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[Bengt Nordstr�m <bengt AT cs.chalmers.se>]

                   TYPES Summer School 2005

       Proofs of Programs and Formalisation of Mathematics

             August 15-26 2005, Goteborg, Sweden

      http://www.cs.chalmers.se/Cs/Research/Logic/TypesSS05/


During the last ten years major achievements have been made in using
computers for interactive proof developments to produce secure
software and to show interesting mathematical results. Recent major
results are, for instance, the complete formalisation of a proof of
the four colour theorem, and a formalisation of the prime number
theorem.

This two weeks' course is for postgraduate students, researchers and
industrials who want to learn about interactive proof development.
The present school follows the format of previous TYPES summer school
(in Baastad 1993, Giens 1999, Giens 2002).  There will be introductory
and advanced lectures on lambda calculus, type theory, logical
frameworks, program extraction, and other topics with relevant
theoretical background.  Several talks will be devoted to
applications.

During these two weeks we will present three proof assistants: Coq,
Isabelle and Agda, which are state-of-the-art interactive theorem
provers.  Participants will get extensive opportunities to use the
systems for developing their own proofs. No previous knowledge of
type theory and lambda calculus is required.

The school is organised by the TYPES working group "Types for Proofs
and Programs", which is a project in the IST (Information Society
Technologies) program of the European Union. A limited number of grants
covering part of travel, fees and ackommodation are available. Neither
participation nor grants are restricted to TYPES participants.

Lecturers:
---------
                                                        
Jeremy Avigad, Carnegie-Mellon     Connor McBride, Nottingham
                                                        
Yves Bertot, INRIA Sophia          Alexandre Miquel, Paris 7
                                                        
Thierry Coquand, Chalmers          Tobias Nipkow, TU Munich
                                                        
Catarina Coquand, Chalmers         Bengt Nordstrom, Chalmers
                                                        
Gilles Dowek, INRIA Futurs         Erik Palmgren, Uppsala       
                                                        
Peter Dybjer, Chalmers             Christine Paulin, Paris Sud
                                                        
Herman Geuvers, Nijmegen           Laurent Thery, INRIA Sophia
                                                        
John Harrison, INTEL               Freek Wiedijk, Nijmegen

Per Martin-Lof, Stockholm




TENTATIVE PROGRAM
-----------------

Introduction to Type Theory:
    Lambda-calculus
    Propositions-as-types
    Inductive sets and families of sets
    Predicative and non-predicative theories

Foundations:

Introduction to Systems:
    Coq
    Isabelle
    Agda

Advanced applications and tools:
    Proving properties of Java programs
    Reasoning about Programming Languages
    Coinduction
    Correctness of floating-point algorithms

Dependently typed programming:
    Dependently typed datastructures
    Compiling dependent types

Formalisation of mathematics:
    Introduction
    Fundamental theorem of algebra
    Bishop' set theory
    Other examples, e.g. prime number theorem


The organising committee: Andreas Abel, Ana Bove, Catarina Coquand,
Thierry Coquand, Peter Dybjer and Bengt Nordstrom.