java aztec barcode library INTRODUCTION TO THE RELATIONAL MODEL in Software

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INTRODUCTION TO THE RELATIONAL MODEL
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The main construct for representing data in the relational model is a relation A relation consists of a relation schema and a relation instance The relation instance
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The Relational Model
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is a table, and the relation schema describes the column heads for the table We rst describe the relation schema and then the relation instance The schema speci es the relation s name, the name of each eld (or column, or attribute), and the domain of each eld A domain is referred to in a relation schema by the domain name and has a set of associated values We use the example of student information in a university database from 1 to illustrate the parts of a relation schema: Students(sid: string, name: string, login: string, age: integer, gpa: real) This says, for instance, that the eld named sid has a domain named string The set of values associated with domain string is the set of all character strings We now turn to the instances of a relation An instance of a relation is a set of tuples, also called records, in which each tuple has the same number of elds as the relation schema A relation instance can be thought of as a table in which each tuple is a row, and all rows have the same number of elds (The term relation instance is often abbreviated to just relation, when there is no confusion with other aspects of a relation such as its schema) An instance of the Students relation appears in Figure 31 The instance S1 contains
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FIELDS (ATTRIBUTES, COLUMNS) Field names
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name
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login dave@cs jones@cs smith@ee smith@math guldu@music
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age 19 18 18 19 11 12
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gpa 33 34 32 38 18 20
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50000 Dave 53666 Jones TUPLES (RECORDS, ROWS) 53688 Smith 53650 Smith 53832 Guldu
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53831 Madayan madayan@music
An Instance S1 of the Students Relation
six tuples and has, as we expect from the schema, ve elds Note that no two rows are identical This is a requirement of the relational model each relation is de ned to be a set of unique tuples or rows1 The order in which the rows are listed is not important Figure 32 shows the same relation instance If the elds are named, as in
practice, commercial systems allow tables to have duplicate rows, but we will assume that a relation is indeed a set of tuples unless otherwise noted
1 In
3
sid 53831 53832 53688 53650 53666 50000
name Madayan Guldu Smith Smith Jones Dave
login madayan@music guldu@music smith@ee smith@math jones@cs dave@cs
age 11 12 18 19 18 19
gpa 18 20 32 38 34 33
An Alternative Representation of Instance S1 of Students
our schema de nitions and gures depicting relation instances, the order of elds does not matter either However, an alternative convention is to list elds in a speci c order and to refer to a eld by its position Thus sid is eld 1 of Students, login is eld 3, and so on If this convention is used, the order of elds is signi cant Most database systems use a combination of these conventions For example, in SQL the named elds convention is used in statements that retrieve tuples, and the ordered elds convention is commonly used when inserting tuples A relation schema speci es the domain of each eld or column in the relation instance These domain constraints in the schema specify an important condition that we want each instance of the relation to satisfy: The values that appear in a column must be drawn from the domain associated with that column Thus, the domain of a eld is essentially the type of that eld, in programming language terms, and restricts the values that can appear in the eld More formally, let R(f1 :D1, , fn :Dn) be a relation schema, and for each fi , 1 i n, let Domi be the set of values associated with the domain named Di An instance of R that satis es the domain constraints in the schema is a set of tuples with n elds: { f1 : d1 , , fn : dn | d1 Dom1 , , dn Domn }
The angular brackets identify the elds of a tuple Using this notation, the rst Students tuple shown in Figure 31 is written as sid: 50000, name: Dave, login: dave@cs, age: 19, gpa: 33 The curly brackets { } denote a set (of tuples, in this de nition) The vertical bar | should be read such that, the symbol should be read in, and the expression to the right of the vertical bar is a condition that must be satis ed by the eld values of each tuple in the set Thus, an instance of R is de ned as a set of tuples The elds of each tuple must correspond to the elds in the relation schema Domain constraints are so fundamental in the relational model that we will henceforth consider only relation instances that satisfy them; therefore, relation instance means relation instance that satis es the domain constraints in the relation schema
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