UID:
almafu_9960117027102883
Format:
1 online resource (xii, 301 pages) :
,
digital, PDF file(s).
ISBN:
1-316-04385-1
,
1-316-09875-3
,
1-139-17275-1
Content:
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, Gröbner 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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Cover -- Half Title -- Title Page -- Copyright -- Contents -- Preface -- 1 Motivating Examples -- 2 Abstract Reduction Systems -- 2.1 Equivalence and reduction -- 2.2 Well-founded induction -- 2.3 Proving termination -- 2.4 Lexicographic orders -- 2.5 Multiset orders -- 2.6 Orders in ML -- 2.7 Proving confluence -- 2.8 Bibliographic notes -- 3 Universal Algebra -- 3.1 Terms, substitutions, and identities -- 3.2 Algebras, homomorphisms, and congruences -- 3.3 Free algebras -- 3.4 Term algebras -- 3.5 Equational classes -- 4 Equational Problems -- 4.1 Deciding ≈[sub(E)] -- 4.2 Term rewriting systems -- 4.3 Congruence closure -- 4.4 Congruence closure on graphs -- 4.5 Syntactic unification -- 4.6 Unification by transformation -- 4.7 Unification and term rewriting in ML -- 4.8 Unification of term graphs -- 4.9 Bibliographic notes -- 5 Termination -- 5.1 The decision problem -- 5.2 Reduction orders -- 5.3 The interpretation method -- 5.4 Simplification orders -- 5.5 Bibliographic notes -- 6 Confluence -- 6.1 The decision problem -- 6.2 Critical pairs -- 6.3 Orthogonality -- 6.4 Beyond orthogonality -- 6.5 Bibliographic notes -- 7 Completion -- 7.1 The basic completion procedure -- 7.2 An improved completion procedure -- 7.3 Proof orders -- 7.4 Huet's completion procedure -- 7.5 Huet's completion procedure in ML -- 7.6 Bibliographic notes -- 8 Grӧbner Bases and Buchberger's Algorithm -- 8.1 The ideal membership problem -- 8.2 Polynomial reduction -- 8.3 Grӧbner bases -- 8.4 Buchberger's algorithm -- 8.5 Bibliographic notes -- 9 Combination Problems -- 9.1 Basic notions -- 9.2 Termination -- 9.3 Confluence -- 9.4 Combining word problems -- 9.5 Bibliographic notes -- 10 Equational Unification -- 10.1 Basic definitions and results -- 10.2 Commutative functions -- 10.3 Associative and commutative functions -- 10.4 Boolean rings -- 10.5 Bibliographic notes.
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11 Extensions -- 11.1 Rewriting modulo equational theories -- 11.2 Ordered rewriting -- 11.3 Conditional identities and conditional rewriting -- 11.4 Higher-order rewrite systems -- 11.5 Reduction strategies -- 11.6 Narrowing -- Appendix 1 Ordered Sets -- Appendix 2 A Bluffer's Guide to ML -- Bibliography -- Index.
,
English
Additional Edition:
ISBN 0-521-77920-0
Additional Edition:
ISBN 0-521-45520-0
Language:
English
Subjects:
Computer Science
URL:
https://doi.org/10.1017/CBO9781139172752
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