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Semantics of Mizar as an Isabelle Object Logic

  • Cezary Kaliszyk
  • Karol Pąk
Open Access
Article

Abstract

We formally define the foundations of the Mizar system as an object logic in the Isabelle logical framework. For this, we propose adequate mechanisms to represent the various components of Mizar. We express Mizar types in a uniform way, provide a common type intersection operation, allow reasoning about type inhabitation, and develop a type inference mechanism. We provide Mizar-like definition mechanisms which require the same proof obligations and provide same derived properties. Structures and set comprehension operators can be defined as definitional extensions. Re-formalized proofs from various parts of the Mizar Library show the practical usability of the specified foundations.

Notes

Acknowledgements

Open access funding provided by University of Innsbruck and Medical University of Innsbruck. We would like to thank the anonymous reviewers, as well as Josef Urban, Chad Brown, and Julian Parsert for their comments on the previous versions of this paper. This work has been supported by the European Research Council (ERC) Grant No. 714034 SMART, OeAD Scientific & Technological Cooperation with Poland grant, and the PolishNational Science Center granted by decision noDEC-2015/19/D/ST6/01473.

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Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of InnsbruckInnsbruckAustria
  2. 2.Institute of InformaticsUniversity of BiałystokBiałystokPoland

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