A formal framework for compositional compilation

We define a general framework for compositional compilation, meant as the ability of building an executable application by separate compilation and linking of single fragments, opposed to global compilation of the complete source application code. More precisely, compilation of a source code fragment in isolation generates a corresponding binary fragment equipped with type information, formally modeled as a typing, allowing type safe linking of fragments without re-inspecting code. We formally define a notion of soundness and completeness of compositional compilation w.r.t. global compilation, and show how linking can be in practice expressed by an entailment relation on typings. Then, we provide a sucient condition on such entailment to ensure soundness and completeness of compositional compilation, and compare this condition with the principal typings property. Furthermore, we show that this entailment relation can often be modularly expressed by an entailment relation on type environments and a subtyping relation. We illustrate the generality of our approach by instantiating the framework on three main examples: simply typed lambda calculus, where the problem of compositional compilation reduces to compositional type inference; Featherweight Java, where the generated binary code depends on the compilation context; and an extension of Featherweight Java with a boxing/unboxing mechanism, to illustrate how the framework can also support more sophisticated forms of linking-time binary code specialization.