Predicate Calculus And Program Semantics

Author : Edsger W. Dijkstra
Publisher : Springer Science & Business Media
ISBN 13 : 1461232287
Total Pages : 234 pages
Book Rating : 4.85/5 ( download)

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Download or read book Predicate Calculus and Program Semantics written by Edsger W. Dijkstra and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This booklet presents a reasonably self-contained theory of predicate trans former semantics. Predicate transformers were introduced by one of us (EWD) as a means for defining programming language semantics in a way that would directly support the systematic development of programs from their formal specifications. They met their original goal, but as time went on and program derivation became a more and more formal activity, their informal introduction and the fact that many of their properties had never been proved became more and more unsatisfactory. And so did the original exclusion of unbounded nondeterminacy. In 1982 we started to remedy these shortcomings. This little monograph is a result of that work. A possible -and even likely- criticism is that anyone sufficiently versed in lattice theory can easily derive all of our results himself. That criticism would be correct but somewhat beside the point. The first remark is that the average book on lattice theory is several times fatter (and probably less self contained) than this booklet. The second remark is that the predicate transformer semantics provided only one of the reasons for going through the pains of publication.

Author : Jan van Eijck
Publisher : Cambridge University Press
ISBN 13 : 1139490907
Total Pages : 422 pages
Book Rating : 4.00/5 ( download)

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Download or read book Computational Semantics with Functional Programming written by Jan van Eijck and published by Cambridge University Press. This book was released on 2010-09-23 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational semantics is the art and science of computing meaning in natural language. The meaning of a sentence is derived from the meanings of the individual words in it, and this process can be made so precise that it can be implemented on a computer. Designed for students of linguistics, computer science, logic and philosophy, this comprehensive text shows how to compute meaning using the functional programming language Haskell. It deals with both denotational meaning (where meaning comes from knowing the conditions of truth in situations), and operational meaning (where meaning is an instruction for performing cognitive action). Including a discussion of recent developments in logic, it will be invaluable to linguistics students wanting to apply logic to their studies, logic students wishing to learn how their subject can be applied to linguistics, and functional programmers interested in natural language processing as a new application area.

Author : Pascal Hitzler
Publisher : CRC Press
ISBN 13 : 1439829624
Total Pages : 305 pages
Book Rating : 4.22/5 ( download)

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Download or read book Mathematical Aspects of Logic Programming Semantics written by Pascal Hitzler and published by CRC Press. This book was released on 2016-04-19 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the authors' own state-of-the-art research results, this book presents a rigorous, modern account of the mathematical methods and tools required for the semantic analysis of logic programs. It significantly extends the tools and methods from traditional order theory to include nonconventional methods from mathematical analysis that depend on topology, domain theory, generalized distance functions, and associated fixed-point theory. The authors closely examine the interrelationships between various semantics as well as the integration of logic programming and connectionist systems/neural networks.

Author : Yannai A. Gonczarowski
Publisher : Cambridge University Press
ISBN 13 : 1108957692
Total Pages : 286 pages
Book Rating : 4.94/5 ( download)

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Download or read book Mathematical Logic through Python written by Yannai A. Gonczarowski and published by Cambridge University Press. This book was released on 2022-07-31 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a unique pedagogical approach, this text introduces mathematical logic by guiding students in implementing the underlying logical concepts and mathematical proofs via Python programming. This approach, tailored to the unique intuitions and strengths of the ever-growing population of programming-savvy students, brings mathematical logic into the comfort zone of these students and provides clarity that can only be achieved by a deep hands-on understanding and the satisfaction of having created working code. While the approach is unique, the text follows the same set of topics typically covered in a one-semester undergraduate course, including propositional logic and first-order predicate logic, culminating in a proof of Gödel's completeness theorem. A sneak peek to Gödel's incompleteness theorem is also provided. The textbook is accompanied by an extensive collection of programming tasks, code skeletons, and unit tests. Familiarity with proofs and basic proficiency in Python is assumed.

Author : Glynn Winskel
Publisher : MIT Press
ISBN 13 : 9780262731034
Total Pages : 388 pages
Book Rating : 4.37/5 ( download)

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Download or read book The Formal Semantics of Programming Languages written by Glynn Winskel and published by MIT Press. This book was released on 1993-02-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs. Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.

Author : Ernest G. Manes
Publisher :
ISBN 13 : 9780521420365
Total Pages : 223 pages
Book Rating : 4.69/5 ( download)

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Download or read book Predicate Transformer Semantics written by Ernest G. Manes and published by . This book was released on 1992 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a rigorous foundation for defining Boolean categories, in which the relationship between specification and behavior is explored. Boolean categories provide a rich interface between program constructs and techniques familiar from algebra, for instance matrix- or ideal-theoretic methods. The book's distinction is that the approach relies on a single program construct (the first-order theory of categories); others are derived mathematically from four axioms. Development of these axioms (which are obeyed by an abundance of program paradigms) yields Boolean algebras of "predicates" loop-free constructs, and a calculus of partial and total correctness, which is shown to be the standard one of Hoare, Dijkstra, Pratt, and Kozen.

Author : Lloyd Allison
Publisher : Cambridge University Press
ISBN 13 : 9780521314237
Total Pages : 150 pages
Book Rating : 4.32/5 ( download)

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Download or read book A Practical Introduction to Denotational Semantics written by Lloyd Allison and published by Cambridge University Press. This book was released on 1986 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basics - Notation - Lattices - A simple language - Direct semantics - Control - Data structures and data types - A prolog semantics - Miscellaneous.

Author : Simon Gay
Publisher : Cambridge University Press
ISBN 13 : 052151374X
Total Pages : 497 pages
Book Rating : 4.46/5 ( download)

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Download or read book Semantic Techniques in Quantum Computation written by Simon Gay and published by Cambridge University Press. This book was released on 2010 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores quantum computation from the perspective of the branch of theoretical computer science known as semantics.

Author : Gabriel Ciobanu
Publisher : Springer
ISBN 13 : 3540483217
Total Pages : 582 pages
Book Rating : 4.12/5 ( download)

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Download or read book Fundamentals of Computation Theory written by Gabriel Ciobanu and published by Springer. This book was released on 2003-07-31 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Symposium on Fundamentals of Computation Theory, FCT '99, held in Iasi, Romania in August/September 1999. The 42 revised full papers presented together with four invited papers were carefully selected from a total of 102 submissions. Among the topics addressed are abstract data types, algorithms and data structures, automata and formal languages, categorical and topological approaches, complexity, computational geometry, concurrency, cryptology, distributed computing, logics in computer science, process algebras, symbolic computation, molecular computing, quantum computing, etc.

Author : Uwe Schöning
Publisher : Springer Science & Business Media
ISBN 13 : 0817647635
Total Pages : 173 pages
Book Rating : 4.36/5 ( download)

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Download or read book Logic for Computer Scientists written by Uwe Schöning and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the notions and methods of formal logic from a computer science standpoint, covering propositional logic, predicate logic, and foundations of logic programming. The classic text is replete with illustrative examples and exercises. It presents applications and themes of computer science research such as resolution, automated deduction, and logic programming in a rigorous but readable way. The style and scope of the work, rounded out by the inclusion of exercises, make this an excellent textbook for an advanced undergraduate course in logic for computer scientists.