Axiomatic Domain Theory In Categories Of Partial Maps

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Axiomatic Domain Theory In Categories Of Partial Maps

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Author : Marcelo P. Fiore
language : en
Publisher: Cambridge University Press
Release Date : 2004-03-25

Axiomatic Domain Theory In Categories Of Partial Maps written by Marcelo P. Fiore and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-25 with Computers categories.

First systematic account of axiomatic categorical domain theory and functional programming.

Axiomatic Domain Theory In Categories Of Partial Maps

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Author : Marcelo Pablo Fiore
language : en
Publisher:
Release Date : 1994

Axiomatic Domain Theory In Categories Of Partial Maps written by Marcelo Pablo Fiore and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Axiomatic set theory categories.

This thesis is an investigation into axiomatic categorical domain theory as needed for the denotational semantics of deterministic programming languages. To provide a direct semantic treatment of non-terminating computations, we make partiality the core of our theory. Thus, we focus on categories of partial maps. We study representability of partial maps and show its equivalence with classifiability. We observe that, once partiality is taken as primitive, a notion of approximation may be derived. In fact, two notions of approximation, contextual approximation and specialisation, based on testing and observing partial maps are considered and shown to coincide. Further we characterise when the approximation relation between partial maps is domain-theoretic in the (technical) sense that the category of partial maps Cpo-enriches with respect to it. Concerning the semantics of type constructors in categories of partial maps, we present a characterisation of colimits of diagrams of total maps; study order-enriched partial cartesian closure; and provide conditions to guarantee the existence of the limits needed to solve recursive type equations. Concerning the semantics of recursive types, we motivate the study of enriched algebraic compactness and make it the central concept when interpreting recursive types. We establish the fundamental property of algebraically compact categories, namely that recursive types on them admit canonical interpretations, and show that in algebraically compact categories recursive types reduce to inductive types. Special attention is paid to Cpo-algebraic compactness, leading to the identification of a 2-category of kinds with very strong closure properties. As an application of the theory developed, enriched categorical models of the metalanguage FPC (a type theory with sums, products, exponentials and recursive types) are defined and two abstract examples of models, including domain-theoretic models, are axiomatised. Further, FPC is considered as a programming language with a call-by-value operational semantics and a denotational semantics defined on top of a categorical model. Operational and denotational semantics are related via a computational soundness result. The interpretation of FPC expressions in domain-theoretic Poset-models is observed to be representation-independent. And, to culminate, a computational adequacy result for an axiomatisation of absolute non-trivial domain-theoretic models is proved.

Category Theory And Computer Science

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Author : Eugenio Moggi
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-08-20

Category Theory And Computer Science written by Eugenio Moggi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-20 with Computers categories.

This book constitutes the refereed proceedings of the 7th International Conference on Category Theory and Computer Science, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997. Category theory attracts interest in the theoretical computer science community because of its ability to establish connections between different areas in computer science and mathematics and to provide a few generic principles for organizing mathematical theories. This book presents a selection of 15 revised full papers together with three invited contributions. The topics addressed include reasoning principles for types, rewriting, program semantics, and structuring of logical systems.

Logical Approaches To Computational Barriers

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Author : Arnold Beckmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-26

Logical Approaches To Computational Barriers written by Arnold Beckmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-26 with Computers categories.

This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.

Typed Lambda Calculi And Applications

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Author : Philippe de Groote
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-03-12

Typed Lambda Calculi And Applications written by Philippe de Groote and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-12 with Computers categories.

This book constitutes the refereed proceedings of the Third International Conference on Typed Lambda Calculi and Applications, TLCA '97, held in Nancy, France, in April 1997. The 24 revised full papers presented in the book were carefully selected from a total of 54 submissions. The book reports the main research advances achieved in the area of typed lambda calculi since the predecessor conference, held in 1995, and competently reflects the state of the art in the area.

Foundations Of Software Science And Computation Structures

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Author : Bart Jacobs
language : en
Publisher: Springer
Release Date : 2016-03-22

Foundations Of Software Science And Computation Structures written by Bart Jacobs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-22 with Computers categories.

This book constitutes the proceedings of the 19th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2016, which took place in Eindhoven, The Netherlands, in April 2016, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2016. The 31 full papers presented in this volume were carefully reviewed and selected from 85 submissions. They were organized in topical sections named: types; recursion and fixed-points; verification and program analysis; automata, logic, games; probabilistic and timed systems; proof theory and lambda calculus; algorithms for infinite systems; and monads.

Domains And Lambda Calculi

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Author : Roberto M. Amadio
language : en
Publisher: Cambridge University Press
Release Date : 1998-07-02

Domains And Lambda Calculi written by Roberto M. Amadio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-02 with Computers categories.

Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.

Interactive Theorem Proving

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Author : Gerwin Klein
language : en
Publisher: Springer
Release Date : 2014-06-28

Interactive Theorem Proving written by Gerwin Klein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.

This book constitutes the proceedings of the 5th International Conference on Interactive Theorem Proving, ITP 2014, Held as Part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 35 papers presented in this volume were carefully reviewed and selected from 59 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematics.

Automata Languages And Programming

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Author : Michele Bugliesi
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-30

Automata Languages And Programming written by Michele Bugliesi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-30 with Computers categories.

The two-volume set LNCS 4051 and LNCS 4052 constitutes the refereed proceedings of the 33rd International Colloquium on Automata, Languages and Programming, ICALP 2006, held in Venice, Italy, July 2006. In all, these volumes present more 100 papers and lectures. Volume II (4052) presents 2 invited papers and 2 additional conference tracks with 24 papers each, focusing on algorithms, automata, complexity and games as well as on security and cryptography foundation.

Computer Science Logic

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Author : Georg Gottlob
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-04-28

Computer Science Logic written by Georg Gottlob and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-28 with Computers categories.