An Introduction to Relational Database Theory

HUGH DARWEN

AN INTRODUCTION TO RELATIONAL DATABASE THEORY

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Hugh Darwen

An Introduction to Relational Database Theory

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An Introduction to Relational Database Theory © 2010 Hugh Darwen & Ventus Publishing ApS ISBN 978-87-7681-500-4

This book is dedicated to the researchers at IBM United Kingdom’s Scientific Research Centre, Peterlee, UK, in the 1970s, who designed and implemented the relational database language, ISBL, that has been my guide ever since.

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An Introduction to Relational Database Theory

Contents

Contents

Preface

10

1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14

Introduction Introduction What Is a Database? “Organized Collection of Symbols” “To Be Interpreted as a True Account” “Collection of Variables” What Is a Relational Database? “Relation” Not Equal to “Table” Anatomy of a Relation What Is a DBMS? What Is a Database Language? What Does a DBMS Do? Creating and Destroying Variables Taking Note of Integrity Rules Taking Note of Authorisations

14 14 14 15 16 17 18 19 21 22 23 23 24 26 27

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An Introduction to Relational Database Theory

Contents

Updating Variables Providing Results of Queries EXERCISE

27 30 32

2. 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13

Values, Types, Variables, Operators Introduction Anatomy of A Command Important Distinctions A Closer Look at a Read-Only Operator (+) Read-only Operators in Tutorial D What Is a Type? What Is a Type Used For? The Type of a Relation Relation Literals Types and Representations What Is a Variable? Updating a Variable Conclusion EXERCISES Getting Started with Rel

33 33 33 36 37 37 40 42 42 43 47 49 50 52 54 55

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1.15 1.16

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An Introduction to Relational Database Theory

Contents

Predicates and Propositions Introduction What Is a Predicate? Substitution and Instantiation How a Relation Represents an Extension Deriving Predicates from Predicates EXERCISES

63 63 63 68 69 75 84

4. 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10

Relational Algebra – The Foundation Introduction Relations and Predicates Relational Operators and Logical Operators JOIN and AND RENAME Projection and Existential Quantification Restriction and AND Extension and AND UNION and OR Semidifference and NOT

85 85 88 89 90 93 97 103 106 108 111

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3. 3.1 3.2 3.3 3.4 3.5

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An Introduction to Relational Database Theory

Contents

4.11

Concluding Remarks EXERCISES Working with a Database in Rel

114 115 117

5. 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

Building on The Foundation Introduction Semijoin and Composition Aggregate Operators Relations within a Relation Using Aggregate Operators with Nested Relations SUMMARIZE GROUP and UNGROUP WRAP and UNWRAP

120 120 121 125 129 131 132 135 139

5.9 5.10

Relation Comparison Other Operators on Relations and Tuples EXERCISES

141 146 148

6. 6.1 6.2

Constraints and Updating Introduction A Closer Look at Constraints and Consistency

150 150 151

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An Introduction to Relational Database Theory

Contents

6.3 6.4 6.5

Expressing Constraint Conditions Useful Shorthands for Expressing Constraints Updating Relvars EXERCISES

152 159 165 172

7. 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9

Database Design I: Projection-Join Normalization Introduction Avoiding Redundancy Join Dependencies Fifth Normal Form Functional Dependencies Keys The Role of FDs and Keys in Optimization Boyce-Codd Normal Form (BCNF) JDs Not Arising from FDs EXERCISES

173 173 173 175 183 188 193 194 195 203 208

8. 8.1

Database Design II: Other Issues Group-Ungroup and Wrap-Unwrap Normalization

211 211



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678' to the left of the menu on the input (lower) pane. These are greyed out initially but after you have executed a couple of statements you will be able to use them to recall previously executed statements to the input pane. Note the toolbars on both panes. As you do the exercises, decide which options suit you best. Note that you can save the contents of either pane into a local file, and that you can load the contents of a local file into the input area. Note the check boxes on the right of the toolbars. They are fairly self-explanatory, apart from “Enhanced”, which we will examine later. The box at the top of the upper pane, labelled “Location:”, identifies the directory containing the database you are working with. You can switch to another directory by clicking on the little button to the right of the box, labelled with three dots (…).

3. Type the following into the lower pane: output 2+2 ; Execute what you have typed, either by clicking on Evaluate (F5) shown at the bottom of the window or by pressing F5. Now delete the semicolon and try executing what remains. (If necessary, use the < button on the lower pane to recall the statement.) You will see how Rel handles errors.



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