A Bottom-Up Approach to a Unified Semantic Interface for Verified Compositional Compilation

Verified compositional compilation (VCC) is a notion of modular verification of compilers that supports compilation of heterogeneous programs. The key to achieve VCC is to design a semantic interface that enables composition of correctness theorems for compiling individual modules. Most of the existing techniques for VCC fix a semantic interface from the very beginning and force it down to every single compiler pass. This requires significant changes to the existing framework and makes it difficult to understand the relationship between conditions enforced by the semantic interface and the actual requirements of compiler passes. A different approach is to design appropriate semantic interfaces for individual compiler passes and combine them into a unified interface which faithfully reflects the requirements of underlying compiler passes. However, this requires vertically composable simulation relations, which were traditionally considered very difficult to construct even with extensive changes to compiler verification frameworks. We propose a solution to construction of unified semantic interfaces for VCC with a bottom-up approach. Our starting point is CompCertO, an extension of CompCert -- the state-of-the-art verified compiler -- that supports VCC but lacks a unified interface. We discover that a CompCert Kripke Logical Relation (CKLR) in CompCertO provides a uniform notion of memory protection for evolving memory states across modules and is transitively composable. Based on this uniform and composable CKLR, we then merge the simulation relations for all the compiler pass in CompCertO (except for three value analysis passes) into a unified interface. We demonstrate the conciseness and effectiveness of this unified interface by applying it to verify the compositional compilation of a non-trivial heterogeneous program with mutual recursion.