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Titlebook: Universal Algebra for Computer Scientists; Wolfgang Wechler Book 1992 Springer-Verlag Berlin Heidelberg 1992 Abstrakter Datentyp.Algebraic

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发表于 2025-3-21 19:15:23 | 显示全部楼层 |阅读模式
书目名称Universal Algebra for Computer Scientists
编辑Wolfgang Wechler
视频video
丛书名称Monographs in Theoretical Computer Science. An EATCS Series
图书封面Titlebook: Universal Algebra for Computer Scientists;  Wolfgang Wechler Book 1992 Springer-Verlag Berlin Heidelberg 1992 Abstrakter Datentyp.Algebraic
描述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.
出版日期Book 1992
关键词Abstrakter Datentyp; Algebraic Semantics; Algebraische Semantik; Algebraische Spezifikation; Fixpiont Me
版次1
doihttps://doi.org/10.1007/978-3-642-76771-5
isbn_softcover978-3-642-76773-9
isbn_ebook978-3-642-76771-5Series ISSN 1431-2654 Series E-ISSN 2193-2069
issn_series 1431-2654
copyrightSpringer-Verlag Berlin Heidelberg 1992
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发表于 2025-3-21 21:22:42 | 显示全部楼层
Applications,ption of our objects are interpreted as operations in an algebra. Semantics is then definable as a model class. However, the crucial point is that such model classes only become manageable if we are able to select “standard models”. As we shall see, free or initial algebras play this role.
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Preliminaries,re the key tool in Section 1.2. The fundamental concepts of generation, induction, recursion and deduction are based upon them. Section 1.3 deals with relations. Union, product and star of relations are called regular operations. It turns out that they are essential for our development. Furthermore,
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Universal Algebra,yntax and semantics, data abstraction, etc., are mainly investigated by methods of universal algebra. To describe, for example, the semantics of abstract data types or program schemes, algebras are generally needed as models in which all syntactic symbols involved in the considered objects are inter
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978-3-642-76773-9Springer-Verlag Berlin Heidelberg 1992
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