Selected Papers on Automath

Selected Papers on Automath
Title Selected Papers on Automath PDF eBook
Author R.P. Nederpelt
Publisher Elsevier
Pages 1045
Release 1994-10-20
Genre Mathematics
ISBN 008088718X

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The present volume contains a considered choice of the existing literature on Automath. Many of the papers included in the book have been published in journals or conference proceedings, but a number have only circulated as research reports or have remained unpublished. The aim of the editors is to present a representative selection of existing articles and reports and of material contained in dissertations, giving a compact and more or less complete overview of the work that has been done in the Automath research field, from the beginning to the present day. Six different areas have been distinguished, which correspond to Parts A to F of the book. These areas range from general ideas and motivation, to detailed syntactical investigations.

Twenty Five Years of Constructive Type Theory

Twenty Five Years of Constructive Type Theory
Title Twenty Five Years of Constructive Type Theory PDF eBook
Author Giovanni Sambin
Publisher Clarendon Press
Pages 292
Release 1998-10-15
Genre Mathematics
ISBN 0191606936

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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.

Programs as Diagrams

Programs as Diagrams
Title Programs as Diagrams PDF eBook
Author Dusko Pavlovic
Publisher Springer Nature
Pages 261
Release 2023-09-19
Genre Computers
ISBN 3031348273

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It is not always clear what computer programs mean in the various languages in which they can be written, yet a picture can be worth 1000 words, a diagram 1000 instructions. In this unique textbook/reference, programs are drawn as string diagrams in the language of categories, which display a universal syntax of mathematics (Computer scientists use them to analyze the program semantics; programmers to display the syntax of computations). Here, the string-diagrammatic depictions of computations are construed as programs in a single-instruction programming language. Such programs as diagrams show how functions are packed in boxes and tied by strings. Readers familiar with categories will learn about the foundations of computability; readers familiar with computability gain access to category theory. Additionally, readers familiar with both are offered many opportunities to improve the approach. Topics and features: Delivers a ‘crash’ diagram-based course in theory of computation Uses single-instruction diagrammatic programming language Offers a practical introduction into categories and string diagrams as computational tools Reveals how computability is programmability, rather than an ‘ether’ permeating computers Provides a categorical model of intensional computation is unique up to isomorphism Serves as a stepping stone into research of computable categories In addition to its early chapters introducing computability for beginners, this flexible textbook/resource also contains both middle chapters that expand for suitability to a graduate course as well as final chapters opening up new research. Dusko Pavlovic is a professor at the Department of Information and Computer Sciences at the University of Hawaii at Manoa, and by courtesy at the Department of Mathematics and the College of Engineering. He completed this book as an Excellence Professor at Radboud University in Nijmegen, The Netherlands.

Automated Deduction -- CADE-24

Automated Deduction -- CADE-24
Title Automated Deduction -- CADE-24 PDF eBook
Author Maria Paola Bonacina
Publisher Springer
Pages 479
Release 2013-06-04
Genre Computers
ISBN 3642385745

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This book constitutes the proceedings of the 24th International Conference on Automated Deduction, CADE-24, held in Lake Placid, NY, USA, in June 2013. The 31 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 71 initial submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, ranging from theoretical and methodological issues to the presentation of new theorem provers, solvers and systems.

Lambda-Calculus and Combinators

Lambda-Calculus and Combinators
Title Lambda-Calculus and Combinators PDF eBook
Author J. Roger Hindley
Publisher Cambridge University Press
Pages 346
Release 2008-07-24
Genre Computers
ISBN 1139473247

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Combinatory logic and lambda-calculus, originally devised in the 1920s, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this version is thoroughly revised and offers an account of the subject with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.

Design and Application of Strategies/Tactics in Higher Order Logics

Design and Application of Strategies/Tactics in Higher Order Logics
Title Design and Application of Strategies/Tactics in Higher Order Logics PDF eBook
Author Myla Archer
Publisher
Pages 120
Release 2003
Genre
ISBN

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Intelligent Computer Mathematics

Intelligent Computer Mathematics
Title Intelligent Computer Mathematics PDF eBook
Author James H. Davenport
Publisher Springer
Pages 323
Release 2011-07-18
Genre Computers
ISBN 3642226736

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This book constitutes the joint refereed proceedings of three international events, namely the 18th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2011, the 10th International Conference on Mathematical Knowledge Management, MKM 2011, and a new track on Systems and Projects descriptions that span both the Calculemus and MKM topics, all held in Bertinoro, Italy, in July 2011. All 51 submissions passed through a rigorous review process. A total of 15 papers were submitted to Calculemus, of which 9 were accepted. Systems and Projects track 2011 there have been 12 papers selected out of 14 submissions while MKM 2011 received 22 submissions, of which 9 were accepted for presentation and publication. The events focused on the use of AI techniques within symbolic computation and the application of symbolic computation to AI problem solving; the combination of computer algebra systems and automated deduction systems; and mathematical knowledge management, respectively.