This is the first English language textbook offering 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 and Gröbner
bases. 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 efficient 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, detailed proofs of almost all theorems are provided, and each chapter closes with a guide to the literature.
1. Motivating examples; 2. Abstract reduction systems; 3. Universal algebra; 4. Equational problems; 5. Termination; 6. Confluence; 7. Completion; 8. Gröbner 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.