Higher-Order Tarski Grothendieck as a Foundation for Formal Proof
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F19%3A00337659" target="_blank" >RIV/68407700:21730/19:00337659 - isvavai.cz</a>
Result on the web
<a href="https://drops.dagstuhl.de/opus/volltexte/2019/11064/" target="_blank" >https://drops.dagstuhl.de/opus/volltexte/2019/11064/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.ITP.2019.9" target="_blank" >10.4230/LIPIcs.ITP.2019.9</a>
Alternative languages
Result language
angličtina
Original language name
Higher-Order Tarski Grothendieck as a Foundation for Formal Proof
Original language description
We formally introduce a foundation for computer verified proofs based on higher-order Tarski-Grothendieck set theory. We show that this theory has a model if a 2-inaccessible cardinal exists. This assumption is the same as the one needed for a model of plain Tarski-Grothendieck set theory. The foundation allows the co-existence of proofs based on two major competing foundations for formal proofs: higher-order logic and TG set theory. We align two co-existing Isabelle libraries, Isabelle/HOL and Isabelle/Mizar, in a single foundation in the Isabelle logical framework. We do this by defining isomorphisms between the basic concepts, including integers, functions, lists, and algebraic structures that preserve the important operations. With this we can transfer theorems proved in higher-order logic to TG set theory and vice versa. We practically show this by formally transferring Lagrange's four-square theorem, Fermat 3-4, and other theorems between the foundations in the Isabelle framework.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
R - Projekt Ramcoveho programu EK
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
10th International Conference on Interactive Theorem Proving (ITP 2019)
ISBN
978-3-95977-122-1
ISSN
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e-ISSN
1868-8969
Number of pages
16
Pages from-to
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Publisher name
Schloss Dagstuhl - Leibniz Center for Informatics
Place of publication
Wadern
Event location
Portland
Event date
Sep 10, 2019
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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