Jacob A. Matthews, Laurent Dubreuil, Imane Terhmina, Yunci Sun, Matthew Wilkens, Marten Van Schijndel. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.

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.

Abstract This paper presents an operational semantics for the core of Scheme. Our specification improves over the denotational semantics from the Revised 5 Report on Scheme specification in four ways. First, it covers a larger part of the language, specifically eval , quote , dynamic-wind , and the top level. Second, it models multiple values in a way that does not require changes to unrelated parts of the language. Third, it provides a faithful model of Scheme's undefined order of evaluation. Finally, we have implemented our specification in PLT Redex, a domain-specific language for writing operational semantics. The implementation allows others to experiment with our specification and allows us to build a specification test suite, which improves our confidence that our system is a faithful model of Scheme. In addition to a specification of Scheme, this paper contributes three novel modeling techniques for Felleisen Hieb-style rewriting semantics. All three techniques are applicable to a wider range of problems than modeling Scheme, and they combine seamlessly in our model, suggesting that they would scale to complete models of other languages.

The analogy between types and contracts raises the question of how many features of static type systems can be expressed as dynamic contracts. An important feature missing in prior work on contracts is parametricity, as represented by the polymorphic types in languages like Standard ML.

Inter-language interoperability is big business, as the success of Microsoft's .NET and COM and Sun's JVM show. Programming language designers are designing programming languages that reflect that fact --- SML#, Mondrian, and Scala, to name just a few examples, all treat interoperability with other languages as a central design feature. Still, current multi-language research tends not to focus on the semantics of interoperation features, but only on how to implement them efficiently. In this paper, we take first steps toward higher-level models of interoperating systems. 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 and observable equivalence.Beyond giving simple expressive models that are natural compositions of single-language models, our studies have uncovered several interesting facts about interoperability. For example, higher-order contracts naturally emerge as the glue to ensure that interoperating languages respect each other's type systems. While we present our results in an abstract setting, they shed light on real multi-language systems and tools such as the JNI, SWIG, and Haskell's stable pointers.