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Advanced Topics in Term Rewriting

  • Textbook
  • © 2002

Overview

Authors:
  1. Enno Ohlebusch

    1. Research Group in Practical Computer Science, Faculty of Technology, University of Bielefeld, Bielefeld, Germany

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  • First book on advanced topics in term rewriting
  • Covers the newest techniques for proving termination of rewrite systems
  • Contains a comprehensive chapter on conditional term rewriting systems
  • Contains a state-of-the-art survey of modularity in term rewriting
  • Presents a uniform framework for term and graph rewriting, as well as the first result on conditional graph rewriting

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Motivation

    • Enno Ohlebusch
    Pages 1-5

  3. Abstract Reduction Systems

    • Enno Ohlebusch
    Pages 7-35

  4. Term Rewriting Systems

    • Enno Ohlebusch
    Pages 37-43

  5. Confluence

    • Enno Ohlebusch
    Pages 45-56

  6. Termination

    • Enno Ohlebusch
    Pages 57-126

  7. Relative Undecidability

    • Enno Ohlebusch
    Pages 127-178

  8. Conditional Rewrite Systems

    • Enno Ohlebusch
    Pages 179-242

  9. Modularity

    • Enno Ohlebusch
    Pages 243-323

  10. Graph Rewriting

    • Enno Ohlebusch
    Pages 325-349

  11. Proving Termination of Logic Programs

    • Enno Ohlebusch
    Pages 351-377

  12. Back Matter

    Pages 379-414
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Keywords

About this book

Term rewriting techniques are applicable in various fields of computer sci­ ence: in software engineering (e.g., equationally specified abstract data types), in programming languages (e.g., functional-logic programming), in computer algebra (e.g., symbolic computations, Grabner bases), in pro­ gram verification (e.g., automatically proving termination of programs), in automated theorem proving (e.g., equational unification), and in algebra (e.g., Boolean algebra, group theory). In other words, term rewriting has applications in practical computer science, theoretical computer science, and mathematics. Roughly speaking, term rewriting techniques can suc­ cessfully be applied in areas that demand efficient methods for reasoning with equations. One of the major problems one encounters in the theory of term rewriting is the characterization of classes of rewrite systems that have a desirable property like confluence or termination. If a term rewriting system is conflu­ ent, then the normal form of a given term is unique. A terminating rewrite system does not permit infinite computations, that is, every computation starting from a term must end in a normal form. Therefore, in a system that is both terminating and confluent every computation leads to a result that is unique, regardless of the order in which the rewrite rules are applied. This book provides a comprehensive study of termination and confluence as well as related properties.

Reviews

From the reviews:

"The book Advanced Topics in Term Rewriting (ATITR) begins with an Abstract Reduction System ARS. … there are not many textbooks written in English on term rewriting. … if you like mathematics, already know the basics of term rewriting and you are a researcher or a postgraduate then this book is definitely recommended." (Nimish Shah, Journal of Functional Programming, Vol. 16 (2), 2006)

"A well-written overview of recent research with many references to the literature, and hence has clearly an added value over a collection of papers. … contains a pleasant surprise in the form of a chapter on termination of logic programs. … it can be very well used for a seminar for advanced students who already know the basics of term rewriting. … it is written in a clear and rigorous way. … I very much recommend the book for researchers and advanced students … ." (Femke van Raamsdonk, Theory and Practice of Logic Programming, Vol. 4 (4), 2004)

"The book starts with some motivating examples of Term Rewriting Systems (TRSs) (e.g. ‘coffee can problem’). … There are other books on TRSs but these are in fact introductory textbooks whereas Ohlebusch’s book covers several important fields in term rewriting that go beyond the scope of an introductory book – especially fields to which the author himself made essential contributions. In this way this monograph is an outstanding one, suitable for all Computer scientists who study and use term rewriting." (A. Widiger, Zentralblatt MATH, Vol. 999 (24), 2002)

Authors and Affiliations

  • Research Group in Practical Computer Science, Faculty of Technology, University of Bielefeld, Bielefeld, Germany

    Enno Ohlebusch

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