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.