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Listing 3-1. Cartesian Product Between Two Tables Member X Type
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Inner Join
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If you look at the table in Figure 3-2, you can see that most of the rows are quite meaningless. For example, the second and third rows that have our junior member Melissa McKenzie alongside information about the senior and social membership types are pointless. However, the first row where the member types from each table match is useful because it allows us to see what fee Melissa pays. If we take just the subset of rows where the value in the MemberType column matches the value in the Type column, then we have useful information about the fees for each of our members. This combination of a Cartesian product followed by a select operation is known as an inner join (often just called a join). The condition for the rows we want to retrieve is known as the join condition. Listing 3-2 shows the algebra expression to retrieve members with their appropriate fees. On the left side of the equation, the bow tie symbol represents the join between the two tables Member and Type, and the join condition is expressed in the subscript. On the right side of the equation, we perform a select operation on the result of the Cartesian product.
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Listing 3-2. A Join (Left Side) Is Defined As a Cartesian Product Followed by a Select
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Member
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MemberType=TypeType
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MemberType=Type(Member
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X Type)
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Figure 3-3 depicts the process.
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a) Cartesian product select b) Join
Select just those rows where these two columns have the same value
Figure 3-3. A join is a Cartesian product followed by a select.
The two columns that we are comparing for equality (MemberType and Type) must be what is sometimes referred to as join compatible. In the pure relational theory, this means
CHAPTER 3 A FIRST LOOK AT JOIN S
they must both come from the same set of possible values (formally known as a domain). In practical terms, join compatibility usually means that the columns in each of the tables have the same data type. For example, they are both integers or both dates. Different database products may interpret join compatibility differently. Some might let you join on a float (number with a decimal point) in one table and an integer in another. Some may be fussy about whether text fields are the same length (such as CHAR(10) or CHAR(15)), and others may not. I recommend you don t try to join on fields with different types unless you are very clear what your particular product does. As always, the best thing is to make sure that when you design your tables, those fields that are likely to be joined have the same types.
SQL for Cartesian Product and Join
As I pointed out in the previous section, not all versions of SQL are the same. In 1992 keywords representing some algebra operations were added to the SQL standard,1 and there have been a number of updates since then. However, not all vendors incorporate all parts of the standard, and some add extras. You might find that some SQL versions may not implement all the algebra-related keywords that we use in this book, but there are usually a number of ways to retrieve the information required. You can express all the relational algebra operations using relational calculus expressions, and they will always work for you. In the meantime, let s look at the SQL statements that reflect the algebra operations. We ll look at other equivalent calculus statements later in this chapter. The SQL key phrase for a Cartesian product is CROSS JOIN. It is not often that you have a question that requires a CROSS JOIN, but for completeness Listing 3-3 shows it being used to retrieve the table shown in Figure 3-3a. As in all our other SQL queries, SELECT * just means retrieve all the columns.
Listing 3-3. SQL for a Cartesian Product to Produce Table in Figure 3-3a SELECT * FROM Member m CROSS JOIN Type t
The SQL phrase for a join is INNER JOIN. The join condition (which in this case allows us to select those rows where the member type is the same in both tables) follows the keyword ON, as shown in Listing 3-4.
Listing 3-4. SQL for a Join to Produce Table in Figure 3-3b SELECT * FROM Member m INNER JOIN Type t ON m.MemberType = t.Type
1. International Organization for Standardization. Information technology Database languages SQL. ISO, Geneva, Switzerland, 1992. ISO/IEC 9075:1992.
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