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Silberschatz Korth Sudarshan: Database System Concepts, Fourth Edition
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3 Relational Model
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The relational model is today the primary data model for commercial data-processing applications It has attained its primary position because of its simplicity, which eases the job of the programmer, as compared to earlier data models such as the network model or the hierarchical model In this chapter, we rst study the fundamentals of the relational model, which provides a very simple yet powerful way of representing data We then describe three formal query languages; query languages are used to specify requests for information The three we cover in this chapter are not user-friendly, but instead serve as the formal basis for user-friendly query languages that we study later We cover the rst query language, relational algebra, in great detail The relational algebra forms the basis of the widely used SQL query language We then provide overviews of the other two formal languages, the tuple relational calculus and the domain relational calculus, which are declarative query languages based on mathematical logic The domain relational calculus is the basis of the QBE query language A substantial theory exists for relational databases We study the part of this theory dealing with queries in this chapter In 7 we shall examine aspects of relational database theory that help in the design of relational database schemas, while in s 13 and 14 we discuss aspects of the theory dealing with ef cient processing of queries
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A relational database consists of a collection of tables, each of which is assigned a unique name Each table has a structure similar to that presented in 2, where we represented E-R databases by tables A row in a table represents a relationship among a set of values Since a table is a collection of such relationships, there is a close correspondence between the concept of table and the mathematical concept of
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3 Relational Model
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3
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relation, from which the relational data model takes its name In what follows, we introduce the concept of relation In this chapter, we shall be using a number of different relations to illustrate the various concepts underlying the relational data model These relations represent part of a banking enterprise They differ slightly from the tables that were used in 2, so that we can simplify our presentation We shall discuss criteria for the appropriateness of relational structures in great detail in 7
311 Basic Structure
Consider the account table of Figure 31 It has three column headers: account-number, branch-name, and balance Following the terminology of the relational model, we refer to these headers as attributes (as we did for the E-R model in 2) For each attribute, there is a set of permitted values, called the domain of that attribute For the attribute branch-name, for example, the domain is the set of all branch names Let D1 denote the set of all account numbers, D2 the set of all branch names, and D3 the set of all balances As we saw in 2, any row of account must consist of a 3-tuple (v1 , v2 , v3 ), where v1 is an account number (that is, v1 is in domain D1 ), v2 is a branch name (that is, v2 is in domain D2 ), and v3 is a balance (that is, v3 is in domain D3 ) In general, account will contain only a subset of the set of all possible rows Therefore, account is a subset of D1 D2 D3 In general, a table of n attributes must be a subset of D1 D2 Dn 1 Dn Mathematicians de ne a relation to be a subset of a Cartesian product of a list of domains This de nition corresponds almost exactly with our de nition of table The only difference is that we have assigned names to attributes, whereas mathematicians rely on numeric names, using the integer 1 to denote the attribute whose domain appears rst in the list of domains, 2 for the attribute whose domain appears second, and so on Because tables are essentially relations, we shall use the mathematical account-number A-101 A-102 A-201 A-215 A-217 A-222 A-305 Figure 31 branch-name Downtown Perryridge Brighton Mianus Brighton Redwood Round Hill balance 500 400 900 700 750 700 350
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