Logical Relations for Session-Typed Concurrency
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Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical relations. Logical relations only recently were adopted for session types – but exclusively for terminating languages. This paper scales logical relations to general recursive session types. It develops a logical relation for progress-sensitive noninterference (PSNI) for intuitionistic linear logic session types (ILLST), tackling the challenges non-termination and concurrency pose, and shows that logical equivalence is sound and complete with regard to closure of weak bisimilarity under parallel composition, using a biorthogonality argument. A distinguishing feature of the logical relation is its stratification with an observation index (as opposed to a step or unfolding index), a crucial shift to make the logical relation closed under parallel composition in a concurrent setting. To demonstrate practicality of the logical relation, the paper develops an information flow control (IFC) refinement type system for ILLST, with support of secrecy-polymorphic processes, and shows that well-typed programs are self-related by the logical relation and thus enjoy PSNI. The refinement type system has been implemented in a type checker, featuring local security theories to support secrecy-polymorphic processes.
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