Selected Papers On Automath

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in journals or conference proceedings, but a number have only circulated as research reports or have remained unpublished.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

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.

This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.

This volume presents the proceedings of the 7th International Workshop on Higher Order Logic Theorem Proving and Its Applications held in Valetta, Malta in September 1994. Besides 3 invited papers, the proceedings contains 27 refereed papers selected from 42 submissions. In total the book presents many new results by leading researchers working on the design and applications of theorem provers for higher order logic. In particular, this book gives a thorough state-of-the-art report on applications of the HOL system, one of the most widely used theorem provers for higher order logic.

This book constitutes the thoroughly refereed post-proceedings of the International Workshop of the TYPES Working Group, TYPES 2000, held in Durham, UK in December 2000. The 15 revised full papers presented were carefully reviewed and selected during two rounds of refereeing and revision. All current issues on type theory and type systems and their applications to programming, systems design, and proof theory are addressed.

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.

TheInternationalConferenceonMathematicalKnowledgeManagementhasnow reached its third edition, creating and establishing an original and stimulating scienti?ccommunitytransversaltomanydi?erent?eldsandresearchtopics. The broad goal of MKM is the exploration of innovative, semantically enriched, d- ital encodings of mathematical information, and the study of new services and tools exploiting the machine-understandable nature of the information. MKM is naturally located in the border area between digital libraries and the mec- nization of mathematics, devoting a particular interest to the new developments in information technology, and fostering their application to the realm of ma- ematical information. The conference is meant to be a forum for presenting, discussing and comparing new tools and systems, standardization e?orts, cri- calsurveys,largeexperiments,andcasestudies. Atpresent,wearestillgettingto knoweachother,tounderstandtheworkdonebyotherpeople,andthepotenti- ities o?ered by their work to our own research activity. However, the conference is rapidly acquiring scienti?c strength and academic interest, attracting more and more people and research groups, and o?ering a challenging alternative to older, more conservative conferences. July 2004 Andrea Asperti Grzegorz Bancerek Andrzej Trybulec Organization MKM 2004 was organized by the Institute of Computer Science, University of Bia lystokinco-operationwiththeFacultyofComputerScience,Bia lystokTe- nical University and the Association of Mizar Users. Program Committee Andrzej Trybulec (Chair) University of Bia lystok, Poland Andrew A. Adams University of Reading, UK Andrea Asperti University of Bologna, Italy Bruno Buchberger RISC Linz, Austria Roy McCasland University of Edinburgh, UK James Davenport University of Bath, UK William M.

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.