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Theorie Des Types
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Book Synopsis Twenty Five Years of Constructive Type Theory by : Giovanni Sambin
Download or read book Twenty Five Years of Constructive Type Theory written by Giovanni Sambin and published by Clarendon Press. This book was released on 1998-10-15 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.
Book Synopsis Séminaire de Théorie Des Nombres by : D. Sinnou
Download or read book Séminaire de Théorie Des Nombres written by D. Sinnou and published by Springer Science & Business Media. This book was released on 1992 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Le travail ci-dessous developpe sur quelques points les tex:tes fondamentaux de C.L. Siegel [13[ et de K. Ramachandra [2). Remerclements C'est au Max Planck Institut de Bonn que la plus grande part des resultats (th. 2 et 3, ex:ception faite du point 3 d et th. 4 et 5) ont ete soit rectiges soit con~s. La rectaction definitive de ce travail a eu lieu ä l'Institut Fourier de Grenoble durant l'hiver 1990. Le th. 1 tel qu'il apparait ici, et le corollaire du th. 6 cf. identite (13), sont nouveaux. On trouvera une rectaction detailleedes th. 2 et 3 dans [51 et, parmi d'autres resultats, des th. 4, 5 et 6 dans [7). Que tous mes collegues et les deux equipes de secretartat recoivent ici mes remerciements les plus chaleureux. 2 1) On pose e( x) = e 1rix, x E C. Pour L un reseau complex:e, on note une base positivement olientee de L = lw + lw c'est-ä-dire teile que 1 2 On definit alors une forme modulaire .,.p> de poids 1 par 1](2)(w) ~fn (21l"i)ql/12 IJ ( - qn)2 1 { w2 n>l 1 12 q = e(W) , q 1 = e(W/12) , W = wt!w2 .
Book Synopsis Études D'économie Sociale (théorie de la Répartition de la Richesse Sociale) by : Léon Walras
Download or read book Études D'économie Sociale (théorie de la Répartition de la Richesse Sociale) written by Léon Walras and published by . This book was released on 1896 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Intuitionistic Type Theory by : Per Martin-Löf
Download or read book Intuitionistic Type Theory written by Per Martin-Löf and published by . This book was released on 1984 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Séminaire de Théorie Des Nombres by : Sinnou David
Download or read book Séminaire de Théorie Des Nombres written by Sinnou David and published by Springer Science & Business Media. This book was released on 1993-12-23 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the 13th annual volume of papers based on lectures given at the Seminaire des Nombres de Paris. The results presented here by an international group of mathematicians reflect recent work in many areas of number theory and should form a basis for further discussion on these topics.
Book Synopsis Basic Simple Type Theory by : J. Roger Hindley
Download or read book Basic Simple Type Theory written by J. Roger Hindley and published by Cambridge University Press. This book was released on 1997 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.
Book Synopsis Modern Perspectives in Type-Theoretical Semantics by : Stergios Chatzikyriakidis
Download or read book Modern Perspectives in Type-Theoretical Semantics written by Stergios Chatzikyriakidis and published by Springer. This book was released on 2017-02-07 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collective volume that reports the state of the art in the applications of type theory to linguistic semantics. The volume fills a 20 year gap from the last published book on the issue and aspires to bring researchers closer to cutting edge alternatives in formal semantics research. It consists of unpublished work by some key researchers on various issues related to the type theoretical study of formal semantics and further exemplifies the advantages of using modern type theoretical approaches to linguistic semantics. Themes that are covered include modern developments of type theories in formal semantics, foundational issues in linguistic semantics like anaphora, modality and plurals, innovational interdisciplinary research like the introduction of probability theory to type theories as well as computational implementations of type theoretical approaches. This volume will be of great interest to formal semanticists that are looking for alternative ways to study linguistic semantics, but will also be of interest to theoretical computer scientists and mathematicians that are interested in the applications of type theory.
Book Synopsis Categorical Logic and Type Theory by : B. Jacobs
Download or read book Categorical Logic and Type Theory written by B. Jacobs and published by Gulf Professional Publishing. This book was released on 2001-05-10 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Book Synopsis Types for Proofs and Programs by : Thorsten Altenkirch
Download or read book Types for Proofs and Programs written by Thorsten Altenkirch and published by Springer. This book was released on 2007-09-13 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refereed post-proceedings of the International Workshop of the Types Working Group are presented in this volume. The 17 papers address all current issues in formal reasoning and computer programming based on type theory, including languages and computerized tools for reasoning; applications in several domains, such as analysis of programming languages; certified software; formalization of mathematics; and mathematics education.
Book Synopsis Categories for Types by : Roy L. Crole
Download or read book Categories for Types written by Roy L. Crole and published by Cambridge University Press. This book was released on 1993 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Higher-Order Logic and Type Theory by : John L. Bell
Download or read book Higher-Order Logic and Type Theory written by John L. Bell and published by Cambridge University Press. This book was released on 2022-03-31 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element is an exposition of second- and higher-order logic and type theory. It begins with a presentation of the syntax and semantics of classical second-order logic, pointing up the contrasts with first-order logic. This leads to a discussion of higher-order logic based on the concept of a type. The second Section contains an account of the origins and nature of type theory, and its relationship to set theory. Section 3 introduces Local Set Theory (also known as higher-order intuitionistic logic), an important form of type theory based on intuitionistic logic. In Section 4 number of contemporary forms of type theory are described, all of which are based on the so-called 'doctrine of propositions as types'. We conclude with an Appendix in which the semantics for Local Set Theory - based on category theory - is outlined.
Book Synopsis Programming in Martin-Löf's Type Theory by : Bengt Nordström
Download or read book Programming in Martin-Löf's Type Theory written by Bengt Nordström and published by Oxford University Press, USA. This book was released on 1990 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-Löf. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.
Book Synopsis Types for Proofs and Programs by : Herman Geuvers
Download or read book Types for Proofs and Programs written by Herman Geuvers and published by Springer. This book was released on 2003-08-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Type Theory and Formal Proof by : Rob Nederpelt
Download or read book Type Theory and Formal Proof written by Rob Nederpelt and published by Cambridge University Press. This book was released on 2014-11-06 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.
Book Synopsis La science de l'information : Origines, théories et paradigmes by : IBEKWE-SANJUAN Fidelia
Download or read book La science de l'information : Origines, théories et paradigmes written by IBEKWE-SANJUAN Fidelia and published by Lavoisier. This book was released on 2012-10-01 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cet ouvrage de synthèse sur les fondements théoriques et épistémologiques de la science de l’information répond à trois questions : – existe-t-il une science de l’information à part entière ? – comment se définit l’information, objet de cette science ? – y a-t-il une spécificité française de la science de l’information ? Ce livre compare les chemins parcourus par la science de l’information en France et dans le reste du monde. Il contextualise cette évolution à l’aune d’une diversité d’inscriptions disciplinaires. L’enjeu de la science de l’information est de concilier l’approche réaliste de la connaissance, l’approche individualiste des sciences cognitives et l’approche collectiviste où les domaines sont façonnés et les comportements sont modulés par les environnements, les cultures et les construits sociaux partagés. Cette étude sera utile à tous les chercheurs, étudiants et professionnels désirant approfondir leurs connaissances sur les fondements théoriques de la science de l’information.
Book Synopsis The Theory of Logical Types by : Irving Copi
Download or read book The Theory of Logical Types written by Irving Copi and published by Routledge. This book was released on 2011-02-28 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its various different formulations (Simple and Ramified), the difficulties connected with each, and the criticisms that have been directed against it. Professor Copi seeks to make the subject accessible to the non-specialist and yet provide a sufficiently rigorous exposition for the serious student to see exactly what the theory is and how it works.
Book Synopsis Théorie de la communication et éthique relationnelle (Collection forme et sens) by : FOURNOUT Olivier
Download or read book Théorie de la communication et éthique relationnelle (Collection forme et sens) written by FOURNOUT Olivier and published by Lavoisier. This book was released on 2012-06-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Théorie de la communication et éthique relationnelle montre, à travers des études de cas, que les discours sur la communication sont marqués d'une structure relationnelle qui prend son origine dans la perception de l'espace, dans le langage, dans l'esprit, mais aussi dans les formes graphiques et mises en page textuelles en circulation dans la société. Cet ouvrage met cette matrice relationnelle à l'épreuve, notamment, de la pensée systémique, de la complexité en science, du dialogisme en littérature, du traitement journalistique des conflits, de l'éthique managériale, des méthodes d'apprentissage de la communication, de campagnes de publicité, d'oeuvres d'artistes, de scénographies, de communications par internet.
