Download or read book Isomorphisms of Types written by Roberto DiCosmo and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on the Curry Howard Isomorphism written by Morten Heine Sørensen and published by Elsevier. This book was released on 2006-07-04 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Computer Science Logic written by Michael Kaminski and published by Springer Science & Business Media. This book was released on 2008-09-10 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Conference Record of the Nineteenth Annual ACM SIGPLAN SIGACT Symposium on Principles of Programming Languages written by Association for Computing Machinery and published by Pearson Education. This book was released on 1992 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Symplectic Type of Isomorphisms of the p Torsion of Elliptic Curves written by Nuno Freitas and published by American Mathematical Society. This book was released on 2022-05-24 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Download or read book Programming Languages Implementations Logics and Programs written by S.Doaitse Swierstra and published by Springer Science & Business Media. This book was released on 1996-09-11 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Isomorphisms Between H1 Spaces written by Paul F.X. Müller and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Logic for Programming Artificial Intelligence and Reasoning written by Franz Baader and published by Springer Science & Business Media. This book was released on 2005-03-07 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2004, held in Montevideo, Uruguay in March 2005. The 33 revised full papers presented together with abstracts of 4 invited papers were carefully reviewed and selected from 77 submissions. The papers address all current issues in logic programming, automated reasoning, and AI logics in particular description logics, fuzzy logic, linear logic, multi-modal logic, proof theory, formal verification, protocol verification, constraint logic programming, programming calculi, theorem proving, etc.
Download or read book A First Course in Linear Algebra written by Kenneth Kuttler and published by . This book was released on 2020 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A First Course in Linear Algebra, originally by K. Kuttler, has been redesigned by the Lyryx editorial team as a first course for the general students who have an understanding of basic high school algebra and intend to be users of linear algebra methods in their profession, from business & economics to science students. All major topics of linear algebra are available in detail, as well as justifications of important results. In addition, connections to topics covered in advanced courses are introduced. The textbook is designed in a modular fashion to maximize flexibility and facilitate adaptation to a given course outline and student profile. Each chapter begins with a list of student learning outcomes, and examples and diagrams are given throughout the text to reinforce ideas and provide guidance on how to approach various problems. Suggested exercises are included at the end of each section, with selected answers at the end of the textbook."--BCcampus website.
Download or read book Theorem Proving in Higher Order Logics written by Yves Bertot and published by Springer. This book was released on 2003-07-31 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics, TPHOLs '99, held in Nice, France, in September 1999. The 20 revised full papers presented together with three invited contributions were carefully reviewed and selected from 35 papers submitted. All current aspects of higher order theorem proving, formal verification, and specification are discussed. Among the theorem provers evaluated are COQ, HOL, Isabelle, Isabelle/ZF, and OpenMath.
Download or read book Foundations of Software Science and Computation Structures written by Furio Honsell and published by Springer. This book was released on 2007-12-03 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: ETAPS 2001 was the fourth instance of the European Joint Conferences on Theory and Practice of Software. ETAPS is an annual federated conference that was established in 1998 by combining a number of existing and new conferences. This year it comprised ve conferences (FOSSACS, FASE, ESOP, CC, TACAS), ten satellite workshops (CMCS, ETI Day, JOSES, LDTA, MMAABS, PFM, RelMiS, UNIGRA, WADT, WTUML), seven invited lectures, a debate, and ten tutorials. The events that comprise ETAPS address various aspects of the system de- lopment process, including speci cation, design, implementation, analysis, and improvement. The languages, methodologies, and tools which support these - tivities are all well within its scope. Di erent blends of theory and practice are represented, with an inclination towards theory with a practical motivation on one hand and soundly-based practice on the other. Many of the issues involved in software design apply to systems in general, including hardware systems, and the emphasis on software is not intended to be exclusive.
Download or read book The Curry Howard Isomorphism written by Philippe De Groote and published by . This book was released on 1995 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Basic Category Theory written by Tom Leinster and published by Cambridge University Press. This book was released on 2014-07-24 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A short introduction ideal for students learning category theory for the first time.
Download or read book The London Edinburgh and Dublin Philosophical Magazine and Journal of Science written by and published by . This book was released on 1908 with total page 856 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Philosophical Magazine written by and published by . This book was released on 1908 with total page 880 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complexity of Infinite Domain Constraint Satisfaction written by Manuel Bodirsky and published by Cambridge University Press. This book was released on 2021-06-10 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Constraint Satisfaction Problems (CSPs) are natural computational problems that appear in many areas of theoretical computer science. Exploring which CSPs are solvable in polynomial time and which are NP-hard reveals a surprising link with central questions in universal algebra. This monograph presents a self-contained introduction to the universal-algebraic approach to complexity classification, treating both finite and infinite-domain CSPs. It includes the required background from logic and combinatorics, particularly model theory and Ramsey theory, and explains the recently discovered link between Ramsey theory and topological dynamics and its implications for CSPs. The book will be of interest to graduate students and researchers in theoretical computer science and to mathematicians in logic, combinatorics, and dynamics who wish to learn about the applications of their work in complexity theory.
Download or read book NonasSociative Algebra and Its Applications written by R Costa and published by CRC Press. This book was released on 2019-05-20 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of lectures presented at the Fourth International Conference on Nonassociative Algebra and its Applications, held in Sao Paulo, Brazil. Topics in algebra theory include alternative, Bernstein, Jordan, lie, and Malcev algebras and superalgebras. The volume presents applications to population genetics theory, physics, and more.
