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Titlebook: Iteration Theories; The Equational Logic Stephen L. Bloom,Zoltán Ésik Book 1993 Springer-Verlag Berlin Heidelberg 1993 Algebraische Semanti

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书目名称Iteration Theories
副标题The Equational Logic
编辑Stephen L. Bloom,Zoltán Ésik
视频video
丛书名称Monographs in Theoretical Computer Science. An EATCS Series
图书封面Titlebook: Iteration Theories; The Equational Logic Stephen L. Bloom,Zoltán Ésik Book 1993 Springer-Verlag Berlin Heidelberg 1993 Algebraische Semanti
描述This monograph contains the results of our joint research over the last ten years on the logic of the fixed point operation. The intended au­ dience consists of graduate students and research scientists interested in mathematical treatments of semantics. We assume the reader has a good mathematical background, although we provide some prelimi­ nary facts in Chapter 1. Written both for graduate students and research scientists in theoret­ ical computer science and mathematics, the book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have been used as semantical models, the equational properties of the fixed point operation are cap­ tured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and in­ finitary regular languages, trees, synchronization trees,
出版日期Book 1993
关键词Algebraische Semantik; Fixed Point Theory; Fixpunkttheorie; Iteration; Notation; Programming Languages; al
版次1
doihttps://doi.org/10.1007/978-3-642-78034-9
isbn_softcover978-3-642-78036-3
isbn_ebook978-3-642-78034-9Series ISSN 1431-2654 Series E-ISSN 2193-2069
issn_series 1431-2654
copyrightSpringer-Verlag Berlin Heidelberg 1993
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Theory Facts,In this chapter we collect some technical results about the category . of theories, as well as document some observations which will be used frequently in later chapters. In the last section, we introduce the concept of a 2-theory.
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Iterative Theories,In this chapter, we define both ideal and iterative theories. The main definitions are in Sections 1 and 2. Section 3 has a more technical nature, and most details may be omitted at first reading. However, the results of Section 3 will be applied in later sections.
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Iteration Theories,Iteration theories are a generalization of iterative theories. In iteration theories, the dagger operation can be applied to all morphisms .: . → . + ., producing a canonical solution of the iteration equation for .. The properties of iteration are captured equationally.
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Floyd-Hoare Logic,Suppose that .: . → . is a partial function on a set ., where we might think of . as a set of “states” of a machine. If α and β are predicates on ., i.e. total maps . → {TRUE, FALSE}, . {.} . {.}, pca for short, means ..
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Monographs in Theoretical Computer Science. An EATCS Serieshttp://image.papertrans.cn/i/image/476559.jpg
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https://doi.org/10.1007/978-3-642-78034-9Algebraische Semantik; Fixed Point Theory; Fixpunkttheorie; Iteration; Notation; Programming Languages; al
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