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Translating specifications from nominal logic to CIC with the theory of contexts

Authors:

Marino Miculan,

Ivan Scagnetto,

Furio HonsellAuthors Info & Claims

MERLIN '05: Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding

Pages 41 - 49

https://doi.org/10.1145/1088454.1088460

Published: 27 September 2005 Publication History

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Abstract

We study the relation between Nominal Logic and the Theory of Contexts, two approaches for specifying and reasoning about datatypes with binders. We consider a natural-deduction style proof system for intuitionistic nominal logic, called NINL, inspired by a sequent proof system recently proposed by J. Cheney. We present a translation of terms, formulas and judgments of NINL, into terms and propositions of CIC, via a weak HOAS encoding. It turns out that the (translation of the) axioms and rules of NINL are derivable in CIC extended with the Theory of Contexts (CIC/ToC), and that in the latter we can prove also sequents which are not derivable in NINL. Thus, CIC/ToC can be seen as a strict extension of NINL.

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M. P. Fiore, G. D. Plotkin, and D. Turi. Abstract syntax and variable binding. In G. Longo, editor, Proc. 14th LICS, pages 193--202, Trento, Italy, 1999. IEEE Computer Society Press.]]

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Ciaffaglione AScagnetto IFelty APientka B(2014)Internal Adequacy of Bookkeeping in CoqProceedings of the 2014 International Workshop on Logical Frameworks and Meta-languages: Theory and Practice10.1145/2631172.2631180(1-8)Online publication date: 17-Jul-2014
https://dl.acm.org/doi/10.1145/2631172.2631180
Cheney J(2014)A simple sequent calculus for nominal logicJournal of Logic and Computation10.1093/logcom/exu02426:2(699-726)Online publication date: 19-May-2014
https://doi.org/10.1093/logcom/exu024
Ciaffaglione AScagnetto I(2013)A weak HOAS approach to the POPLmark ChallengeElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.113.11113(109-124)Online publication date: 28-Mar-2013
https://doi.org/10.4204/EPTCS.113.11
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MERLIN '05: Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding

September 2005

72 pages

ISBN:1595930728

DOI:10.1145/1088454

Program Chair:
Randy Pollack
University of Edinburgh, UK

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 27 September 2005

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Ciaffaglione AScagnetto IFelty APientka B(2014)Internal Adequacy of Bookkeeping in CoqProceedings of the 2014 International Workshop on Logical Frameworks and Meta-languages: Theory and Practice10.1145/2631172.2631180(1-8)Online publication date: 17-Jul-2014
https://dl.acm.org/doi/10.1145/2631172.2631180
Cheney J(2014)A simple sequent calculus for nominal logicJournal of Logic and Computation10.1093/logcom/exu02426:2(699-726)Online publication date: 19-May-2014
https://doi.org/10.1093/logcom/exu024
Ciaffaglione AScagnetto I(2013)A weak HOAS approach to the POPLmark ChallengeElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.113.11113(109-124)Online publication date: 28-Mar-2013
https://doi.org/10.4204/EPTCS.113.11
Cheney J(2012)A dependent nominal type theoryLogical Methods in Computer Science10.2168/LMCS-8(1:8)20128:1Online publication date: 20-Feb-2012
https://doi.org/10.2168/LMCS-8(1:8)2012
Pucella R(2005)SIGACT news logic column 14ACM SIGACT News10.1145/1107523.110753736:4(47-69)Online publication date: 1-Dec-2005
https://dl.acm.org/doi/10.1145/1107523.1107537

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Permissive-nominal logic: First-order logic over nominal terms and sets

Permissive-nominal logic

A Full Formalization of SLD-Resolution in the Calculus of Inductive Constructions

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