Operational semantics for multi-language programs

Interoperability is big business, a fact to which .NET, the JVM, and COM can attest. Language designers are well aware of this, and they are designing programming languages that reflect it—for instance, SML.NET, F#, Mondrian, and Scala all treat interoperability as a central design feature. Still, current multi-language research tends not to focus on the semantics of these features, but only on how to implement them efficiently. In this article, we attempt to rectify that by giving a technique for specifying the operational semantics of a multi-language system as a composition of the models of its constituent languages. Our technique abstracts away the low-level details of interoperability like garbage collection and representation coherence, and lets us focus on semantic properties like type-safety, equivalence, and termination behavior. In doing so it allows us to adapt standard theoretical techniques such as subject-reduction, logical relations, and operational equivalence for use on multi-language systems. Generally speaking, our proofs of properties in a multi-language context are mutually referential versions of their single language counterparts. We demonstrate our technique with a series of strategies for embedding a Scheme-like language into an ML-like language. We start by connecting very simple languages with a very simple strategy, and work our way up to languages that interact in sophisticated ways and have sophisticated features such as polymorphism and effects. Along the way, we prove relevant results such as type-soundness and termination for each system we present using adaptations of standard techniques. Beyond giving simple expressive models, our studies have uncovered several interesting facts about interoperability. For example, higher-order function contracts naturally emerge as the glue to ensure that interoperating languages respect each other's type systems. Our models also predict that the embedding strategy where foreign values are opaque is as expressive as the embedding strategy where foreign values are translated to corresponding values in the other language, and we were able to experimentally verify this behavior using PLT Scheme's foreign function interface.