# The Mizar Mathematical Library in OMDoc: Translation and Applications

@article{Iancu2012TheMM, title={The Mizar Mathematical Library in OMDoc: Translation and Applications}, author={Mihnea Iancu and Michael Kohlhase and Florian Rabe and Josef Urban}, journal={Journal of Automated Reasoning}, year={2012}, volume={50}, pages={191-202} }

The Mizar Mathematical Library is one of the largest libraries of formalized and mechanically verified mathematics. Its language is highly optimized for authoring by humans. As in natural languages, the meaning of an expression is influenced by its (mathematical) context in a way that is natural to humans, but harder to specify for machine manipulation. Thus its custom file format can make the access to the library difficult. Indeed, the Mizar system itself is currently the only system that can…

## 52 Citations

Syntactic-Semantic Form of Mizar Articles

- Computer ScienceITP
- 2021

This paper proposes a new XML-based format which combines both syntactic and semantic data and is intended to facilitate various applications of the Mizar library requiring fullest possible information to be retrieved from the formalization files.

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.

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.

Towards a Mizar environment for Isabelle: foundations and language

- Computer ScienceCPP
- 2016

It is shown 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 how they interact with the basic constructs of the Tarski-Grothendieck set theory.

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.

Towards Flexiformal Mathematics

- Computer Science
- 2017

Flexiformalizing mathematics is proposed which addresses the bottlenecks discussed above in two ways: first, by allowing content of flexible formality, it minimizes the starting cost of flexiformalization compared to formalization and second, by co-representing the narration, structure and meaning of mathematical knowledge it forms a basis for not only machine processing but also for building practical, human-oriented applications.

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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