A First-Order Representation of Pure Type Systems Using Superdeduction
Identifieur interne : 003F75 ( Main/Exploration ); précédent : 003F74; suivant : 003F76A First-Order Representation of Pure Type Systems Using Superdeduction
Auteurs : Guillaume Burel [France]Source :
English descriptors
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Abstract
Superdeduction is a formalism closely related to deduction modulo which permits to enrich a deduction system (especially a first-order one such as natural deduction or sequent calculus) with new inference rules automatically computed from the presentation of a theory. We give a natural encoding from every functional Pure Type System (PTS) into superdeduction by defining an appropriate first-order theory. We prove that this translation is correct and conservative, showing a correspondence between valid typing judgments in the PTS and provable sequents in the corresponding superdeductive system. As a byproduct, we also introduce the superdeductive sequent calculus for intuitionistic logic, which was until now only defined for classical logic. We show its equivalence with the superdeductive natural deduction. This implies that superdeduction can be easily used as a logical framework. These results lead to a better understanding of the implementation and the automation of proof search for PTS, as well as to more cooperation between proof assistants.
Url:
DOI: 10.1109/LICS.2008.22
Affiliations:
- France
- Grand Est, Lorraine (région)
- Nancy
- Institut national polytechnique de Lorraine, Université Nancy 2, Université de Lorraine
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Le document en format XML
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We give a natural encoding from every functional Pure Type System (PTS) into superdeduction by defining an appropriate first-order theory. We prove that this translation is correct and conservative, showing a correspondence between valid typing judgments in the PTS and provable sequents in the corresponding superdeductive system. As a byproduct, we also introduce the superdeductive sequent calculus for intuitionistic logic, which was until now only defined for classical logic. We show its equivalence with the superdeductive natural deduction. This implies that superdeduction can be easily used as a logical framework. These results lead to a better understanding of the implementation and the automation of proof search for PTS, as well as to more cooperation between proof assistants.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Nancy</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Burel, Guillaume" sort="Burel, Guillaume" uniqKey="Burel G" first="Guillaume" last="Burel">Guillaume Burel</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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