[TYPES] Announcement: TYPES Summer School, August 15 - 26

[Bengt Nordström]

                    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.