Translating dependency into parametricity
Abadi et al. introduced the dependency core calculus (DCC) as a unifying framework to study many important program analyses such as binding time, information flow, slicing, and function call tracking. DCC uses a lattice of monads and a nonstandard typing rule for their associated bind operations to describe the dependency of computations in a program. Abadi et al. proved a noninterference theorem that establishes the correctness of DCC's type system and thus the correctness of the type systems for the analyses above. In this paper, we study the relationship between DCC and the Girard-Reynolds polymorphic lambda calculus (System F). We encode the recursion-free fragment of DCC into F via a type-directed translation. Our main theoretical result is that, following from the correctness of the translation, the parametricity theorem for F implies the noninterference theorem for DCC. In addition, the translation provides insights into DCC's type system and suggests implementation strategies of dependency calculi in polymorphic languages.
translation dependency parametricity dcc information flow monads noninterference polymorphism lambda calculus languages decurity security logical relations protection contexts haskell