Equivalence-Preserving Compilation

Language-based security relies on the assumption that all potential attacks are bound by the rules of the language in question. When programs are compiled into a different language, this is true only if the translation process preserves observational equivalence. We investigate the problem of fully abstract compilation, i.e., compilation that both preserves and reflects observational equivalence. We give a fully abstract CPS-transformation for the polymorphic λ-calculus with existential and recursive types, and also prove typed closure conversion to be fully abstract. The CPStransformation differs from the standard account in that it does not use a global answer type. Our proofs use operational techniques in the form of a stepindexed logical relation and the construction of certain wrapper terms that “back-translate” from target values to source values. The approach is more general than previous work on fully abstract CPS-conversion since it is not restricted to a simply-typed setting but applies to a language with polymorphic and existential types. Moreover, we rely entirely on parametricity and do not require additional type system features such as linearity to be present in the target language. We are not aware of any previous results on fully abstract closure conversion.