a useful way of expressing queries, especially as they become more complex. I will use the algebra notation in this chapter, but will always give you an SQL equivalent so you can choose which representation you find the most helpful. In this chapter, we will look at four set operations: Union Intersection Difference Division Many implementations of SQL (but not all) have keywords that support the first three of these operations directly. We will look at how to use these keywords, as well as alternative ways to achieve the same result when the keywords are not available.
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CHAPTER 7 SE T OPERA TION S
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Overview of Basic Set Operations
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We will look at each of the set operations in turn, but so that you know where we are heading, I ll begin with a very quick overview of the three most common operations: union ( ), intersection ( ), and difference ( ). Imagine we have membership tables from two golf clubs. We might want to do the following: Determine who is in both clubs. Form a large list that combines all the members. Find out who is in one club but not the other. The basic set operations allow us to carry out all these tasks. Let s assume that the two clubs keep the names of their members in two tables that have exactly the same columns (more about this in the next section). Let s say the two tables are those shown in Figure 7-1. (OK, they are very small clubs!)
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ClubA
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Figure 7-1. Two tables of member names
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ClubB
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The basic set operations on these two tables are summarized in Figure 7-2. The two club tables have been overlaid so that the members in common are superimposed. ClubA is the top table in each picture. The union operator (top left in Figure 7-2) shows all the names from each table (with duplicates removed). The intersect operator (top right) returns the two rows that appear in both tables. The difference operators (bottom) return those rows that are found in one club but not the other.
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C HA PTER 7 S ET O PE RAT IO NS
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Figure 7-2. The basic set operations on the two tables ClubA (top) and ClubB (bottom)
Union-Compatible Tables
The set operations union, intersection, and difference operate between two sets of rows. It does not make any sense to try to compare rows in sets that have very different structures, such as those in Figure 7-3.
CHAPTER 7 SE T OPERA TION S
Member table
Entry table
Figure 7-3. It makes no sense to try to compare rows with different structures.
So what determines whether two sets of rows can be compared using the set operations union, intersection, and difference Formally, the two sets must have the same number of columns, and each column must have the same domain. Strictly speaking, a domain is a set of possible values. However, in practice, the requirement for set operations is that the corresponding columns in each set of rows have the same types both character, both integer, and so on. The names of the columns do not need to be the same. Sets or tables that meet these requirements are referred to as being union compatible, although the requirement is necessary for the intersection and difference operations as well. Figure 7-4 shows pairs of membership tables from different clubs. The two tables on the left are union compatible. Even though the names of the columns are different, they have the same number of columns, and corresponding columns have the same types. The two tables on the right are not union compatible. Even though they have columns with the same names, the order is such that the fourth column has a character type in the top table and a number type in the bottom, and vice versa for the last column. Different implementations of SQL may interpret the strictness of this sameness of domains or types differently. Strictly speaking, two fields defined as CHAR(10) and CHAR(12) have different domains, but many implementations of SQL will allow these to be regarded as the same for the purposes of set operations. Some implementations will also convert numbers into characters to enable set operations to be carried out. I find this particularly scary and don t recommend you let your application make these sorts of decisions for you. The following sections demonstrate how you can use SQL to make your tables union compatible.