An Introduction to Relational Database Theory

This book introduces you to the theory of relational databases, focusing on the application of that theory to the design of computer languages that properly embrace it. The book is intended for those studying relational databases as part of a degree course in Information Technology (IT). Relational database theory, originally proposed by Edgar F. Codd in 1969, is a topic in Computer Science. Codd’s seminal paper (1970) was entitled A Relational Model of Data for Large Shared Data Banks (reference [5] in Appendix B).

An introductory course on relational databases offered by a university’s Computer Science (or similarly named) department is typically broadly divided into a theory component and what we might call an “industrial” component. The “industrial” component typically teaches the language, SQL (Structured Query Language ), that is widely used in the industry for database purposes, and it might also teach other topics of current significance in the industry. Although this book is only about the theory, I hope it will be interesting and helpful to you even if your course’s main thrust is industrial.

1. Introduction
   1. Introduction
   2. What Is a Database?
   3. “Organized Collection of Symbols”
   4. “To Be Interpreted as a True Account”
   5. “Collection of Variables”
   6. What Is a Relational Database?
   7. “Relation” Not Equal to “Table”
   8. Anatomy of a Relation
   9. What Is a DBMS?
   10. What Is a Database Language?
   11. What Does a DBMS Do?
   12. Creating and Destroying Variables
   13. Taking Note of Integrity Rules
   14. Taking Note of Authorisations
   15. Updating Variables
   16. Providing Results of Queries
2. Values, Types, Variables, Operators
   1. Introduction
   2. Anatomy of A Command
   3. Important Distinctions
   4. A Closer Look at a Read-Only Operator (+)
   5. Read-only Operators in Tutorial D
   6. What Is a Type?
   7. What Is a Type Used For?
   8. The Type of a Relation
   9. Relation Literals
   10. Types and Representations
   11. What Is a Variable?
   12. Updating a Variable
   13. Conclusion
3. Predicates and Propositions
   1. Introduction
   2. What Is a Predicate?
   3. Substitution and Instantiation
   4. How a Relation Represents an Extension
   5. Deriving Predicates from Predicates
4. Relational Algebra—The Foundation
   1. Introduction
   2. Relations and Predicates
   3. Relational Operators and Logical Operators
   4. JOIN and AND
   5. RENAME
   6. Projection and Existential Quantification
   7. Restriction and AND
   8. Extension and AND
   9. UNION and OR
   10. Semidifference and NOT
   11. Concluding Remarks
5. Building on The Foundation
   1. Introduction
   2. Semijoin and Composition
   3. Aggregate Operators
   4. Relations within a Relation
   5. Using Aggregate Operators with Nested Relations
   6. SUMMARIZE
   7. GROUP and UNGROUP
   8. WRAP and UNWRAP
   9. Relation Comparison
   10. Other Operators on Relations and Tuples
6. Constraints and Updating
   1. Introduction
   2. A Closer Look at Constraints and Consistency
   3. Expressing Constraint Conditions
   4. Useful Shorthands for Expressing Constraints
   5. Updating Relvars
7. Database Design I: Projection-Join Normalization
   1. Introduction
   2. Avoiding Redundancy
   3. Join Dependencies
   4. Fifth Normal Form
   5. Functional Dependencies
   6. Keys
   7. The Role of FDs and Keys in Optimization
   8. Boyce-Codd Normal Form (BCNF)
   9. JDs Not Arising from FDs
8. Database Design II: Other Issues
   1. Group-Ungroup and Wrap-Unwrap Normalization
   2. Restriction-Union Normalization
   3. Surrogate Keys
   4. Representing “Entity Subtypes”