Isomorphisms Of Types
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Isomorphisms Of Types
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Author : Roberto DiCosmo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Isomorphisms Of Types written by Roberto DiCosmo 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 2012-12-06 with Computers categories.
This is a book about isomorphisms 0/ types, arecent difficult research topic in type theory that turned out to be able to have valuable practical applications both for programming language design and far more human centered information retrieval in software libraries. By means of a deep study of the syntax of the now widely known typed A-ca1culus, it is possible to identify some simple equations between types that on one hand allow to improve the design of the ML language, and on the other hand provide the basis for building radically new information retrieval systems for functional software libraries. We present in this book both the theoretical aspects of these researches and a fully functional implementation of some of their applications in such a way to provide interesting material both for the theoretician looking for proofs and for the practitioner interested in implementation details. In order to make it possible for these different types of readers to use this book effectively, some special signs are used to designate material that is particularly technical or applied or that represents a digression. When the symbol appears at the beginning of a section or a subsection, it warns that the material contained in such section is particularly technical with respect to the general level of the chapter or section where it is located. This material is generally reserved to theoreticians and does not need to be read by the casual reader.
Isomorphisms Of Types
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Author : Roberto Di Cosmo
language : en
Publisher:
Release Date : 1995
Isomorphisms Of Types written by Roberto Di Cosmo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Human-computer interaction categories.
The Curry Howard Isomorphism
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Author : Philippe De Groote
language : en
Publisher:
Release Date : 1995
The Curry Howard Isomorphism written by Philippe De Groote and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Lectures On The Curry Howard Isomorphism
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Author : Morten Heine Sørensen
language : en
Publisher: Elsevier
Release Date : 2006-07-04
Lectures On The Curry Howard Isomorphism written by Morten Heine Sørensen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-04 with Mathematics categories.
The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme.· Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics.· Elaborate study of classical logics and control operators.· Account of dialogue games for classical and intuitionistic logic.· Theoretical foundations of computer-assisted reasoning
Types For Proofs And Programs
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Author : Ralph Matthes
language : en
Publisher: BoD – Books on Demand
Release Date : 2014-07-31
Types For Proofs And Programs written by Ralph Matthes and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-31 with Computers categories.
In this LIPIcs proceedings one can find research papers on the following topics: analysis of the classical principles in intuitionistic calculi, type isomorphisms for intersection types, monads and their semantics in functional programming languages, realizability, extensions of type theory, extensions of linear logic, models of type theory, control operators in type systems, formal verification of programs, program extraction, compiler formalization and modelling of natural language features. All papers obtained at least two reviews, and up to six reviews, counting a second round of review.
On The Symplectic Type Of Isomorphisms Of The P Torsion Of Elliptic Curves
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Author : Nuno Freitas
language : en
Publisher: American Mathematical Society
Release Date : 2022-05-24
On The Symplectic Type Of Isomorphisms Of The P Torsion Of Elliptic Curves written by Nuno Freitas and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-24 with Mathematics categories.
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Computer Science Logic
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Author : Michael Kaminski
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-10
Computer Science Logic written by Michael Kaminski 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 2008-09-10 with Computers categories.
This book constitutes the refereed proceedings of the 22nd International Workshop on Computer Science Logic, CSL 2008, held as the 17th Annual Conference of the EACSL in Bertinoro, Italy, in September 2008. The 31 revised full papers presented together with 4 invited lectures were carefully reviewed and selected from 102 submissions. All current aspects of logic in computer science are addressed, ranging from foundational and methodological issues to application issues of practical relevance. The book concludes with a presentation of this year's Ackermann award.
Lectures On Duflo Isomorphisms In Lie Algebra And Complex Geometry
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Author : Damien Calaque
language : en
Publisher: European Mathematical Society
Release Date : 2011
Lectures On Duflo Isomorphisms In Lie Algebra And Complex Geometry written by Damien Calaque and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Cohomology operations categories.
The Duflo isomorphism first appeared in Lie theory and representation theory. It is an isomorphism between invariant polynomials of a Lie algebra and the center of its universal enveloping algebra, generalizing the pioneering work of Harish-Chandra on semi-simple Lie algebras. Kontsevich later refined Duflo's result in the framework of deformation quantization and also observed that there is a similar isomorphism between Dolbeault cohomology of holomorphic polyvector fields on a complex manifold and its Hochschild cohomology. This book, which arose from a series of lectures by Damien Calaque at ETH, derives these two isomorphisms from a Duflo-type result for $Q$-manifolds. All notions mentioned above are introduced and explained in this book. The only prerequisites are basic linear algebra and differential geometry. In addition to standard notions such as Lie (super) algebras, complex manifolds, Hochschild and Chevalley-Eilenberg cohomologies, spectral sequences, Atiyah and Todd classes, the graphical calculus introduced by Kontsevich in his seminal work on deformation quantization is addressed in detail. This book is well suited for graduate students in mathematics and mathematical physics as well as researchers working in Lie theory, algebraic geometry, and deformation theory.
Programming Languages Implementations Logics And Programs
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Author : S.Doaitse Swierstra
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-09-11
Programming Languages Implementations Logics And Programs written by S.Doaitse Swierstra 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 1996-09-11 with Computers categories.
This book constitutes the refereed proceedings of the Eighth International Symposium on Programming Languages, Implementations, Logics, and Programs, PLILP '96, held in conjunction with ALP and SAS in Aachen, Germany, in September 1996. The 30 revised full papers presented in the volume were selected from a total of 97 submissions; also included are one invited contribution by Lambert Meerlens and five posters and demonstrations. The papers are organized in topical sections on typing and structuring systems, program analysis, program transformation, implementation issues, concurrent and parallel programming, tools and programming environments, lambda-calculus and rewriting, constraints, and deductive database languages.
Isomorphisms Between H1 Spaces
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Author : Paul F.X. Müller
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Isomorphisms Between H1 Spaces written by Paul F.X. Müller 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 2006-03-30 with Mathematics categories.
This book gives a thorough and self contained presentation of H1, its known isomorphic invariants and a complete classification of H1 on spaces of homogeneous type. The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it. Complete proofs are given for the classical martingale inequalities, and for large deviation inequalities. Complex interpolation is treated. Througout, special attention is given to the combinatorial methods developed in the field. An entire chapter is devoted to study the combinatorics of coloured dyadic Intervals.
