Extensible Extraction of Efficient Imperative Programs with Foreign Functions, Manually Managed Memory, and Proofs

We present an original approach to sound program extraction in a proof assistant, using syntax-driven automation to derive correct-by-construction imperative programs from nondeterministic functional source code. Our approach does not require committing to a single inflexible compilation strategy and instead makes it straightforward to create domain-specific code translators. In addition to a small set of core definitions, our framework is a large, user-extensible collection of compilation rules each phrased to handle specific language constructs, code patterns, or data manipulations. By mixing and matching these pieces of logic, users can easily tailor extraction to their own domains and programs, getting maximum performance and ensuring correctness of the resulting assembly code. Using this approach, we complete the first proof-generating pipeline that goes automatically from high-level specifications to assembly code. In our main case study, the original specifications are phrased to resemble SQL-style queries, while the final assembly code does manual memory management, calls out to foreign data structures and functions, and is suitable to deploy on resource-constrained platforms. The pipeline runs entirely within the Coq proof assistant, leading to final, linked assembly code with overall full-functional-correctness proofs in separation logic.