A Brief Overview of Mizar

Naumowicz, Adam; Korniłowicz, Artur

doi:10.1007/978-3-642-03359-9_5

Cited by 47 publications

(23 citation statements)

References 11 publications

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“…1 [33,27] has for goal that the proofs be close to the mathematical vernacular, so that mathematicians may easily use it. This makes the proofs longer but somehow more readable.…”

Section: Mizar Mizarmentioning

confidence: 99%

Coquelicot: A User-Friendly Library of Real Analysis for Coq

2014

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Abstract. Real analysis is pervasive to many applications, if only because it is a suitable tool for modeling physical or socio-economical systems. As such, its support is warranted in proof assistants, so that the users have a way to formally verify mathematical theorems and correctness of critical systems. The Coq system comes with an axiomatization of standard real numbers and a library of theorems on real analysis. Unfortunately, this standard library is lacking some widely used results. For instance, power series are not developed further than their definition. Moreover, the definitions of integrals and derivatives are based on dependent types, which make them especially cumbersome to use in practice. To palliate these inadequacies, we have designed a userfriendly library: Coquelicot. An easier way of writing formulas and theorem statements is achieved by relying on total functions in place of dependent types for limits, derivatives, integrals, power series, and so on. To help with the proof process, the library comes with a comprehensive set of theorems that cover not only these notions, but also some extensions such as parametric integrals, two-dimensional differentiability, asymptotic behaviors. It also offers some automations for performing differentiability proofs. Moreover, Coquelicot is a conservative extension of Coq's standard library and we provide correspondence theorems between the two libraries. We have exercised the library on several use cases: in an exam at university entry level, for the definitions and properties of Bessel functions, and for the solution of the one-dimensional wave equation.

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“…1 [33,27] has for goal that the proofs be close to the mathematical vernacular, so that mathematicians may easily use it. This makes the proofs longer but somehow more readable.…”

Section: Mizar Mizarmentioning

confidence: 99%

Coquelicot: A User-Friendly Library of Real Analysis for Coq

2014

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“…MIZAR [11,23] is a proof assistant used for computerized verification of mathematical proofs. MIZAR is also a common name for the components of the system: a formal language derived from the mathematical vernacular and dozens of computer programs responsible for formal verification, optimization of proofs [24,25].…”

Section: About Mizarmentioning

confidence: 99%

“…So far, in the MIZAR system [11,23], definitional expansions were understood as a method of leading reasonings following natural deduction in the Jaśkowski style, with so called fixed variables (local constants) [17].…”

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confidence: 99%

Definitional Expansions in Mizar

Korniłowicz

2015

J Autom Reasoning

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The MIZAR VERIFIER uses definitional expansions for controlling proof structures. In this paper we propose another use of definitional expansions-enriching verified inferences by expansions of definitions of formulae included in the inferences and increasing the number of premises accessible by CHECKER. This introduces more knowledge to the reasoning, which helps to draw more conclusions. Some statistics about influence of such expansions on the MIZAR MATHEMATICAL LIBRARY are presented.

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“…Introducing new reductions to the already stored Mizar articles can possibly produce irrelevant references and unnecessary proof steps. Then, revisions of articles with tools like Relprem and Reliters [6,9] should be performed.…”

Section: Conclusion and Further Workmentioning

confidence: 99%