Departmental Papers (CIS)

Date of this Version


Document Type

Conference Paper


Jianzhou Zhao, Qi Zhang, and Steve Zdancewic. Relational Parametricity for Polymorphic Linear Lambda Calculus. In Proceedings of the Eighth ASIAN Symposium on Programming Languages and Systems (APLAS), 2010.

© ACM, 2010. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Proceedings of the Eighth ASIAN Symposium on Programming Languages and Systems , {(2010)} Email


This paper presents a novel syntactic logical relation for a polymorphic linear lambda-calculus that treats all types as linear and introduces the constructor ! to account for intuitionistic terms, and Foan extension of System F that uses kinds to distinguish linear from intuitionistic types. We define a logical relation for open values under both open linear and intuitionistic contexts, then extend it for open terms with evaluation and open relation substitutions. Relations that instantiate type quantifiers are for open terms and types. We demonstrate the applicability of this logical relation through its soundness with respect to contextual equivalence, along with free theorems for linearity that are difficult to achieve by closed logical relations. When interpreting types on only closed terms, the model defaults to a closed logical relation that is both sound and complete with respect to contextual equivalence and is sufficient to reason about isomorphisms of type encodings. All of our results have been mechanically verified in Coq.



Date Posted: 18 July 2012