Term Rewriting and All That
This textbook offers a unified and self-contained introduction to the field of term rewriting. It covers all the basic material (abstract reduction systems, termination, confluence, completion, and combination problems), but also some important and closely connected subjects: universal algebra, unification theory, Grobner bases and Buchberger's algorithm. The main algorithms are presented both informally and as programs in the functional language Standard ML (an appendix contains a quick and easy introduction to ML). Certain crucial algorithms like unification and congruence closure are covered in more depth and Pascal programs are developed. The book contains many examples and over 170 exercises. This text is also an ideal reference book for professional researchers: results that have been spread over many conference and journal articles are collected together in a unified notation, proofs of almost all theorems are provided, and each chapter closes with a guide to the literature.
- Online resource
- 05 Jun 2012
- Cambridge University Press (Virtual Publishing)
- Cambridge, United Kingdom
'... a welcome and important addition to the library of any researcher interested in theoretical computer science. It provides a thorough grounding in the subject in a clear style, and gives plenty of indications of further directions, including an extensive bibliography'. The Computer Journal '... a well-balanced textbook ... presenting the subject in a unified and systematic manner.' H. Herre, Zentralblatt MATH '... a highly welcome addition to the literature on term rewriting ... It is very readable, well written and likeable book. it should be of great value to students and researchers alike.' Jan Willem Klop, Journal of Functioning Programming
Table of contents
Preface; 1. Motivating examples; 2. Abstract reduction systems; 3. Universal algebra; 4. Equational problems; 5. Termination; 6. Confluence; 7. Completion; 8. Grobner bases and Buchberger's algorithm; 9. Combination problems; 10. Equational unification; 11. Extensions; Appendix 1. Ordered sets; Appendix 2. A bluffer's guide to ML; Bibliography; Index.