• Corpus ID: 172375

A Guide to the Mizar Soft Type System

@inproceedings{Naumowicz2016AGT,
  title={A Guide to the Mizar Soft Type System},
  author={Adam Naumowicz and Josef Urban},
  year={2016}
}
Introduction Mizar [1, 3] is in a way both typed and untyped. In a foundational sense, Mizar is based on untyped set theory. The set-theoretical world initially consists of many objects of “just one type”. However, the objects can have various properties (a number, ordinal number, complex number, Conway number, a relation, function, complex function, complex matrix), however none of them is considered to be of “foundational importance”, and all these properties are treated as equal “adjectives… 

References

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TLDR
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.
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TLDR
A survey of the most important Mizari¾?features that distinguish it from other popular proof checkers is given and most important current trends and lines of development that go beyond the state-of-the-art system are described.
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TLDR
This paper presents a translation of the Mizar library into the OMDoc format (Open Mathematical Documents), an XML-based representation format for mathematical knowledge, and exemplifies interoperability by indexing the translated library in the MathWebSearch engine, which provides an “applicable theorem search” service (almost) out of the box.
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TLDR
The implementation of the MPTP system is described, which makes the largest existing corpus of formalized mathematics available to theorem provers, and the design and structure of the system, the main problems encountered in this kind of system, their solutions, current limitations, and planned extensions.
Reconstruction of the Mizar Type System in the HOL Light System
TLDR
The basic idea is to represent Mizar types as predicates and express the dynamic part of the Mizar type system as proved theorems in HOL Light and the reconstruction was partialy implemented.
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This special issue is dedicated to works related to Mizar, the theorem proving project started by Andrzej Trybulec in the 1970s, and other automated proof checking systems used for formalizing
ENHANCED PROCESSING OF ADJECTIVES IN MIZAR
TLDR
An enhancement of the Mizar proof checker is described which enables a more complete automation of notions encoded as adjectives, and concerns the Equalizer – Mizar’s module responsible for handling equality.