The title of this book is a misnomer; it suggests a work in recursion theory. In fact, this monograph shows how the Z and Vienna development method (VDM) specification languages, which are based on set theory, can have computable models. Turner also discusses semantic models that are based on data types, a topic widely covered in other books. (For example, Fitting’s text [1] on the subject is excellent, despite sticking to conventional first-order logic programming.)

The principal contribution of this book is the focus on specification languages rather than programming languages. Unfortunately, it lacks historical information and reads like a dry manual. Also, it only includes three examples: in chapter 10, a library database; in chapter 18, event formalism; and, in chapter 21, a treatment of reals. Furthermore, the examples are unclear and inapplicable.

Irritatingly, the same references, more or less, are repeated at the end of every chapter. There are many glaring typographic errors.

To avoid buying this long-winded book, read Turner’s paper [2] for a concise treatment of the issues. I also recommend Mitchell’s survey [3] on computable models for various features of type systems.