On Multi-Language Abstraction

Modern software development rarely takes place within a single programming language. Often, programmers appeal to cross-language interoperability. Examples are exploitation of novel features of one language within another, and cross-language code reuse. Previous works developed a theory of so-called multi-languages, which arise by combining existing languages, defining a precise notion of (algebraic) multi-language semantics. As regards static analysis, the heterogeneity of the multi-language context opens up new and unexplored scenarios. In this paper, we provide a general theory for the combination of abstract interpretations of existing languages, regardless of their inherent nature, in order to gain an abstract semantics of multi-language programs. As a part of this general theory, we show that formal properties of interest of multi-language abstractions (e.g., soundness and completeness) boil down to the features of the interoperability mechanism that binds the underlying languages together. We extend many of the standard concepts of abstract interpretation to the framework of multi-languages.