3 research outputs found
Proving Noninterference by a Fully Complete Translation to the Simply Typed lambda-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 lambda-calculus, using a
fully complete translation to the simply typed lambda-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.Comment: 31 page
Modalities, Cohesion, and Information Flow
It is informally understood that the purpose of modal type constructors in
programming calculi is to control the flow of information between types. In
order to lend rigorous support to this idea, we study the category of
classified sets, a variant of a denotational semantics for information flow
proposed by Abadi et al. We use classified sets to prove multiple
noninterference theorems for modalities of a monadic and comonadic flavour. The
common machinery behind our theorems stems from the the fact that classified
sets are a (weak) model of Lawvere's theory of axiomatic cohesion. In the
process, we show how cohesion can be used for reasoning about multi-modal
settings. This leads to the conclusion that cohesion is a particularly useful
setting for the study of both information flow, but also modalities in type
theory and programming languages at large
Proving Noninterference by a Fully Complete Translation to the Simply Typed lambda-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 lambda-calculus, using a
fully complete translation to the simply typed lambda-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