# Towards a Mizar environment for Isabelle: foundations and language

@article{Kaliszyk2016TowardsAM, title={Towards a Mizar environment for Isabelle: foundations and language}, author={C. Kaliszyk and Karol Pak and Josef Urban}, journal={Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs}, year={2016} }

In this paper we explore the possibility of emulating the Mizar environment as close as possible inside the Isabelle logical framework. We introduce adaptations to the Isabelle/FOL object logic that correspond to the logic of Mizar, as well as Isar inner syntax notations that correspond to these of the Mizar language. We show how Isabelle types can be used to differentiate between the syntactic categories of the Mizar language, such as sets and Mizar types including modes and attributes, and…

## 23 Citations

Presentation and Manipulation of Mizar Properties in an Isabelle Object Logic

- Computer ScienceCICM
- 2017

This paper discusses various elements of the Mizar language and the possible ways how these can be represented in the Isabelle framework in order to allow a suitable way of working in typed set theory.

Isabelle Import Infrastructure for the Mizar Mathematical Library

- Computer ScienceCICM
- 2018

An infrastructure that allows importing an initial part of the Mizar Mathematical Library into the Isabelle/Mizar object logic is presented and it is shown that the imported 100 articles give rise to a usable Isabelle environment.

Mizar Set Comprehension in Isabelle Framework

- Computer Science, MathematicsFedCSIS
- 2018

The progress in the development of the Isabelle/Mizar project whose main goal is independent cross-verification of the MML in Isabelle is presented and an infrastructure that provides a more elegant and recursive approach to construct and to provide the main property of set comprehension operators is proposed.

Semantics of Mizar as an Isabelle Object Logic

- Computer ScienceJournal of Automated Reasoning
- 2018

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…

Progress in the independent certification of mizar mathematical library in isabelle

- Computer Science, Mathematics2017 Federated Conference on Computer Science and Information Systems (FedCSIS)
- 2017

This paper improves the mechanism for defining Mizar structures and shows that it permits simpler validation of proof developments involving such objects and performs a complete translation of the Mizar net of basic algebraic structures including their attributes and certify all the corresponding proofs in Isabelle.

Isabelle Formalization of Set Theoretic Structures and Set Comprehensions

- Computer ScienceMACIS
- 2017

This paper reformalize a number of Mizar definitions and theorems related to structures and set comprehensions, including both mathematical and programming language examples: groups, machines and properties of computer memory states.

A Guide to the Mizar Soft Type System

- Computer Science
- 2016

The soft-typing mechanisms of Mizar have been actively used in MML already before 1990, i.e., before languages like Haskell started to be developed and provided motivation for the recent soft-TYping (“type-class”) mechanisms in systems like Coq and Isabelle.

The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar

- Computer ScienceJournal of Automated Reasoning
- 2017

This paper shows the process of forming this library, the evolution of its design principles, and also presents some data showing its current use with the modern version of the Mizar proof checker, but also as a rich corpus of semantically linked mathematical data.

Combining the Syntactic and Semantic Representations of Mizar Proofs

- Computer Science2018 Federated Conference on Computer Science and Information Systems (FedCSIS)
- 2018

This article shows that it can simultaneously maintain the richness of the language and provide access to the derived proof information and discusses how such combined information closer corresponds to that present in other proof assistant languages, for example that of Isabelle /Isar.

Interactive Theorem Proving

- Computer ScienceLecture Notes in Computer Science
- 2017

The metaprogramming language currently in use in Lean, a new open source theorem prover that is designed to bridge the gap between interactive use and automation, is described and evidence is provided to show that the implementation is performant, and that it provides a convenient and flexible way of writing not only small-scale interactive tactics, but also more substantial kinds of automation.

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