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

Authors:
Marino Miculan;Ivan Scagnetto;Furio Honsell
Affiliations:
University of Udine, Udine, Italy;University of Udine, Udine, Italy;University of Udine, Udine, Italy
Venue:
Proceedings of the 3rd ACM SIGPLAN workshop on Mechanized reasoning about languages with variable binding
Year:
2005

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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.