Types for Proofs and Programs

1. Front Matter

   Pages I-VIII

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2. (Co-)Iteration for Higher-Order Nested Datatypes

   • Andreas Abel, Ralph Matthes

   Pages 1-20

3. Program Extraction in Simply-Typed Higher Order Logic

   • Stefan Berghofer

   Pages 21-38

4. General Recursion in Type Theory

   • Ana Bove

   Pages 39-58

5. Using Theory Morphisms for Implementing Formal Methods Tools

   • Achim D. Brucker, Burkhart Wolff

   Pages 59-77

6. Subsets, Quotients and Partial Functions in Martin-Löf’s Type Theory

   • Jesper Carlström

   Pages 78-94

7. Mathematical Quotients and Quotient Types in Coq

   • Laurent Chicli, Loïc Pottier, Carlos Simpson

   Pages 95-107

8. A Constructive Formalization of the Fundamental Theorem of Calculus

   • Luís Cruz-Filipe

   Pages 108-126

9. Two Behavioural Lambda Models

   • Mariangiola Dezani-Ciancaglini, Silvia Ghilezan

   Pages 127-147

10. A Unifying Approach to Recursive and Co-recursive Definitions

    • Pietro Di Gianantonio, Marino Miculan

    Pages 148-161

11. Holes with Binding Power

    • Georgi I. Jojgov

    Pages 162-181

12. Typing with Conditions and Guarantees for Functional In-place Update

    • Michal Konečný

    Pages 182-199

13. A New Extraction for Coq

    • Pierre Letouzey

    Pages 200-219

14. Weak Transitivity in Coercive Subtyping

    • Yong Luo, Zhaohui Luo, Sergei Soloviev

    Pages 220-239

15. The Not So Simple Proof-Irrelevant Model of CC

    • Alexandre Miquel, Benjamin Werner

    Pages 240-258

16. Structured Proofs in Isar/HOL

    • Tobias Nipkow

    Pages 259-278

17. Java as a Functional Programming Language

    • Anton Setzer

    Pages 279-298

18. Monad Translating Inductive and Coinductive Types

    • Tarmo Uustalu

    Pages 299-315

19. A Finite First-Order Presentation of Set Theory

    • Stéphane Vaillant

    Pages 316-330

20. Back Matter

    Pages 331-331

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These proceedings contain a refereed selection of papers presented at the Second Annual Workshop of the Types Working Group (Computer-Assisted Reasoning based on Type Theory, EUIST project 29001), which was held April 24–28, 2002 in Hotel Erica, Berg en Dal (close to Nijmegen), The Netherlands. The workshop was attended by about 90 researchers. On April 27, there was a special afternoon celebrating the 60th birthday of Per Martin-L¨of, one of the founding fathers of the Types community. The afternoon consisted of the following three invited talks: “Constructive Validity Revisited” by Dana Scott, “From the Rules of Logic to the Logic of Rules” by Jean-Yves Girard, and “The Varieties of Type Theories” by Peter Aczel. The contents of these contributions were not laid down in these proceedings, but the videos of the talks and the slides used by the speakers are available at http://www. cs. kun. nl/fnds/MartinLoefDay/LoefTalks. htm The previous workshop of the Types Working Group under EUIST project 29001 was held in 2000 in Durham, UK. The workshops Types 2000 and Types 2002 followed a series of meetings organized in the period 1993 – 1999 whithin previous Types projects (ESPRIT BRA 6435 and ESPRIT Working Group 21900). The proceedings of these earlier Types workshops were also published in the LNCS series, as volumes 806, 996, 1158, 1512, 1657, 1956 and 2277. ESPRIT BRA 6453 was a continuation of ESPRIT Action 3245, Logical Frameworks: - sign, Implementation and Experiments.

• Coq
• formal methods
• formal specification
• formal verification
• inductive types
• lambda calculus
• program semantics
• programming
• programming logic
• programming theory
• proof theory
• rewriting systems
• subtyping
• type systems
• types

• Department of Computer Science, University of Nijmegen, Nijmegen, The Netherlands

  Herman Geuvers, Freek Wiedijk

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