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Semantics of Mizar as an Isabelle Object Logic.

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Title: Semantics of Mizar as an Isabelle Object Logic.
Authors: Kaliszyk, Cezary1 cezary.kaliszyk@uibk.ac.at, Pąk, Karol2 pakkarol@uwb.edu.pl
Source: Journal of Automated Reasoning. Oct2019, Vol. 63 Issue 3, p557-595. 39p.
Subjects: Semantics, Libraries, Manifolds (Engineering), Programming languages, Automation
Abstract: We formally define the foundations of the Mizar system as an object logic in the Isabelle logical framework. For this, we propose adequate mechanisms to represent the various components of Mizar. We express Mizar types in a uniform way, provide a common type intersection operation, allow reasoning about type inhabitation, and develop a type inference mechanism. We provide Mizar-like definition mechanisms which require the same proof obligations and provide same derived properties. Structures and set comprehension operators can be defined as definitional extensions. Re-formalized proofs from various parts of the Mizar Library show the practical usability of the specified foundations. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 138341460
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Semantics of Mizar as an Isabelle Object Logic.
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  Data: <searchLink fieldCode="AR" term="%22Kaliszyk%2C+Cezary%22">Kaliszyk, Cezary</searchLink><relatesTo>1</relatesTo><i> cezary.kaliszyk@uibk.ac.at</i><br /><searchLink fieldCode="AR" term="%22Pąk%2C+Karol%22">Pąk, Karol</searchLink><relatesTo>2</relatesTo><i> pakkarol@uwb.edu.pl</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Automated+Reasoning%22">Journal of Automated Reasoning</searchLink>. Oct2019, Vol. 63 Issue 3, p557-595. 39p.
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  Data: <searchLink fieldCode="DE" term="%22Semantics%22">Semantics</searchLink><br /><searchLink fieldCode="DE" term="%22Libraries%22">Libraries</searchLink><br /><searchLink fieldCode="DE" term="%22Manifolds+%28Engineering%29%22">Manifolds (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Programming+languages%22">Programming languages</searchLink><br /><searchLink fieldCode="DE" term="%22Automation%22">Automation</searchLink>
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  Label: Abstract
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  Data: We formally define the foundations of the Mizar system as an object logic in the Isabelle logical framework. For this, we propose adequate mechanisms to represent the various components of Mizar. We express Mizar types in a uniform way, provide a common type intersection operation, allow reasoning about type inhabitation, and develop a type inference mechanism. We provide Mizar-like definition mechanisms which require the same proof obligations and provide same derived properties. Structures and set comprehension operators can be defined as definitional extensions. Re-formalized proofs from various parts of the Mizar Library show the practical usability of the specified foundations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Automated Reasoning is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s10817-018-9479-z
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        Text: English
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      – SubjectFull: Libraries
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      – SubjectFull: Manifolds (Engineering)
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      – SubjectFull: Programming languages
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      – SubjectFull: Automation
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      – TitleFull: Semantics of Mizar as an Isabelle Object Logic.
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              Text: Oct2019
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