Lambda Calculus With Types
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Lambda Calculus With Types
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Author : Henk Barendregt
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-20
Lambda Calculus With Types written by Henk Barendregt 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 2013-06-20 with Mathematics categories.
This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Lambda Calculus With Types
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Author : Hendrik Pieter Barendregt
language : en
Publisher:
Release Date : 2013
Lambda Calculus With Types written by Hendrik Pieter Barendregt and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Lambda calculus categories.
"This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types."--Publisher's website.
Lambda Calculus Types And Models
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Author : Jean Louis Krivine
language : en
Publisher: Prentice Hall
Release Date : 1993
Lambda Calculus Types And Models written by Jean Louis Krivine and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This introduction to lambda-calculus looks at aspects of the theory: combinatory logic, models, and type streams, showing how they interlink and underpin computer science.
Typed Lambda Calculi And Applications
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Author : Martin Hofmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-05-27
Typed Lambda Calculi And Applications written by Martin Hofmann 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 2003-05-27 with Mathematics categories.
The refereed proceedings of the 6th International Conference on Typed Lambda Calculi and Applications, TLCA 2003, held in Valencia, Spain in June 2003. The 21 revised full papers presented were carefully reviewed and selected from 40 submissions. The volume reports research results on all current aspects of typed lambda calculi, ranging from theoretical and methodological issues to the application of proof assistants.
Typed Lambda Calculi And Applications
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Author : Jean-Yves Girard
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-03-24
Typed Lambda Calculi And Applications written by Jean-Yves Girard 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 1999-03-24 with Computers categories.
This book constitutes the refereed proceedings of the 4th International Conference on Typed Lambda Calculi and Applications, TLCA'99, held in L'Aquila, Italy in April 1999. The 25 revised full papers presented were carefully reviewed and selected from a total of 50 submissions. Also included are two invited demonstrations. The volume reports research results on various aspects of typed lambda calculi. Among the topics addressed are noncommutative logics, type theory, algebraic data types, logical calculi, abstract data types, and subtyping.
Types For Proofs And Programs
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Author : Herman Geuvers
language : en
Publisher: Springer
Release Date : 2003-08-03
Types For Proofs And Programs written by Herman Geuvers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-03 with Computers categories.
These proceedings contain a refereed selection of papers presented at the Second Annual Workshop of the Types Working Group (Computer-Assisted Reasoning based on Type Theory, EUIST project 29001), which was held April 24–28, 2002 in Hotel Erica, Berg en Dal (close to Nijmegen), The Netherlands. The workshop was attended by about 90 researchers. On April 27, there was a special afternoon celebrating the 60th birthday of Per Martin-L ̈of, one of the founding fathers of the Types community. The afternoon consisted of the following three invited talks: “Constructive Validity Revisited” by Dana Scott, “From the Rules of Logic to the Logic of Rules” by Jean-Yves Girard, and “The Varieties of Type Theories” by Peter Aczel. The contents of these contributions were not laid down in these proceedings, but the videos of the talks and the slides used by the speakers are available at http://www. cs. kun. nl/fnds/MartinLoefDay/LoefTalks. htm The previous workshop of the Types Working Group under EUIST project 29001 was held in 2000 in Durham, UK. The workshops Types 2000 and Types 2002 followed a series of meetings organized in the period 1993 – 1999 whithin previous Types projects (ESPRIT BRA 6435 and ESPRIT Working Group 21900). The proceedings of these earlier Types workshops were also published in the LNCS series, as volumes 806, 996, 1158, 1512, 1657, 1956 and 2277. ESPRIT BRA 6453 was a continuation of ESPRIT Action 3245, Logical Frameworks: - sign, Implementation and Experiments.
Typed Lambda Calculi And Applications
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Author : Marc Bezem
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-03-03
Typed Lambda Calculi And Applications written by Marc Bezem 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 1993-03-03 with Computers categories.
The lambda calculus was developed in the 1930s by Alonzo Church. The calculus turned out to be an interesting model of computation and became theprototype for untyped functional programming languages. Operational and denotational semantics for the calculus served as examples for otherprogramming languages. In typed lambda calculi, lambda terms are classified according to their applicative behavior. In the 1960s it was discovered that the types of typed lambda calculi are in fact appearances of logical propositions. Thus there are two possible views of typed lambda calculi: - as models of computation, where terms are viewed as programs in a typed programming language; - as logical theories, where the types are viewed as propositions and the terms as proofs. The practical spin-off from these studies are: - functional programming languages which are mathematically more succinct than imperative programs; - systems for automated proof checking based on lambda caluli. This volume is the proceedings of TLCA '93, the first international conference on Typed Lambda Calculi and Applications,organized by the Department of Philosophy of Utrecht University. It includes29 papers selected from 51 submissions.
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 Mathematics 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.
Lambda Calculus Types And Models
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Author : Jean Louis Krivine
language : en
Publisher: Prentice Hall
Release Date : 1993
Lambda Calculus Types And Models written by Jean Louis Krivine and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This introduction to lambda-calculus looks at aspects of the theory: combinatory logic, models, and type streams, showing how they interlink and underpin computer science.
The Parametric Lambda Calculus
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Author : Simona Ronchi Della Rocca
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Parametric Lambda Calculus written by Simona Ronchi Della Rocca 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 2013-03-09 with Mathematics categories.
The book contains a completely new presentation of classical results in the field of Lambda Calculus, together with new results. The text is unique in that it presents a new calculus (Parametric Lambda Calculus) which can be instantiated to obtain already known lambda-calculi. Some properties, which in the literature have been proved separately for different calculi, can be proved once for the Parametric one. The lambda calculi are presented from a Computer Science point of view, with a particular emphasis on their semantics, both operational and denotational.