Types for Proofs and Programs International Workshop, TYPES 2006, No

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Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Moshe Y. Vardi Rice University, Houston, TX, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany

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Thorsten Altenkirch Conor McBride (Eds.)

Types for Proofs and Programs International Workshop, TYPES 2006 Nottingham, UK, April 18-21, 2006 Revised Selected Papers

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Volume Editors Thorsten Altenkirch Conor McBride University of Nottingham School of Computer Science and Information Technology Jubilee Campus, Wollaton Road, Nottingham NG8 1BB, UK E-mail: {txa, ctm}@cs.nott.ac.uk

Library of Congress Control Number: 2007936170 CR Subject Classification (1998): F.3.1, F.4.1, D.3.3, I.2.3 LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues ISSN ISBN-10 ISBN-13

0302-9743 3-540-74463-0 Springer Berlin Heidelberg New York 978-3-540-74463-4 Springer Berlin Heidelberg New York

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Preface

These proceedings contain a selection of refereed papers presented at or related to the Annual Workshop of the TYPES project (EU coordination action 510996), which was held April 18–21, 2006 at the University of Nottingham, UK. The topic of this workshop was formal reasoning and computer programming based on type theory: languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, formalization of mathematics and mathematics education. The workshop was attended by more than 100 researchers and included more than 60 presentations. We also had the plea