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1. Verified sequential Malloc/Free

   https://doi.org/10.1145/3381898.3397211  

   Appel, Andrew W.; Naumann, David A. (June 2020, International Symposium on Memory Management)

   null (Ed.)

   We verify the functional correctness of an array-of-bins (segregated free-lists) single-thread malloc/free system with respect to a correctness specification written in separation logic. The memory allocator is written in standard C code compatible with the standard API; the specification is in the Verifiable C program logic, and the proof is done in the Verified Software Toolchain within the Coq proof assistant. Our "resource-aware" specification can guarantee when malloc will successfully return a block, unlike the standard Posix specification that allows malloc to return NULL whenever it wants to. We also prove subsumption (refinement): the resource-aware specification implies a resource-oblivious spec. 

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2. A Verified Foreign Function Interface between Coq and C

   https://doi.org/10.1145/3704860  

   Korkut, Joomy; Stark, Kathrin; Appel, Andrew W (January 2025, Proceedings of the ACM on Programming Languages)

   One can write dependently typed functional programs in Coq, and prove them correct in Coq; one can write low-level programs in C, and prove them correct with a C verification tool. We demonstrate how to write programs partly in Coq and partly in C, and interface the proofs together. The Verified Foreign Function Interface (VeriFFI) guarantees type safety and correctness of the combined program. It works by translating Coq function types (and constructor types) along with Coq functional models into VST function-specifications; if the user can prove in VST that the C functions satisfy those specs, then the C functions behave according to the user-specified functional models (even though the C implementation might be very different) and the proofs of Coq functions that call the C code can rely on that behavior. To achieve this translation, we employ a novel, hybrid deep/shallow description of Coq dependent types. 

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3. Relational compilation for performance-critical applications: extensible proof-producing translation of functional models into low-level code

   https://doi.org/10.1145/3519939.3523706  

   Pit-Claudel, Clément; Philipoom, Jade; Jamner, Dustin; Erbsen, Andres; Chlipala, Adam (June 2022, PLDI 2022)

   There are typically two ways to compile and run a purely functional program verified using an interactive theorem prover (ITP): automatically extracting it to a similar language (typically an unverified process, like Coq to OCaml) or manually proving it equivalent to a lower-level reimplementation (like a C program). Traditionally, only the latter produced both excellent performance and end-to-end proofs. This paper shows how to recast program extraction as a proof-search problem to automatically derive correct-by-construction, high-performance code from purely functional programs. We call this idea relational compilation — it extends recent developments with novel solutions to loop-invariant inference and genericity in kinds of side effects. Crucially, relational compilers are incomplete, and unlike traditional compilers, they generate good code not because of a fixed set of clever built-in optimizations but because they allow experts to plug in domain-specific extensions that give them complete control over the compiler's output. We demonstrate the benefits of this approach with Rupicola, a new compiler-construction toolkit designed to extract fast, verified, idiomatic low-level code from annotated functional models. Using case studies and performance benchmarks, we show that it is extensible with minimal effort and that it achieves performance on par with that of handwritten C programs. 

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4. Verified Software Units

   https://doi.org/10.1007/978-3-030-72019-3_5  

   Beringer, Lennart (March 2021, Programming Languages and Systems. ESOP 2021.)

   Yoshida, Nobuko (Ed.)

   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. 

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5. Abstraction and subsumption in modular verification of C programs

   https://doi.org/10.1007/s10703-020-00353-1  

   Beringer, Lennart; Appel, Andrew W. (March 2021, Formal Methods in System Design)

   null (Ed.)

   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). 

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