Abstract: "This paper describes the simply-typed 2-[lambda]- calculus, a language with three levels: types, terms and rewrites. The types and terms are those of the simply-typed [lambda]-calculus, and the rewrites are expressions denoting sequences of [beta]-reductions and [eta]- expansions. An equational theory is imposed on the rewrites, based on 2- categorical justifications, and the word problem for this theory is solved by finding a canonical expression in each equivalence class. The canonical form of rewrites allows us to prove several properties of the calculus, including a strong form of confluence and a classification of the long-[beta]-[eta]-normal forms in terms of their rewrites. Finally we use these properties as the basic definitions of a theory of categorical rewriting, and find that the expected relationships between confluence, strong normalisation and normal forms hold."

This book constitutes the refereed proceedings of the 15th International Conference on Rewriting Techniques and Applications, RTA 2004, held in Aachen, Germany in June 2004.

This book constitutes the refereed proceedings of the 13th International Conference on Rewriting Techniques and Applications, RTA 2002, held in Copenhagen, Denmark, in July 2002. The 20 regular papers, two application papers, and four system descriptions presented together with three invited contributions were carefully reviewed and selected from 49 submissions. All current aspects of rewriting are addressed.

Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This 2003 book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appeared here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.

The theory and practice of term rewriting is now well-established and the focus of growing interest in the world of computer science. This book brings together a collection of original research contributions and surveys of existing knowledge. Some of the most significant developments in term rewriting theory are reviewed, as well as a history of the most important discovery in the field, namely the notion of a critical pair and its natural consequence, the completion algorithm. Many of the new ideas developed have important applications in other fields of theoretical computing. Therefore, this book should be of interest to researchers from areas such as logic programming, computer algebra, and functional programming.

Unified and self-contained introduction to term-rewriting; suited for students or professionals.

Jean-Pierre Jouannaud has played a leading role in the field of rewriting and its technology. This Festschrift volume, published to honor him on his 60th Birthday, includes 13 refereed papers by leading researchers, current and former colleagues. The papers are grouped in thematic sections on Rewriting Foundations, Proof and Computation, and a final section entitled Towards Safety and Security.