The refereed post-proceedings of the International Workshop of the Types Working Group are presented in this volume. The 17 papers address all current issues in formal reasoning and computer programming based on type theory, including languages and computerized tools for reasoning; applications in several domains, such as analysis of programming languages; certified software; formalization of mathematics; and mathematics education.

This book constitutes the thoroughly refereed post-proceedings of the Third International Workshop of the Types Working Group, TYPES 2003, held in Torino, Italy in April/May 2003. The 25 revised full papers presented were carefully selected during two rounds of reviewing and improvement. All current issues in type theory and type systems and their applications to programming, systems design, and proof theory are addressed. Among the systems dealt with are Isabelle/Isar, PAF!, and Coq.

The refereed post-proceedings of the International Workshop of the Types Working Group are presented in this volume. The 17 papers address all current issues in formal reasoning and computer programming based on type theory, including languages and computerized tools for reasoning; applications in several domains, such as analysis of programming languages; certified software; formalization of mathematics; and mathematics education.

The 17 revised full papers presented here cover all current issues of formal reasoning and computer programming based on type theory are addressed; in particular languages and computerised tools for reasoning, and applications in several domains such as analysis of programming languages, certified software, formalisation of mathematics and mathematics education.

This volume contains thoroughly refereed and revised full papers selected from the presentations at the first workshop held under the auspices of the ESPRIT Basic Research Action 6453 Types for Proofs and Programs in Nijmegen, The Netherlands, in May 1993. As the whole ESPRIT BRA 6453, this volume is devoted to the theoretical foundations, design and applications of systems for theory development. Such systems help in designing mathematical axiomatisation, performing computer-aided logical reasoning, and managing databases of mathematical facts; they are also known as proof assistants or proof checkers.

This book constitutes the thoroughly refereed post-proceedings of the Second International Workshop of the TYPES Working Group, TYPES 2002, held in Berg en Dal, The Netherlands in April 2002. The 18 revised full papers presented were carefully selected during two rounds of reviewing and improvement. All current issues in type theory and type systems and their applications to programming, systems design, and proof theory are addressed. Among the systems dealt with are Coq and Isar/HOL.

This book constitutes the thoroughly refereed post-conference proceedings of TYPES 2007, the concluding conference of the Types project, held in Cividale del Friuli, Italy, in May 2007. The 13 revised full papers presented were carefully reviewed and selected from 22 submissions. The topic of this last annual workshop of the Types Working Group was formal reasoning and computer programming based on type theory. Great importance was attached to 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.

This book constitutes the thoroughly refereed post-workshop proceedings of the Third International Workshop, TYPES'99, organized by the ESPRIT Working Group 21900, in Lökeberg, Sweden, in June 1999. The 11 revised full papers presented in the volume were carefully reviewed and selected during two rounds of refereeing. All current issues on type theory and type systems and their applications to programming and proof theory are addressed.

This book constitutes the thoroughly refereed post-conference proceedings of TYPES 2008, the last of a series of meetings of the TYPES working group funded by the European Union between 1993 and 2008; the workshop has been held in Torino, Italy, in March 2008. The 19 revised full papers presented were carefully reviewed and selected from 27 submissions. The topic of the 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, mobile code, formalization of mathematics, mathematics education.

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.