• 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.
Mizar: State-of-the-art and Beyond
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
The presented theory is an approach to the structure of Mizar types as a sup-semilattice with widening (subtyping) relation as the order.
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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
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TLDR
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