A new model-theoretic approach to universal algebra is offered in this book. Written for computer scientists, it presents a systematic development of the methods and results of universal algebra that are useful in a variety of applications in computer science. The notation is simple and the concepts are clearly presented. The book concerns the algebraic characterization of axiomatic classes of algebras (equational, implicational, and universal Horn classes) by closure operators generalizing the famous Birkhoff Variety Theorem, and the algebraic characterization of the related theories. The book also presents a thorough study of term rewriting systems. Besides basic notions, the Knuth-Bendix completion procedure and termination proof methods are considered. A third main topic is that of fixpoint techniques and complete ordered algebras. Algebraic specifications of abstract data types and algebraic semantics of recursive program schemes are treated as applications. The book is self-contained and suitable both as a textbook for graduate courses and as a reference for researchers.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Illustrationen
1 s/w Abbildung
XII, 339 p. 1 illus.
Dateigröße
ISBN-13
978-3-642-76771-5 (9783642767715)
DOI
10.1007/978-3-642-76771-5
Schweitzer Klassifikation
1 Preliminaries.- 1.1 Basic Notions.- 1.2 Generation, Structural Induction, Algebraic Recursion and Deductive Systems.- 1.3 Relations.- 1.4 Trees.- 1.5 ?-Complete Posets and Fixpoint Theorem.- 2 Reductions.- 2.1 Word Problem.- 2.2 Reduction Systems.- 3 Universal Algebra.- 3.1 Basic Constructions.- 3.2 Equationally Defined Classes of Algebras.- 3.3 Implicationally Defined Classes of Algebras.- 4 Applications.- 4.1 Algebraic Specification of Abstract Data Types.- 4.2 Algebraic Semantics of Recursive Program Schemes.- References.- Appendix 1: Sets and Classes.- Appendix 2: Ordered Algebras as First-Order Structures.
