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Reviewer: Boumediene Belkhouche

This book reflects the growing importance of denotational semantics and the increasing interest it has commanded since its introduction by Scott and Strachey. The book can be logically divided into three major components: (1) a general introduction, which includes the introduction and chapters 1 and 2; (2) a discussion of applications of denotational semantics, which includes chapters 4 and 5 and 7 through 10; and (3) the coverage of domain theory, which includes chapters 3, 6, 11, and 12. The first part provides a brief overview of approaches to syntax and formal semantics and a review of set and function concepts usually covered in a discrete mathematics course. The material presented is elementary, and seems to be included only to serve the need for a self-contained textbook. The book's main theme is treated in the second part. The author's presentation of denotational semantics follows what he calls an “engineering viewpoint,” which is similar to approaches used to teach applications of mathematics to engineering students. That is, the emphasis is on how to construct semantic definitions. First, a specific format to be used in denotational definitions is described and adopted throughout the book. The format consists of an abstract syntax section to describe the syntactic domains and constructs, a semantic algebra section to describe the semantic domain in terms of abstract data types (cf. algebraic approach), and a valuation functions section to describe the semantics of each syntactic class. The format thus provides a logical structure and a modularization mechanism for constructing semantic specifications. Several examples of semantic definitions are used to illustrate the author's approach. These examples are gradually augmented to cover the spectrum of fundamental concepts in programming languages. The third part is devoted to the theory underlying denotational semantics. The introduction to domain theory is fairly basic; nonetheless, this is the first textbook that systematically covers the theory and practice behind denotational semantics. The organization of the book is highly pedagogical. Each chapter includes numerous exercises and an extensive list of suggested readings. I think that this book is a good addition to the area of formal semantics. It can be used effectively as a textbook to introduce denotational semantics to college seniors.