A consistent foundation for Isabelle/HOL

Conference paper

Kunčar, O. and Popescu, A. 2015. A consistent foundation for Isabelle/HOL. 6th conference on Interactive Theorem Proving (ITP). Nanjing, China 24 - 27 Aug 2015 Springer. pp. 234-252 https://doi.org/10.1007/978-3-319-22102-1_16
TypeConference paper
TitleA consistent foundation for Isabelle/HOL
AuthorsKunčar, O. and Popescu, A.
Abstract

The interactive theorem prover Isabelle/HOL is based on 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.

Research GroupFoundations of Computing group
Conference6th conference on Interactive Theorem Proving (ITP)
Page range234-252
ISSN0302-9743
ISBN
Hardcover9783319221014
PublisherSpringer
Publication dates
Online19 Aug 2015
Publication process dates
Deposited19 May 2015
Accepted05 Jun 2015
Output statusPublished
Accepted author manuscript
Copyright Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-22102-1_16

Additional information

Cite this paper as:
Kunčar O., Popescu A. (2015) A Consistent Foundation for Isabelle/HOL. In: Urban C., Zhang X. (eds) Interactive Theorem Proving. ITP 2015. Lecture Notes in Computer Science, vol 9236. Springer, Cham

Digital Object Identifier (DOI)https://doi.org/10.1007/978-3-319-22102-1_16
LanguageEnglish
Book titleInteractive Theorem Proving. ITP 2015
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