Semantic Soundness for Language Interoperability

Programs are rarely implemented in a single language, and thus questions of type soundness should address not only the semantics of a single language, but how it interacts with others. Even between type-safe languages, disparate features can frustrate interoperability, as invariants from one language can easily be violated in the other. In their seminal 2007 paper, Matthews and Findler proposed a multi-language construction that augments the interoperating languages with a pair of boundaries that allow code from one language to be embedded in the other. While this technique has been widely applied, their syntactic source-level interoperability doesn't reflect practical implementations, where the behavior of interaction is only defined after compilation to a common target, and any safety must be ensured by target invariants or inserted target-level "glue code." In this paper, we present a novel framework for the design and verification of sound language interoperability that follows an interoperation-after-compilation strategy. Language designers specify what data can be converted between types of the two languages via a convertibility relation tau(A) similar to tau(B) ("tau(A) is convertible to tau(B)") and specify target-level glue code implementing the conversions. Then, by giving a semantic model of source-language types as sets of target-language terms, they can establish not only the meaning of the source types, but also soundness of conversions: i.e., whenever tau(A) similar to tau(B), the corresponding pair of conversions (glue code) convert target terms that behave like tau(A) to target terms that behave like tau(B), and vice versa. With this, they can prove semantic type soundness for the entire system. We illustrate our framework via a series of case studies that demonstrate how our semantic interoperation-after-compilation approach allows us both to account for complex differences in language semantics and make efficiency trade-offs based on particularities of compilers or targets.