Summary: REVIEWS 223
products and ultraproducts; the notion of a (model theoretic) type does not appear. There
is an extensive treatment of Turing machines and of recursive and recursively enumerable
sets. The incompleteness theorem is not treated; nor is there any mention of Church's thesis.
This book could serve well for a reading course with an extremely strong undergraduate or
beginning graduate student. In the United States, its best use may be as a study guide for
students preparing for a comprehensive exam in logic.
John T. Baldwin
Department of Mathematics, Statistics and Computer Science, University of Illinois at
Terese. Term rewriting systems, edited by Marc Bezem, Jan Willem Klop, and Roel de
Vrijer, Cambridge Tracts in Theoretical Computer Science, vol. 55. Cambridge Univer
sity Press, 2003, xxii + 884 pp.
Term rewriting is a fundamental concept which historically emerged out of the lambda
calculus and combinatory logic. It forms the basis of functional programming languages and
has applications in many areas of computer science and mathematics (e.g., algebraic speci
fication, implementation of programming languages, automated theorem proving, recursion
theory, computer algebra, etc.).
This book is a collaboration of leading members of the Dutch research community on term
rewriting. This community met regularly at a ``Term rewriting seminar'' at the Free University