Proving Noninterference by a Fully Complete Translation to the Simply Typed Λ-calculus

Tse and Zdancewic have formalized the notion of noninterference for Abadi et al.’s DCC in terms of logical relations and given a proof of noninterference by reduction to parametricity of System F. Unfortunately, their proof contains errors in a key lemma that their translation from DCC to System F preserves the logical relations defined for both calculi. In fact, we have found a counterexample for it. In this article, instead of DCC, we prove noninterference for sealing calculus, a new variant of DCC, by reduction to the basic lemma of a logical relation for the simply typed λ-calculus, using a fully complete translation to the simply typed λ-calculus. Full completeness plays an important role in showing preservation of the two logical relations through the translation. Also, we investigate relationship among sealing calculus, DCC, and an extension of DCC by Tse and Zdancewic and show that the first and the last of the three are equivalent.