Domain-Theoretic Foundations of Functional Programming

Domain-Theoretic Foundations of Functional Programming PDF

Author: Thomas Streicher

Publisher: World Scientific Publishing Company

Published: 2006-12-04

Total Pages: 132

ISBN-13: 9813106867

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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.

Logical Foundations of Functional Programming

Logical Foundations of Functional Programming PDF

Author: Gérard Huet

Publisher: Addison Wesley Publishing Company

Published: 1990

Total Pages: 520

ISBN-13:

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Looks at the new partnerships between public officials and private entrepreneurs that have helped revitalize the downtown areas of many American cities, and presents studies of big-city malls in Boston, St. Paul, Seattle, and San Diego.

Programming Language Foundations

Programming Language Foundations PDF

Author: Aaron Stump

Publisher: John Wiley & Sons

Published: 2013-09-23

Total Pages: 144

ISBN-13: 1118007476

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Stump’s Programming Language Foundations is a short concise text that covers semantics, equally weighting operational and denotational semantics for several different programming paradigms: imperative, concurrent, and functional. Programming Language Foundations provides: an even coverage of denotational, operational an axiomatic semantics; extensions to concurrent and non-deterministic versions; operational semantics for untyped lambda calculus; functional programming; type systems; and coverage of emerging topics and modern research directions.

The Formal Semantics of Programming Languages

The Formal Semantics of Programming Languages PDF

Author: Glynn Winskel

Publisher: MIT Press

Published: 1993-02-05

Total Pages: 388

ISBN-13: 9780262731034

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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.

Basic Category Theory for Computer Scientists

Basic Category Theory for Computer Scientists PDF

Author: Benjamin C. Pierce

Publisher: MIT Press

Published: 1991-08-07

Total Pages: 117

ISBN-13: 0262326450

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Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading

Logic and Theory of Algorithms

Logic and Theory of Algorithms PDF

Author: Arnold Beckmann

Publisher: Springer

Published: 2008-06-11

Total Pages: 613

ISBN-13: 3540694072

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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.

Foundations of Logic and Functional Programming

Foundations of Logic and Functional Programming PDF

Author: Mauro Boscarol

Publisher: Springer Science & Business Media

Published: 1988-04-27

Total Pages: 228

ISBN-13: 9783540191292

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This volume consists of some of the papers that were delivered during the workshop on "Foundations of Logic and Functional Programming" held in Trento, Italy, from December 15th to 19th, 1986. The meeting centered on themes and trends in Functional Programming and in Logic Programming. This book contains five papers contributed by the invited speakers and five selected contributions.

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