Extension of Types-to-Sets

Mihails Milehins 📧

September 6, 2021

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.


In their article titled From Types to Sets by Local Type Definitions in Higher-Order Logic and published in the proceedings of the conference Interactive Theorem Proving in 2016, Ondřej Kunčar and Andrei Popescu propose an extension of the logic Isabelle/HOL and an associated algorithm for the relativization of the type-based theorems to more flexible set-based theorems, collectively referred to as Types-To-Sets. One of the aims of their work was to open an opportunity for the development of a software tool for applied relativization in the implementation of the logic Isabelle/HOL of the proof assistant Isabelle. In this article, we provide a prototype of a software framework for the interactive automated relativization of theorems in Isabelle/HOL, developed as an extension of the proof language Isabelle/Isar. The software framework incorporates the implementation of the proposed extension of the logic, and builds upon some of the ideas for further work expressed in the original article on Types-To-Sets by Ondřej Kunčar and Andrei Popescu and the subsequent article Smooth Manifolds and Types to Sets for Linear Algebra in Isabelle/HOL that was written by Fabian Immler and Bohua Zhan and published in the proceedings of the International Conference on Certified Programs and Proofs in 2019.
BSD License

Change history

[2021-11-15] integration with SpecCheck (revision 61e152c118d4)


Theories of Types_To_Sets_Extension