Term Rewriting and All ThatThis textbook offers a unified, self-contained introduction to the field of term rewriting. Baader and Nipkow cover 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. They present the main algorithms both informally and as programs in the functional language Standard ML (An appendix contains a quick and easy introduction to ML). Key chapters cover crucial algorithms such as unification and congruence closure in more depth and develop efficient Pascal programs. The book contains many examples and over 170 exercises. This is also an ideal reference book for professional researchers: results spread over many conference and journal articles are collected here in a unified notation, detailed proofs of almost all theorems are provided, and each chapter closes with a guide to the literature. |
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Contents
II | 1 |
III | 7 |
IV | 13 |
V | 16 |
VI | 18 |
VII | 21 |
VIII | 26 |
IX | 28 |
XXXV | 160 |
XXXVI | 164 |
XXXVII | 172 |
XXXVIII | 178 |
XXXIX | 182 |
XL | 184 |
XLI | 187 |
XLII | 189 |
X | 33 |
XI | 34 |
XII | 47 |
XIII | 49 |
XIV | 58 |
XV | 59 |
XVI | 61 |
XVII | 62 |
XVIII | 65 |
XIX | 71 |
XX | 73 |
XXI | 79 |
XXII | 82 |
XXIII | 91 |
XXIV | 93 |
XXV | 101 |
XXVI | 104 |
XXVII | 111 |
XXVIII | 131 |
XXIX | 134 |
XXX | 135 |
XXXI | 145 |
XXXII | 151 |
XXXIII | 157 |
XXXIV | 158 |
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Common terms and phrases
addition algebra algorithm applied arbitrary assume basic C-unification called closed closure collapsing completion completion procedure computation confluent congruence consequence consider constants contains corresponding critical pairs decidable decision defined definition denote direction easy elements equational equivalent example Exercise exists extended fact finite function symbols given ground hence holds homomorphism identities implementation implies induction infinite instance integer interpretation Lemma length lexicographic linear mapping means minimal monomial multiset nodes normal form Note obtained Obviously occurs orthogonal polynomial position problem programming proof prove reduction reduction order relation replaced requires result rules satisfies sequence shown signature solution solved step strict substitution subterm syntactic term rewriting system termination Theorem theory transitive trivial true turn unification unifier variables write yields
References to this book
Software Engineering with OBJ: Algebraic Specification in Action Joseph A. Goguen,Grant Malcolm No preview available - 2000 |
Isabelle/HOL: A Proof Assistant for Higher-Order Logic Tobias Nipkow,Lawrence C. Paulson,Markus Wenzel No preview available - 2002 |
Bibliographic information
| Title | Term Rewriting and All That Term Rewriting and All that, Tobias Nipkow |
| Authors | Franz Baader, Tobias Nipkow |
| Edition | illustrated, reprint, revised |
| Publisher | Cambridge University Press, 1999 |
| ISBN | 0521779200, 9780521779203 |
| Length | 301 pages |
| Subjects | › › Computers / Programming / Algorithms Computers / Programming Languages / General Computers / Software Development & Engineering / General Mathematics / Discrete Mathematics |
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