Domain-theoretic Foundations Of Functional Programming PDF Download
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Author: Thomas Streicher
Publisher: World Scientific Publishing Company
ISBN: 9813106867
Category : Computers
Languages : en
Pages : 132
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Book Description
This textbook provides a basis for a PhD course on domain-theoretic semantics of functional programming languages and their meta-mathematical properties. It introduces basic domain theory and the technique of logical relations as developed by Scott and Plotkin. The solution of recursive domain equations is explained in detail.A complete discussion of the famous full abstraction problem for PCF (a functional Kernel language due to Scott and Plotkin) is given including a construction of the fully abstract Milner model using Kripke logical relations.A final chapter introduces computability in Scott domains and shows that this model is fully abstract and universal for appropriate extensions of PCF by parallel language constructs.
Author: Thomas Streicher
Publisher: World Scientific Publishing Company
ISBN: 9813106867
Category : Computers
Languages : en
Pages : 132
Get Book Here
Book Description
This textbook provides a basis for a PhD course on domain-theoretic semantics of functional programming languages and their meta-mathematical properties. It introduces basic domain theory and the technique of logical relations as developed by Scott and Plotkin. The solution of recursive domain equations is explained in detail.A complete discussion of the famous full abstraction problem for PCF (a functional Kernel language due to Scott and Plotkin) is given including a construction of the fully abstract Milner model using Kripke logical relations.A final chapter introduces computability in Scott domains and shows that this model is fully abstract and universal for appropriate extensions of PCF by parallel language constructs.
Author: Glynn Winskel
Publisher: MIT Press
ISBN: 9780262731034
Category : Computers
Languages : en
Pages : 388
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Book Description
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: Greg Michaelson
Publisher: Courier Corporation
ISBN: 0486280292
Category : Mathematics
Languages : en
Pages : 338
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Book Description
Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.
Author: Arnold Beckmann
Publisher: Springer
ISBN: 3540694072
Category : Computers
Languages : en
Pages : 613
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Book Description
CiE 2008: Logic and Theory of Algorithms Athens, Greece, June 15–20, 2008 Computability in Europe (CiE) is an informal network of European scientists working on computability theory, including its foundations, technical devel- ment, and applications. Among the aims of the network is to advance our t- oretical understanding of what can and cannot be computed, by any means of computation. Its scienti?c vision is broad: computations may be performed with discrete or continuous data by all kinds of algorithms, programs, and - chines. Computations may be made by experimenting with any sort of physical system obeying the laws of a physical theory such as Newtonian mechanics, quantum theory, or relativity. Computations may be very general, depending on the foundations of set theory; or very speci?c, using the combinatorics of ?nite structures. CiE also works on subjects intimately related to computation, especially theories of data and information, and methods for formal reasoning about computations. The sources of new ideas and methods include practical developments in areas such as neural networks, quantum computation, natural computation, molecular computation, computational learning. Applications are everywhere,especially, in algebra,analysisand geometry, or data types and p- gramming. Within CiE there is general recognition of the underlying relevance of computability to physics and a broad range of other sciences, providing as it does a basic analysis of the causal structure of dynamical systems. Thisvolume,Logic andTheory of Algorithms,istheproceedingsofthefourth in a series of conferences of CiE that was held at the University of Athens, June 15–20, 2008.
Author: Jean Goubault-Larrecq
Publisher: Cambridge University Press
ISBN: 1107328772
Category : Mathematics
Languages : en
Pages : 499
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Book Description
This unique book on modern topology looks well beyond traditional treatises and explores spaces that may, but need not, be Hausdorff. This is essential for domain theory, the cornerstone of semantics of computer languages, where the Scott topology is almost never Hausdorff. For the first time in a single volume, this book covers basic material on metric and topological spaces, advanced material on complete partial orders, Stone duality, stable compactness, quasi-metric spaces and much more. An early chapter on metric spaces serves as an invitation to the topic (continuity, limits, compactness, completeness) and forms a complete introductory course by itself. Graduate students and researchers alike will enjoy exploring this treasure trove of results. Full proofs are given, as well as motivating ideas, clear explanations, illuminating examples, application exercises and some more challenging problems for more advanced readers.
Author: John Longley
Publisher: Springer
ISBN: 3662479923
Category : Computers
Languages : en
Pages : 587
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Book Description
This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers
Author: M. Broy
Publisher: Springer Science & Business Media
ISBN: 9400978936
Category : Mathematics
Languages : en
Pages : 655
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Book Description
Papers presented at the Marktoberdorf Summer School on Theoretical Foundations of Programming Methodology, organized under the auspices of the Technical University Münich and sponsored by the NATO Scientific Affairs Division, Germany, 1981
Author: Manindra Agrawal
Publisher: Springer Science & Business Media
ISBN: 3540792279
Category : Computers
Languages : en
Pages : 610
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Book Description
This book constitutes the refereed proceedings of the 5th International Conference on Theory and Applications of Models of Computation, TAMC 2008, held in Xi'an, China in April 2008. The 48 revised full papers presented together with 2 invited talks and 1 plenary lecture were carefully reviewed and selected from 192 submissions. The papers address current issues of all major areas in computer science, mathematics (especially logic) and the physical sciences - computation, algorithms, complexity and computability theory in particular. With this crossdisciplinary character the conference is given a special flavor and distinction.
Author: Bor-Yuh Evan Chang
Publisher: Springer
ISBN: 3319712373
Category : Computers
Languages : en
Pages : 559
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Book Description
This book constitutes the proceedings of the 15th Asian Symposium on Programming Languages and Systems, APLAS 2017, held in Suzhou, China, in November 2017. The 24 papers presented in this volume were carefully reviewed and selected from 56 submissions. They were organized in topical sections named: security; heap and equivalence reasoning; concurrency and verification; domain-specific languages; semantics; and numerical reasoning. The volume also contains two invited talks in full-paper length.
Author: Luke Ong
Publisher: Springer Science & Business Media
ISBN: 3642120318
Category : Computers
Languages : en
Pages : 402
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Book Description
This book constitutes the refereed proceedings of the 13th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2010, held in Paphos, Cyprus, in March 2010, as part of ETAPS 2010, the European Joint Conferences on Theory and Practice of Software. The 25 revised full papers presented together with the abstract of the keynote lecture were carefully reviewed and selected from 86 full paper submissions. The papers are organized in topical sections on semantics of programming languages, probabilistic and randomised computation, concurrency and process theory, modal and temporal logics, verification, categorical and coalgebraic methods, as well as lambda calculus and types.
