  We present FunTAL, the first multi-language system to formalize safe
interoperability between a high-level functional language and low-level
assembly code while supporting compositional reasoning about the mix. A central
challenge in developing such a multi-language is bridging the gap between
assembly, which is staged into jumps to continuations, and high-level code,
where subterms return a result. We present a compositional stack-based typed
assembly language that supports components, comprised of one or more basic
blocks, that may be embedded in high-level contexts. We also present a logical
relation for FunTAL that supports reasoning about equivalence of high-level
components and their assembly replacements, mixed-language programs with
callbacks between languages, and assembly components comprised of different
numbers of basic blocks.
