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Modularity - the partitioning of software into units of functionality that interact with each other via interfaces - has been the mainstay of software development for half a century. In case of the C language, the main mechanism for modularity is the compilation unit / header file abstraction. This paper complements programmatic modularity for C with modularity idioms for specification and verification in the context of Verifiable C, an expressive separation logic for CompCert Clight. Technical innovations include (i) abstract predicate declarations – existential packages that combine Parkinson & Bierman’s abstract predicates with their client-visible reasoning principles; (ii) residual predicates, which help enforcing data abstraction in callback-rich code; and (iii) an application to pure (Smalltalk-style) objects that connects code verification to model-level reasoning about features such as subtyping, self, inheritance, and late binding. We introduce our techniques using concrete example modules that have all been verified using the Coq proof assistant and combine to fully linked verified programs using a novel, abstraction-respecting component composition rule for Verifiable C. 

The type-theoretic notions of existential abstraction, subtyping, subsumption, and intersection have useful analogues in separation-logic proofs of imperative programs. We have implemented these as an enhancement of the verified software toolchain (VST). VST is an impredicative concurrent separation logic for the C language, implemented in the Coq proof assistant, and proved sound in Coq. For machine-checked functional-correctness verification of software at scale, VST embeds its expressive program logic in dependently typed higher-order logic (CiC). Specifications and proofs in the program logic can leverage the expressiveness of CiC—so users can overcome the abstraction gaps that stand in the way of top-to-bottom verification: gaps between source code verification, compilation, and domain-specific reasoning, and between different analysis techniques or formalisms. Until now, VST has supported the specification of a program as a flat collection of function specifications (in higher-order separation logic)—one proves that each function correctly implements its specification, assuming the specifications of the functions it calls. But what if a function has more than one specification? In this work, we exploit type-theoretic concepts to structure specification interfaces for C code. This brings modularity principles of modern software engineering to concrete program verification. Previous work used representation predicates to enable data abstraction in separation logic. We go further, introducing function-specification subsumption and intersection specifications to organize the multiple specifications that a function is typically associated with. As in type theory, if 𝜙 is a of 𝜓, that is 𝜙<:𝜓, then 𝑥:𝜙 implies 𝑥:𝜓, meaning that any function satisfying specification 𝜙 can be used wherever a function satisfying 𝜓 is demanded. Subsumption incorporates separation-logic framing and parameter adaptation, as well as step-indexing and specifications constructed via mixed-variance functors (needed for C’s function pointers).