Comprehending Isabelle/HOL's consistency

Kunčar, Ondřej and Popescu, Andrei (2017) Comprehending Isabelle/HOL's consistency. Programming Languages and Systems. ESOP 2017.. In: ESOP 2017: 26th European Symposium on Programming (ESOP), 22-29 Apr 2017, Uppsala, Sweden. ISBN 9783662544334. ISSN 0302-9743 [Conference or Workshop Item] (doi:10.1007/978-3-662-54434-1_27)

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Abstract

The proof assistant Isabelle/HOL is based on an extension of Higher-Order Logic (HOL) with ad hoc overloading of constants. It turns out that the interaction between the standard HOL type definitions and the Isabelle-specific ad hoc overloading is problematic for the logical consistency. In previous work, we have argued that standard HOL semantics is no longer appropriate for capturing this interaction, and have proved consistency using a nonstandard semantics. The use of an exotic semantics makes that proof hard to digest by the community. In this paper, we prove consistency by proof-theoretic means—following the healthy intuition of definitions as abbreviations, realized in HOLC, a logic that augments HOL with comprehension types. We hope that our new proof settles the Isabelle/HOL consistency problem once and for all. In addition, HOLC offers a framework for justifying the consistency of new deduction schemas that address practical user needs.

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