Selected Papers on Automath


Author: R.P. Nederpelt,J.H. Geuvers,R.C. de Vrijer
Publisher: Elsevier
ISBN: 9780080887180
Category: Mathematics
Page: 1021
View: 553

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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published in journals or conference proceedings, but a number have only circulated as research reports or have remained unpublished.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.

Functional and Logic Programming

5th International Symposium, FLOPS 2001, Tokyo, Japan, March 7-9, 2001. Proceedings
Author: Herbert Kuchen,Kazunori Ueda
Publisher: Springer
ISBN: 3540447164
Category: Computers
Page: 398
View: 9110

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Thirty Five Years of Automating Mathematics


Author: F.D. Kamareddine
Publisher: Springer Science & Business Media
ISBN: 9401702535
Category: Mathematics
Page: 320
View: 9942

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THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. By then, his contributions in mathematics were numerous and extremely influential. His book on advanced asymptotic methods, North Holland 1958, was a classic and was subsequently turned into a book in the well known Dover book series. His work on combinatorics yielded influential notions and theorems of which we mention the de Bruijn-sequences of 1946 and the de Bruijn-Erdos theorem of 1948. De Bruijn's contributions to mathematics also included his work on generalized function theory, analytic number theory, optimal control, quasicrystals, the mathematical analysis of games and much more. In the 1960s de Bruijn became fascinated by the new computer technology and as a result, decided to start the new AUTOMATH project where he could check, with the help of the computer, the correctness of books of mathematics. In each area that de Bruijn approached, he shed a new light and was known for his originality and for making deep intellectual contributions. And when it came to automating mathematics, he again did it his way and introduced the highly influential AUTOMATH. In the past decade he has also been working on theories of the human brain.

Mathematics, Computer Science and Logic - A Never Ending Story

The Bruno Buchberger Festschrift
Author: Peter Paule
Publisher: Springer Science & Business Media
ISBN: 3319009664
Category: Computers
Page: 113
View: 8340

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This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come. The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director. More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic. Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger’s successor as director of the Research Institute for Symbolic Computation.

SOFSEM 2002: Theory and Practice of Informatics

29th Conference on Current Trends in Theory and Practice of Informatics, Milovy, Czech Republic, November 22-29, 2002, Proceedings
Author: William I. Grosky,Frantisek Plasil
Publisher: Springer
ISBN: N.A
Category: Computer software
Page: 10
View: 5589

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This book constitutes the refereed proceedings of the 29th Conference on Current Trends in Theory and Practice of Informatics, SOFSEM 2002, held in Milovy, Czech Republic, in November 2002. The volume presents 10 invited lectures and the report on a panel discussion on GRID computing together with 11 revised full papers selected from 22 submissions. Among the topics covered are system design and testing related theory, distributed and parallel systems, type theory, multimedia, databases, computer vision, and soft computing.

Types for Proofs and Programs

International Workshop, TYPES '95, Torino, Italy, June 5 - 8, 1995 Selected Papers
Author: Stefano Berardi,Mario Coppo
Publisher: Springer
ISBN: N.A
Category: Automatic theorem proving
Page: 296
View: 6540

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This volume contains a refereed selection of revised full papers chosen from the contributions presented during the Third Annual Workshop held under the auspices of the ESPRIT Basic Research Action 6453 Types for Proofs and Programs. The workshop took place in Torino, Italy, in June 1995. Type theory is a formalism in which theorems and proofs, specifications and programs can be represented in a uniform way. The 19 papers included in the book deal with foundations of type theory, logical frameworks, and implementations and applications; all in all they constitute a state-of-the-art survey for the area of type theory.

Proof Style


Author: University of Cambridge. Computer Laboratory,John Robert Harrison
Publisher: N.A
ISBN: N.A
Category: Automatic theorem proving
Page: 22
View: 2606

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Abstract: "We are concerned with how to communicate a mathematical proof to a computer theorem prover. This can be done in many ways, while allowing the machine to generate a completely formal proof object. The most obvious choice is the amount of guidance required from the user, or from the machine perspective, the degree of automation provided. But another important consideration, which we consider particularly significant, is the bias towards a 'procedural' or 'declarative' proof style. We will explore this choice in depth, and discuss the strengths and weaknesses of declarative and procedural styles for proofs in pure mathematics and for verification applications. We conclude with a brief summary of our own experiments in trying to combine both approaches."

Mathematical Knowledge Management

4th International Conference, MKM 2005, Bremen, Germany, July 15-17, 2005 ; Revised Selected Papers
Author: Michael Kohlhase
Publisher: N.A
ISBN: N.A
Category: Computers
Page: 403
View: 8120

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Twenty Five Years of Constructive Type Theory


Author: Giovanni Sambin,Jan M. Smith
Publisher: Clarendon Press
ISBN: 0191606936
Category: Mathematics
Page: 292
View: 7653

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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.

Categorical Logic and Type Theory


Author: Bart Jacobs
Publisher: Gulf Professional Publishing
ISBN: 9780444508539
Category: Mathematics
Page: 760
View: 7945

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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.

Tools and Techniques in Modal Logic


Author: Marcus Kracht
Publisher: North-Holland
ISBN: N.A
Category: Computers
Page: 559
View: 9843

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This book treats modal logic as a theory, with several subtheories, such as completeness theory, correspondence theory, duality theory and transfer theory and is intended as a course in modal logic for students who have had prior contact with modal logic and who wish to study it more deeply. It presupposes training in mathematical or logic. Very little specific knowledge is presupposed, most results which are needed are proved in this book.

Classical recursion theory


Author: Piergiorgio Odifreddi
Publisher: North Holland
ISBN: 9780444502056
Category: Computers
Page: 949
View: 9580

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Volume II of Classical Recursion Theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from small time and space bounds to the elementary functions, with a particular attention to polynomial time and space computability. It also deals with primitive recursive functions and larger classes, which are of interest to the proof theorist. The second half of the book starts with the classical theory of recursively enumerable sets and degrees, which constitutes the core of Recursion or Computability Theory. Unlike other texts, usually confined to the Turing degrees, the book covers a variety of other strong reducibilities, studying both their individual structures and their mutual relationships. The last chapters extend the theory to limit sets and arithmetical sets. The volume ends with the first textbook treatment of the enumeration degrees, which admit a number of applications from algebra to the Lambda Calculus. The book is a valuable source of information for anyone interested in Complexity and Computability Theory. The student will appreciate the detailed but informal account of a wide variety of basic topics, while the specialist will find a wealth of material sketched in exercises and asides. A massive bibliography of more than a thousand titles completes the treatment on the historical side.