Type Inheritance and Relational Theory

Chapter 4

The Inheritance Model

O England! model to thy inward greatness,

Like little body with a mighty heart,

What mightst thou do, that honour would thee do,

Were all thy children kind and natural!

—William Shakespeare:King Henry the Fifth (1598-1599)

This chapter provides, for purposes of subsequent reference, a precise statement of the 28 IM prescriptions that make up our inheritance model. It’s based on Chapter 19 of the book Database Explorations: Essays on The Third Manifesto and Related Topics, by Hugh Darwen and myself (available free online at the website www.thethirdmanifesto.com). However, I’ve found it necessary, or at least convenient, to perform a certain amount of revision on some of the prescriptions, as will be made clear in subsequent chapters. I’ve also added two new ones (numbers 23 and 26, according to the numbering below). Note: Whenever there’s a technical discrepancy between the present chapter—or anything else in this book, come to that—and previous publications by Darwen and myself on this topic, the present text should be taken as superseding. At the same time, please note that it’s my intention that any such discrepancies be called out explicitly and justified.

Throughout this chapter, as well as elsewhere in this book, I use the symbols T and T′ as generic names for a pair of types such that T′ is a subtype of T (equivalently, such that T is a supertype of T′). You might find it helpful to think of T and T′ as ELLIPSE and CIRCLE, respectively; however, ...