On multi-language abstraction: Towards a static analysis of multi-language programs

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. Our 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.