Semantic Domains of Natural Transformations, Completeness, and Cartesian Closedness of Categories of Domains PDF Download
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Author: Michael Huth
Publisher:
ISBN:
Category : Lambda calculus
Languages : en
Pages : 11
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Book Description
If C is a full subcategory of DCPO such that it is closed under domains of natural transformations, then C is cartesian closed and complete; if additionally C contains an isomorphic copy of the flat natural numbers, then C has a non-algebraic object."
Author: Michael Huth
Publisher:
ISBN:
Category : Lambda calculus
Languages : en
Pages : 11
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Book Description
If C is a full subcategory of DCPO such that it is closed under domains of natural transformations, then C is cartesian closed and complete; if additionally C contains an isomorphic copy of the flat natural numbers, then C has a non-algebraic object."
Author: G. Zhang
Publisher: Springer Science & Business Media
ISBN: 1461204453
Category : Computers
Languages : en
Pages : 264
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Book Description
This monograph studies the logical aspects of domains as used in de notational semantics of programming languages. Frameworks of domain logics are introduced; these serve as foundations for systematic derivations of proof systems from denotational semantics of programming languages. Any proof system so derived is guaranteed to agree with denotational se mantics in the sense that the denotation of any program coincides with the set of assertions true of it. The study focuses on two categories for dena tational semantics: SFP domains, and the less standard, but important, category of stable domains. The intended readership of this monograph includes researchers and graduate students interested in the relation between semantics of program ming languages and formal means of reasoning about programs. A basic knowledge of denotational semantics, mathematical logic, general topology, and category theory is helpful for a full understanding of the material. Part I SFP Domains Chapter 1 Introduction This chapter provides a brief exposition to domain theory, denotational se mantics, program logics, and proof systems. It discusses the importance of ideas and results on logic and topology to the understanding of the relation between denotational semantics and program logics. It also describes the motivation for the work presented by this monograph, and how that work fits into a more general program. Finally, it gives a short summary of the results of each chapter. 1. 1 Domain Theory Programming languages are languages with which to perform computa tion.
Author: Marcelo P. Fiore
Publisher: Cambridge University Press
ISBN: 9780521602778
Category : Computers
Languages : en
Pages : 260
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Book Description
First systematic account of axiomatic categorical domain theory and functional programming.
Author: Roy L. Crole
Publisher: Cambridge University Press
ISBN: 9780521457019
Category : Computers
Languages : en
Pages : 362
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Book Description
This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.
Author: Paul Taylor
Publisher: Cambridge University Press
ISBN: 9780521631075
Category : Mathematics
Languages : en
Pages : 590
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Book Description
This book is about the basis of mathematical reasoning both in pure mathematics itself (particularly algebra and topology) and in computer science (how and what it means to prove correctness of programs). It contains original material and original developments of standard material, so it is also for professional researchers, but as it deliberately transcends disciplinary boundaries and challenges many established attitudes to the foundations of mathematics, the reader is expected to be open minded about these things.
Author: Stephen Brookes
Publisher: Springer Science & Business Media
ISBN: 9783540580270
Category : Computers
Languages : en
Pages : 664
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Book Description
This volume is the proceedings of the Ninth International Conference on the Mathematical Foundations of Programming Semantics, held in New Orleans in April 1993. The focus of the conference series is the semantics of programming languages and the mathematics which supports the study of the semantics. The semantics is basically denotation. The mathematics may be classified as category theory, lattice theory, or logic. Recent conferences and workshops have increasingly emphasized applications of the semantics and mathematics. The study of the semantics develops with the mathematics and the mathematics is inspired by the applications in semantics. The volume presents current research in denotational semantics and applications of category theory, logic, and lattice theory to semantics.
Author: Benjamin C. Pierce
Publisher: MIT Press
ISBN: 9780262660716
Category : Computers
Languages : en
Pages : 126
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Book Description
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
Author: Adrian Fiech
Publisher:
ISBN:
Category : Lambda calculus
Languages : en
Pages : 12
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Book Description
If F, G: [omega] --> SCOTT are two functors such that for all f in mor([omega]) the maps F(f) preserve finite elements and G(f) preserve all non-empty infima, then F --> G is inf-faithful, and all inf-faithful domains are Scott-domains. Familiar notions like 'inverse limits', 'arbitrary products', and 'strict function spaces' are special instances of functors that meet the conditions above."
Author: Peter O'Hearn
Publisher: Springer Science & Business Media
ISBN: 9780817638801
Category : Computers
Languages : en
Pages : 302
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Book Description
In recent years there has been a remarkable convergence of interest in programming languages based on ALGOL 60. Researchers interested in the theory of procedural and object-oriented languages discovered that ALGOL 60 shows how to add procedures and object classes to simple imperative languages in a general and clean way. And, on the other hand, researchers interested in purely functional languages discovered that ALGOL 60 shows how to add imperative mechanisms to functional languages in a way that does not compromise their desirable properties. Unfortunately, many of the key works in this field have been rather hard to obtain. The primary purpose of this collection is to make the most significant material on ALGoL-like languages conveniently available to graduate students and researchers. Contents Introduction to Volume 1 1 Part I Historical Background 1 Part n Basic Principles 3 Part III Language Design 5 Introduction to Volume 2 6 Part IV Functor-Category Semantics 7 Part V Specification Logic 7 Part VI Procedures and Local Variables 8 Part vn Interference, Irreversibility and Concurrency 9 Acknowledgements 11 Bibliography 11 Introduction to Volume 1 This volume contains historical and foundational material, and works on lan guage design. All of the material should be accessible to beginning graduate students in programming languages and theoretical Computer Science.
Author: Andrew D. Gordon
Publisher: Springer Science & Business Media
ISBN: 3540008977
Category : Computers
Languages : en
Pages : 452
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Book Description
This book constitutes the refereed proceedings of the 6th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2003, held in Warsaw, Poland in April 2003. The 26 revised full papers presented together with an invited paper were carefully reviewed and selected from 96 submissions. Among the topics covered are algebraic models; automata and language theory; behavioral equivalences; categorical models; computation processes over discrete and continuous data; computation structures; logics of programs; models of concurrent, reactive, distributed, and mobile systems; process algebras and calculi; semantics of programming languages; software specification and refinement; transition systems; and type systems and type theory.
