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.
Author(s): Andreas Abel, Ralph Matthes (auth.), Herman Geuvers, Freek Wiedijk (eds.)
Series: Lecture Notes in Computer Science 2646
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2003
Language: English
Pages: 336
Tags: Logics and Meanings of Programs; Programming Languages, Compilers, Interpreters; Mathematical Logic and Formal Languages; Artificial Intelligence (incl. Robotics)
(Co-)Iteration for Higher-Order Nested Datatypes....Pages 1-20
Program Extraction in Simply-Typed Higher Order Logic....Pages 21-38
General Recursion in Type Theory....Pages 39-58
Using Theory Morphisms for Implementing Formal Methods Tools....Pages 59-77
Subsets, Quotients and Partial Functions in Martin-Löf’s Type Theory....Pages 78-94
Mathematical Quotients and Quotient Types in Coq....Pages 95-107
A Constructive Formalization of the Fundamental Theorem of Calculus....Pages 108-126
Two Behavioural Lambda Models....Pages 127-147
A Unifying Approach to Recursive and Co-recursive Definitions....Pages 148-161
Holes with Binding Power....Pages 162-181
Typing with Conditions and Guarantees for Functional In-place Update....Pages 182-199
A New Extraction for Coq....Pages 200-219
Weak Transitivity in Coercive Subtyping....Pages 220-239
The Not So Simple Proof-Irrelevant Model of CC....Pages 240-258
Structured Proofs in Isar/HOL....Pages 259-278
Java as a Functional Programming Language....Pages 279-298
Monad Translating Inductive and Coinductive Types....Pages 299-315
A Finite First-Order Presentation of Set Theory....Pages 316-330