"Higher-Order" Mathematics in B
Identifieur interne : 008974 ( Main/Merge ); précédent : 008973; suivant : 008975"Higher-Order" Mathematics in B
Auteurs : Jean-Raymond Abrial ; Dominique Cansell [France] ; Guy LaffitteSource :
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Abstract
In this paper, we investigate the possibility to mechanize the proof of some real complex mathematical theorems in B [1]. For this, we propose a little structure language which allows one to encode mathematical structures and their accompanying theorems. A little tool is also proposed, which translates this language into B, so that Atelier B, the tool associated with B, can be used to prove the theorems. As an illustrative example, we eventually (mechanically) prove the Theorem of Zermelo [6] stating that any set can be well-ordered. The present study constitutes a complete reshaping of an earlier (1993) unpublished work (referenced in [4]) done by two of the authors, where the classical theorems of Haussdorf and Zorn were also proved.
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<author><name sortKey="Abrial, Jean Raymond" sort="Abrial, Jean Raymond" uniqKey="Abrial J" first="Jean-Raymond" last="Abrial">Jean-Raymond Abrial</name>
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<author><name sortKey="Cansell, Dominique" sort="Cansell, Dominique" uniqKey="Cansell D" first="Dominique" last="Cansell">Dominique Cansell</name>
<affiliation><country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="region" nuts="2">Lorraine (région)</region>
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<orgName type="team" n="7">Mosel (Loria)</orgName>
<orgName type="lab">Laboratoire lorrain de recherche en informatique et ses applications</orgName>
<orgName type="university">Université de Lorraine</orgName>
<orgName type="EPST">Centre national de la recherche scientifique</orgName>
<orgName type="EPST">Institut national de recherche en informatique et en automatique</orgName>
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<author><name sortKey="Laffitte, Guy" sort="Laffitte, Guy" uniqKey="Laffitte G" first="Guy" last="Laffitte">Guy Laffitte</name>
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<front><div type="abstract" xml:lang="en" wicri:score="1528">In this paper, we investigate the possibility to mechanize the proof of some real complex mathematical theorems in B [1]. For this, we propose a little structure language which allows one to encode mathematical structures and their accompanying theorems. A little tool is also proposed, which translates this language into B, so that Atelier B, the tool associated with B, can be used to prove the theorems. As an illustrative example, we eventually (mechanically) prove the Theorem of Zermelo [6] stating that any set can be well-ordered. The present study constitutes a complete reshaping of an earlier (1993) unpublished work (referenced in [4]) done by two of the authors, where the classical theorems of Haussdorf and Zorn were also proved.</div>
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