On the structure of Mizar types

@article{Bancerek2003OnTS,
  title={On the structure of Mizar types},
  author={Grzegorz Bancerek},
  journal={Electron. Notes Theor. Comput. Sci.},
  year={2003},
  volume={85},
  pages={69-85}
}
  • G. Bancerek
  • Published 1 September 2003
  • Computer Science, Mathematics
  • Electron. Notes Theor. Comput. Sci.
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46 Citations
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References

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An Overview of the MIZAR Project
TLDR
The Mizar project is a long-term eeort aimed at developing software to support a working mathematician in preparing papers by designing a language for writing formal mathematics based on the Tarski-Grothendieck set theory.
Development of the theory of continuous lattices in Mizar
TLDR
This paper reports on Mizar formalization of the theory of continuous lattices included in the A Compendium of Continuous Lattices, revealing that the substantial element of the convenience is the incorporation of computer algebra into Mizar system.
Commutative Algebra in the Mizar System
We report on the development of algebra in the Mizar system. This includes the construction of formal multivariate power series and polynomials as well as the definition of ideals up to a proof of…
A Compendium of Continuous Lattices in MIZAR
TLDR
This paper reports on the MIZAR formalization of the theory of continuous lattices as presented in Gierz et al.: A Compendium of Continuous Lattices, 1980, which is the most sizable effort aimed at mechanically checking some substantial and relatively recent field of advanced mathematics.
Translating Mizar for First Order Theorem Provers
  • J. Urban
  • Mathematics, Computer Science
    MKM
  • 2003
The constructor system of the Mizar proof checking system is explained here on examples from Mizar articles, and its translation to untyped first-order syntax is described and discussed. This makes…
On Equivalents of Well-foundedness - An experiment in Mizar
Four statements equivalent to well-foundedness (well-founded induction, existence of recursively deened functions, uniqueness of recursively deened functions , and absence of descending !-chains)…
Comparing Mathematical Provers
TLDR
This work compares fifteen systems for the formalizations of mathematics with the computer based on the size of their library, the strength of their logic and their level of automation.
Algebraic Requirements for the Construction of Polynomial Rings
The Mizar construction of polynomials with an arbitrary number of variables has been described in [8]. In this paper, we present an alternative approach for formalizing polynomials with one variable.…
On Equivalents of Well-Foundedness
TLDR
Four statements equivalent to well-foundedness have been proved in Mizar and the proofs mechanically checked for correctness and stressed the importance of a systematic development of a mechanized data base for mathematics in the spirit of the QED Project.
Lim-inf Convergence and its Compactness
We describe the Mizar formalization of the proof of compactness of lim-inf convergence given in (W33) according to (C CL). Lim-inf convergence formalized in (W28) is a Moore-Smith convergence…
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