Universal Algebra for Computer Scientists

Softcover Nachdruck of the original 1. Auflage 1992
ISBN: 978-3-642-76773-9
Verlag: Springer

Buch, Englisch, Band 25, 339 Seiten, Paperback, Format (B × H): 170 mm x 242 mm, Gewicht: 610 g

Reihe: Monographs in Theoretical Computer Science. An EATCS Series

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.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Wechler, Wolfgang

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Software Engineering

Inhaltsverzeichnis

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.