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Missing Information and Null Values
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A relational DBMS is supposed to treat missing information in a systematic and context-insensitive manner. If a value is missing for a specific attribute of a row, it is not always possible to decide whether a certain condition evaluates to true or false. Missing information is represented by null values in the relational world. The term null value is actually misleading, because it does not represent a value; it represents the fact that a value is missing. For example, null marker would be more appropriate. However, null value is the term most commonly used, so this book uses that terminology. Figure 1-2 shows how null values appear in a partial listing of the EMPLOYEES table.
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Figure 1-2. Nulls represent missing values. Null values imply the need for a three-valued logic, such as implemented (more or less) in the SQL language. The third logical value is unknown.
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Note Null values have had strong opponents and defenders. For example, Chris Date is a well-known opponent of null values and three-valued logic. His articles about this subject are highly readable, entertaining, and clarifying.
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RELATIONAL DATABASE SYSTEMS AND ORACLE
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Although most RDBMS vendors support integrity constraint checking in the database these days (Oracle implemented this feature a number of years ago), it is sometimes also desirable to implement constraint checking in client-side database applications. Suppose you have a network between a client-side dataentry application and the database, and the network connection is a bottleneck. In that case, client-side constraint checking probably results in much better response times, because there is no need to access the database each time to check the constraints. Code-generating tools typically allow you to specify whether constraints should be enforced at the database side, the client side, or both sides.
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Caution If you implement certain constraints in your client-side applications only, you risk database users bypassing the corresponding constraint checks by using alternative ways to connect to the database.
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Predicates and Propositions
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To finish this section about relational data structures, there is another interesting way to look at tables and rows in a relational database from a completely different angle, as introduced by Hugh Darwen. This approach is more advanced than the other topics addressed in this chapter, so you might want to revisit this section later. You can associate each relational table with a table predicate and all rows of a table with corresponding propositions. Predicates are logical expressions, typically containing free variables, which evaluate to true or false. For example, this is a predicate: There is a course with title T and duration D, price P, frequency F, and a maximum number of attendees M.
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If we replace the five variables in this predicate (T, D, P, F, and M) with actual values, the result is a proposition. In logic, a proposition is a predicate without free variables; in other words, a proposition is always true or false. This means that you can consider the rows of a relational table as the set of all propositions that evaluate to true.
Relational Data Structure Terms Review
In this section, the following terms were introduced: Tables (or relations) Rows (or tuples) Columns and domains Candidate, primary, and foreign keys Integrity checking at the database level Missing information, null values, and three-valued logic Predicates and propositions
RELATIONAL DATABASE SYSTEMS AND ORACLE
1.6 Relational Operators
To manipulate data, you need operators that can be applied to that data. Multiplication and addition are typical examples of operators in mathematics; you specify two numbers as input, and the operator produces one output value as a result. Multiplication and addition are examples of closed operators, because they produce things of the same type you provided as input (numbers). For example, for integers, addition is closed. Add any two integers, and you get another integer. Try it you can t find two integers that add up to a noninteger. However, division over the integers is not closed; for example, 1 divided by 2 is not an integer. Closure is a nice operator property, because it allows you to (re)use the operator results as input for a next operator. In a database environment, you need operators to derive information from the data stored in the database. In an RDBMS environment, all operators should operate at a high logical level. This means, among other things, that they should not operate on individual rows, but rather on tables, and that the results of these operators should be tables, too. Because tables are defined as sets of rows, relational operators should operate on sets. That s why some operators from the classical set theory such as the union, the difference, and the intersection also show up as relational operators. See Figure 1-3 for an illustration of these three set operators.
Figure 1-3. The three most common set operators Along with these generic operators from set theory that can be applied to any sets, there are some additional relational operators specifically meant to operate on tables. You can define as many relational operators as you like, but, in general, most of these operators can be reduced to (or built with) a limited number of basic relational operators. The most common relational operators are the following: Restriction: This operator results in a subset of the rows of the input table, based on a specified restriction condition. This operator is also referred to as selection.
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