# Mizar

> proof assistant

**Wikidata**: [Q1609529](https://www.wikidata.org/wiki/Q1609529)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Mizar_system)  
**Source**: https://4ort.xyz/entity/mizar

## Summary
Mizar is a proof assistant and declarative programming language designed for automated theorem proving and the formalization of mathematics. Originally created in 1973 by Polish mathematician Andrzej Trybulec, the system is used to communicate instructions to machines for verifying mathematical proofs. It is recognized for its weak typing discipline and its association with the Mizar Mathematical Library.

## Key Facts
- **Inception:** The Mizar system was created in **1973**.
- **Creator:** It was designed by **Andrzej Trybulec**, a Polish mathematician and computer scientist (1941–2013).
- **Primary Use:** The system is utilized for **automated theorem proving**.
- **Instance Type:** Mizar is classified as a **proof assistant**, **software**, and a **programming language**.
- **Programming Paradigm:** It follows a **declarative programming** paradigm.
- **Typing Discipline:** The system employs **weak typing**.
- **License:** As of February 20, 2023, Mizar is distributed under the **GNU General Public License, version 3.0**.
- **Origin:** The project hails from **Poland**.
- **Influences:** The system's design was influenced by **Automath**.
- **File Formats:** It utilizes specific formats known as **Mizar article** and **Mizar article (with rem)** for reading and writing data.

## FAQs
### Q: What is the primary function of Mizar?
A: Mizar functions as a proof assistant and declarative programming language. It is designed for automated theorem proving, allowing users to formalize mathematics and verify proofs.

### Q: Who created Mizar and when?
A: Mizar was designed by the Polish mathematician and computer scientist Andrzej Trybulec in 1973.

### Q: What are the technical characteristics of the Mizar language?
A: Mizar is a declarative language that features weak typing. It is influenced by Automath and serves as both software and a formal language for mathematical communication.

### Q: Is Mizar free to use?
A: Yes, Mizar is released under the GNU General Public License, version 3.0. This licensing status became effective on February 20, 2023.

## Why It Matters
Mizar serves as a significant tool in the intersection of mathematics and computer science, specifically within the realm of formal logic and automated reasoning. By functioning as a proof assistant, it addresses the critical need for rigor in mathematical publications, allowing for the mechanical verification of proofs that might be too complex or lengthy for reliable human checking alone. Its inception in 1973 places it among the earlier efforts in this field, stemming from the work of Andrzej Trybulec and the academic community in Poland.

The system matters because it bridges the gap between abstract mathematical logic and practical software implementation. As a declarative programming language with a distinct "weak typing" discipline, it offers a specific approach to defining objects and proofs that differs from imperative programming languages. Its influence by Automath connects it to the historical lineage of formal verification languages. The continued maintenance and licensing under the GNU GPL (as of 2023) indicate its ongoing relevance and accessibility to researchers and developers working on formalizing mathematics and creating verified software.

## Notable For
- **Pioneering Longevity:** Originating in 1973, Mizar is a long-standing project in the field of automated theorem proving.
- **Unique Architecture:** It is a distinct combination of a proof assistant and a declarative programming language with weak typing.
- **Foundational Influence:** The system was influenced by Automath, a pioneer in formal mathematics, and has itself influenced the structure of formal mathematical libraries.
- **Open Source Transition:** The system notably adopted the GNU General Public License v3.0 in February 2023, making it freely available for modification and distribution.
- **Academic Roots:** It is deeply tied to Polish academia through its creator, Andrzej Trybulec, and its hosting at the University of Białystok (implied by the domain uwb.edu.pl).

## Body
### Origin and History
The Mizar system was initiated in **1973** under the guidance of **Andrzej Trybulec**, a Polish mathematician and university teacher. Trybulec, who lived from 1941 to 2013, is credited as the sole designer of the system. The project is a product of **Poland** and has developed into a comprehensive environment for formalizing mathematics. The system's development was influenced by **Automath**, an earlier language for writing mathematical proofs.

### Technical Overview
Mizar is categorized as a **programming language**, **software**, and **proof assistant**. Its programming paradigm is defined as **declarative programming**, meaning it describes the logic of computation rather than the control flow. Unlike many modern functional programming languages, Mizar utilizes **weak typing**.

The primary application of Mizar is **automated theorem proving**. The system processes specific file formats to function, specifically reading and writing **Mizar article** files, which may include variations with "rem" (remark) extensions.

### Availability and Resources
The system is accessible via its official website at `http://mizar.uwb.edu.pl/` (English language version). As of **February 20, 2023**, the software has been licensed under the **GNU General Public License, version 3.0**. The system maintains a presence across multiple Wikipedia languages, including German, English, French, Hebrew, Italian, Japanese, Polish, and Russian. A visual representation of the system is available through the Mizar MathWiki screenshot hosted on Wikimedia Commons.

## References

1. Freebase Data Dumps. 2013