Ce que l’on conçoit bien, s’énonce clairement et les mots pour le dire, arrivent aisément. (What is well conceived, can be clearly expressed and the words to say it, turn up effortlessly.)
Nicolas Boileau (1636–1711)
You have reached the part of the book where the mathematical foundation laid down in the first four chapters will be applied. In particular, you’ll see how this can be applied to specify database designs.
Chapter 5 will start with some important stepping stones. We’ll familiarize you with how to formally specify a table and a database state. This chapter will also formally introduce you to the most common table operators: union, intersection, difference, projection, restriction, join, attribute renaming, extension, and aggregation.
Chapter 6 will introduce you to the concepts of tuple, table, and database predicates. We’ll use these types of predicates to specify the data integrity constraints of a database design. This chapter will also explore some predicate patterns that often play a role in database designs.
Chapter 7 builds on the previous two chapters and introduces a formal methodology to fully specify a database design. Such a specification is referred to as a database universe. This methodology was originally developed in the 1980s jointly by Bert De Brock and Frans Remmen at the Computer Science department of the Eindhoven University of Technology. We’ll define an extensive example database design using this methodology.
Chapter 8 introduces you to the concept of a transaction universe. You can use this concept to further specify the semantics of a database design. A database universe holds the majority of constraints involved in a database design: static constraints. A transaction universe allows you to specify a different class of constraints referred to as dynamic constraints; they limit the transactions allowed on grounds other than the static constraints.
Chapter 9 deals with data retrieval. By means of a query, you retrieve data from a database. We’ll introduce you to a formal way of specifying a query. This chapter will also be the first chapter that employs SQL to demonstrate the application of the mathematics introduced in this book further, by giving lots of examples.
Chapter 10 introduces a formal way of specifying a transaction. Like Chapter 9, it gives various examples to demonstrate this, both formally and by using SQL expressions.