Types summer school'02: Theory and practice of formal proofs

Giens, France, September 2-13, 2002

Lecture Notes

The lecture notes appeared as an INRIA report.
Additional material, such as copies of slides and introductions to the systems, were available as separated documents.
  • Contents (pdf file)
  • Foreword (pdf file)
  • Introduction and Background:
  • Benjamin Werner and Gilles Dowek, Inria: Proofs, Proof development, Logic, and Lambda-calculus pdf file
  • Herman Geuvers, Nijmegen: Pure Type Systems (not included)
  • Thierry Coquand, Chalmers: Inductive Definitions and Type Theory: an Introduction ps file, pdf file

  • Systems:
    - An overview of each of the two proof assistants to be used in the course, including some short developments of actual proofs:
  • Benjamin Werner, Inria: The Coq system (not included)
  • Tobias Nipkow, München: The Isabelle/HOL system (not included)
  • - A few other systems and man-machine interfaces:
  • Paul Callaghan, Durham: Plastic (not included)
  • Catarina Coquand and Thomas Hallgren, Chalmers: Alfa and Agda ps file, pdf file
  • Christophe Raffalli, Chambery: PhoX ps file, pdf file
  • Carsten Schuermann, Yale: Twelf ps file, pdf file
  • Laurent Théry, Inria: A quick overview of PVS and HOL (not included)
  • David Aspinall, Edinburgh: Proof General: a general man-machine interface for proof assistants ps file, pdf file
  • Yves Bertot, Inria: PCoq, a man-machine interface dedicated to Coq ps file, pdf file

  • Advanced Topics:
  • Per Martin-Löf, Stockholm: Informal Semantics of Type Theory (not included)
  • Peter Dybjer, Chalmers: Dependant Types in Programming
  • Susanne Graf, Verimag: Model Checking, Abstractions (not included)
  • Gregory Morrisett, Cornell: Proof-Carrying Code ps file, pdf file
  • Davide Sangiorgi, Inria: Types for Mobile Process ps file, pdf file

  • Applications:
  • Martin Abadi, UCSC: Security (not included)
  • Paul Jackson, Edinburgh: Hardware Verification (not included)
  • Laurent Théry, Inria: Formalised Mathematics (not included)
  • Slides

  • Martin Abadi, UCSC: Security pdf file
  • Paul Callaghan, Durham: Coercions in Plastic; ps file, pdf file.
  • Thierry Coquand, Chalmers: Inductive Definitions and Type Theory Part I, Part II, Part III (ps files).
  • Peter Dybjer, Chalmers: Dependant Types in Programming; ps files in 2 versions: 1 slide per page - 4 slides per page
  • Susanne Graf, Verimag: Model Checking: algorithmic verification of reactive systems: slides; 2 slides on IF (pdf files).
  • Laurent Théry, Inria: Introduction to HOL and PVS (gzip ps files); ps files: HOL and PVS
  • Introductions to the systems

  • Benjamin Werner, Inria: The Coq system pdf file (37 pages)
  • Tobias Nipkow, München: The Isabelle/HOL system. A compact Overwiew of Structured Proofs in Isar/HOL; ps file.
  • Yves Bertot, Inria: Proof development using Pcoq; ps file, gzip ps file
  • Paul Callaghan, Durham: Coercions in Plastic; ps file