Universal algebra for computer scientists. (English) Zbl 0748.68002

Wechler, Wolfgang

EATCS Monographs on Theoretical Computer Science. 25. Berlin etc.: Springer-Verlag. X, 339 p. (1992).

This book is a beautiful introductory text into universal algebra with emphasis on applications in computer science.
Chapter 1 covers induction, recursion, algebras, terms, relations, trees and posets. In chapter 2 we find the fundamentals about word problems and reduction systems. The third chapter introduces the basic notions of universal algebra and culminates in the proofs of various Birkhoff-type theorems for equational theories, implicational theories and universal horn theories. The final chapter covers algebraic specifications and algebraic semantics. Here the extensions of one-sorted algebras to many sorted algebras and to ordered algebras is given. The book closes with an extensive list of references, two appendices about sets and ordered algebras and a useful subject index.
The book is clearly written and will help the computer scientist to find his way through universal algebras. Obviously it is not designed for the mathematician trying the specialize in universal algebra, since it merely focusses on these subjects relevant to the computer scientist.

Reviewer: H.Werner (Berlin)

MSC:

68-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science
08-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to general algebraic systems
68Q65	Abstract data types; algebraic specification
68Q55	Semantics in the theory of computing
68Q99	Theory of computing

Keywords:

algebras; relations; posets; reduction systems; algebraic specifications; algebraic semantics