The Divergence of the Sum of Prime Reciprocals

Carneiro, Mario

doi:10.2478/forma-2022-0015

Cited by 2 publications

(1 citation statement)

References 4 publications

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“…Luckily, it is possible to obtain a membership, but the price of admission is that one has to write a Mizar article őrst. Thus, for this project the author contributed an article regarding the divergence of the sum of prime reciprocals [5].…”

Section: Introductionmentioning

confidence: 99%

Reimplementing Mizar in Rust

Carneiro

2024

Preprint

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This paper describes a new open-source proof processing tool, \texttt{mizar-rs}, a wholesale reimplementation of the Mizar proof system, written in Rust. In particular, the main Mizar processing tool \texttt{verifier} is implemented, which can be used to verify the Mizar Mathematical Library (MML). This is to our knowledge the first and only external implementation of the system. We have used this to verify the entire MML in 11.8 minutes on 8 cores, a 4.8$\times$ speedup over the original Pascal implementation. Since Mizar is not designed to have a small trusted core, checking Mizar proofs entails following Mizar closely, so our ability to detect bugs is limited. Nevertheless, we were able to find multiple memory errors, four soundness bugs in the original (which were not being exploited in MML), in addition to one non-critical bug which was being exploited in 46 different MML articles. We hope to use this checker as a base for proof export tooling, as well as revitalizing development of the language.

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Section: Introductionmentioning

confidence: 99%

Reimplementing Mizar in Rust

Carneiro

2024

Preprint

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MMLKG: Knowledge Graph for Mathematical Definitions, Statements and Proofs

Tomaszuk,

Szeremeta,

Korniłowicz

2023

Sci Data

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Nowadays, Knowledge Graphs (KGs) are important and developing in different areas. However, there is a lack of genuinely interoperable datasets representing mathematics that allow for information exchange between datasets in the Web ecosystem. In this paper, we address this matter based on the Mizar Mathematical Library (MML), a collection of articles written in the Mizar language. MML includes definitions and theorems with proofs to which authors can easily refer from newly written Mizar articles. However, extracting information directly from Mizar scripts by external projects is not very straightforward. Therefore, we propose a new data storage and retrieval approach based on the Knowledge Organization System (KOS) model and the KG concept that provides a way to organize and access knowledge. We present Mizar Mathematical Library Knowledge Graph (MMLKG), a thesaurus for describing mathematical objects. MMLKG supports semantic interoperability and allows linking data from different sources, e.g., Wikidata. Moreover, it satisfies the FAIR data principles. The data is publicly available via a Cypher endpoint.

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The Divergence of the Sum of Prime Reciprocals

Abstract: Summary This is Erdős’s proof of the divergence of the sum of prime reciprocals, using the Mizar system [2], [3], as reported in “Proofs from THE BOOK” [1].

Cited by 2 publications

References 4 publications

Reimplementing Mizar in Rust

Reimplementing Mizar in Rust

MMLKG: Knowledge Graph for Mathematical Definitions, Statements and Proofs

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