Article

Embedding pure type systems in the lambda-pi-calculus modulo

Authors:

Denis Cousineau,

Gilles DowekAuthors Info & Claims

TLCA'07: Proceedings of the 8th international conference on Typed lambda calculi and applications

Pages 102 - 117

Published: 26 June 2007 Publication History

Abstract

The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension is surprisingly expressive and, in particular, that all functional Pure Type Systems, such as the system F, or the Calculus of Constructions, can be embedded in it. And, moreover, that this embedding is conservative under termination hypothesis.

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Cited By

Rabe F(2018)A Modular Type Reconstruction AlgorithmACM Transactions on Computational Logic10.1145/323469319:4(1-43)Online publication date: 8-Dec-2018
https://dl.acm.org/doi/10.1145/3234693
Chihani ZMiller DRenaud F(2017)A Semantic Framework for Proof EvidenceJournal of Automated Reasoning10.1007/s10817-016-9380-659:3(287-330)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10817-016-9380-6
Miller D(2017)Proof checking and logic programmingFormal Aspects of Computing10.1007/s00165-016-0393-z29:3(383-399)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s00165-016-0393-z
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Published In

cover image Guide Proceedings

TLCA'07: Proceedings of the 8th international conference on Typed lambda calculi and applications

June 2007

396 pages

ISBN:9783540732273

Editor:
Simona Ronchi Della Rocca
Università di Torino, Dipartimento di Informatica, Torino, Italy

Sponsors

GDR Informatique Mathématique
ENSIEE: école Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
Centre National de la Recherche Scientifique
CNAM: Conservatoire des Arts et Métiers
INRIA: Institut Natl de Recherche en Info et en Automatique

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 26 June 2007

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Cited By

Rabe F(2018)A Modular Type Reconstruction AlgorithmACM Transactions on Computational Logic10.1145/323469319:4(1-43)Online publication date: 8-Dec-2018
https://dl.acm.org/doi/10.1145/3234693
Chihani ZMiller DRenaud F(2017)A Semantic Framework for Proof EvidenceJournal of Automated Reasoning10.1007/s10817-016-9380-659:3(287-330)Online publication date: 1-Oct-2017
https://dl.acm.org/doi/10.1007/s10817-016-9380-6
Miller D(2017)Proof checking and logic programmingFormal Aspects of Computing10.1007/s00165-016-0393-z29:3(383-399)Online publication date: 1-May-2017
https://dl.acm.org/doi/10.1007/s00165-016-0393-z
Chihani ZMiller D(2016)Proof Certificates for Equality ReasoningElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2016.06.007323:C(93-108)Online publication date: 11-Jul-2016
https://dl.acm.org/doi/10.1016/j.entcs.2016.06.007
Miller D(2015)Proof Checking and Logic ProgrammingRevised Selected Papers of the 25th International Symposium on Logic-Based Program Synthesis and Transformation - Volume 952710.1007/978-3-319-27436-2_1(3-17)Online publication date: 13-Jul-2015
https://dl.acm.org/doi/10.1007/978-3-319-27436-2_1
Honsell FMomigliano APientka BPollack R(2013)25 years of formal proof culturesProceedings of the Eighth ACM SIGPLAN international workshop on Logical frameworks & meta-languages: theory & practice10.1145/2503887.2503896(37-42)Online publication date: 23-Sep-2013
https://dl.acm.org/doi/10.1145/2503887.2503896
Chihani ZMiller DRenaud F(2013)Foundational proof certificates in first-order logicProceedings of the 24th international conference on Automated Deduction10.1007/978-3-642-38574-2_11(162-177)Online publication date: 9-Jun-2013
https://dl.acm.org/doi/10.1007/978-3-642-38574-2_11
Dowek G(2012)A theory independent curry-de bruijn-howard correspondenceProceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II10.1007/978-3-642-31585-5_2(13-15)Online publication date: 9-Jul-2012
https://dl.acm.org/doi/10.1007/978-3-642-31585-5_2
Burel G(2011)Experimenting with deduction moduloProceedings of the 23rd international conference on Automated deduction10.5555/2032266.2032280(162-176)Online publication date: 31-Jul-2011
https://dl.acm.org/doi/10.5555/2032266.2032280
Burel G(2007)Unbounded proof-length speed-up in deduction moduloProceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic10.5555/2392389.2392436(496-511)Online publication date: 11-Sep-2007
https://dl.acm.org/doi/10.5555/2392389.2392436
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