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A Consistent Foundation for Isabelle/HOL

  • Ondřej Kunčar
  • Andrei Popescu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9236)

Abstract

The interactive theorem prover Isabelle/HOL is based on the well understood Higher-Order Logic (HOL), which is widely believed to be consistent (and provably consistent in set theory by a standard semantic argument). However, Isabelle/HOL brings its own personal touch to HOL: overloaded constant definitions, used to achieve Haskell-like type classes in the user space. These features are a delight for the users, but unfortunately are not easy to get right as an extension of HOL—they have a history of inconsistent behavior. It has been an open question under which criteria overloaded constant definitions and type definitions can be combined together while still guaranteeing consistency. This paper presents a solution to this problem: non-overlapping definitions and termination of the definition-dependency relation (tracked not only through constants but also through types) ensures relative consistency of Isabelle/HOL.

Keywords

Type Class Dependency Relation Type Definition Ground Type Consistency Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We thank Tobias Nipkow, Larry Paulson and Makarius Wenzel for inspiring discussions and the anonymous referees for many useful comments. This paper was partially supported by the DFG project Security Type Systems and Deduction (grant Ni 491/13-3) as part of the program Reliably Secure Software Systems (RS3, priority program 1496).

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Fakultät für InformatikTechnische Universität MünchenMunichGermany
  2. 2.Department of Computer Science, School of Science and TechnologyMiddlesex UniversityLondonUK

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