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1. 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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2. Argosy: verifying layered storage systems with recovery refinement

   https://doi.org/10.1145/3314221.3314585  

   Chajed, Tej; Tassarotti, Joseph; Kaashoek, M. Frans; Zeldovich, Nickolai (June 2019, Proceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI ’19))

   Reasoning about storage systems is challenging because these systems make persistence guarantees even if the system crashes at any point. To achieve these crash-safety guarantees, storage systems include recovery procedures to restore the system to a consistent state after a crash. Moreover, large-scale systems are structured as multiple stacked layers and can require recovery at multiple layers of abstraction. Formal verification can ensure that crash-safety guarantees hold regardless of when the system crashes. To make verification tractable, large-scale systems should be verified in a modular fashion, layer-by-layer in the software stack. Layered recovery makes modularity challenging because the system can crash in the middle of a high-level recovery procedure and must start over from the low-level recovery procedure. We present Argosy, a framework for machine-checked proofs of storage systems that supports layered recovery implementations with modular proofs. The framework is based on combinators for transition relations that are inspired by Kleene algebra, which provides a convenient formalism for specifying and reasoning about crashes and recovery. On top of this framework, we implement Crash Hoare Logic (CHL), the program logic used by FSCQ. Using the logic, we have verified an example of layered recovery featuring a write-ahead log on top of a disk, which itself runs by replicating over two unreliable disks. The metatheory of the framework, the soundness of the program logic, and these examples are all verified in the Coq theorem prover. 

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3. Structural temporal logic for mechanized program verification

   Ioannidis, Eleftherios; Zakowski, Yannick; Zdancewic, Steve; Angel, Sebastian (October 2025, Proceedings of the ACM on programming languages)

   Mechanized verification of liveness properties for infinite programs with effects and nondeterminism is challenging. Existing temporal reasoning frameworks operate at the level of models such as traces and automata. Reasoning happens at a very low-level, requiring complex nested (co-)inductive proof techniques and familiarity with proof assistant mechanics (e.g., the guardedness checker). Further, reasoning at the level of models instead of program constructs creates a verification gap that loses the benefits of modularity and composition enjoyed by structural program logics such as Hoare Logic. To address this verification gap, and the lack of compositional proof techniques for temporal specifications, we propose Ticl, a new structural temporal logic. Using Ticl, we encode complex (co-)inductive proof techniques as structural lemmas and focus our reasoning on variants and invariants. We show that it is possible to perform compositional proofs of general temporal properties in a proof assistant, while working at a high level of abstraction. We demonstrate the benefits of Ticl by giving mechanized proofs of safety and liveness properties for programs with scheduling, concurrent shared memory, and distributed consensus, demonstrating a low proof-to-code ratio. 

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4. Linear types for large-scale systems verification

   https://doi.org/10.1145/3527313  

   Li, Jialin; Lattuada, Andrea; Zhou, Yi; Cameron, Jonathan; Howell, Jon; Parno, Bryan; Hawblitzel, Chris (April 2022, Proceedings of the ACM on Programming Languages)

   Reasoning about memory aliasing and mutation in software verification is a hard problem. This is especially true for systems using SMT-based automated theorem provers. Memory reasoning in SMT verification typically requires a nontrivial amount of manual effort to specify heap invariants, as well as extensive alias reasoning from the SMT solver. In this paper, we present a hybrid approach that combines linear types with SMT-based verification for memory reasoning. We integrate linear types into Dafny, a verification language with an SMT backend, and show that the two approaches complement each other. By separating memory reasoning from verification conditions, linear types reduce the SMT solving time. At the same time, the expressiveness of SMT queries extends the flexibility of the linear type system. In particular, it allows our linear type system to easily and correctly mix linear and nonlinear data in novel ways, encapsulating linear data inside nonlinear data and vice-versa. We formalize the core of our extensions, prove soundness, and provide algorithms for linear type checking. We evaluate our approach by converting the implementation of a verified storage system (about 24K lines of code and proof) written in Dafny, to use our extended Dafny. The resulting system uses linear types for 91% of the code and SMT-based heap reasoning for the remaining 9%. We show that the converted system has 28% fewer lines of proofs and 30% shorter verification time overall. We discuss the development overhead in the original system due to SMT-based heap reasoning and highlight the improved developer experience when using linear types. 

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5. Formally Verified Memory Protection for a Commodity Multiprocessor Hypervisor

   Li, Shih-Wei; Li, Xupeng; Gu, Ronghui; Nieh, Jason; Hui, John Z. (August 2021, Proceedings of the 30th USENIX Security Symposium.)

   Hypervisors are widely deployed by cloud computing providers to support virtual machines, but their growing complexity poses a security risk, as large codebases contain many vulnerabilities. We present SeKVM, a layered Linux KVM hypervisor architecture that has been formally verified on multiprocessor hardware. Using layers, we isolate KVM's trusted computing base into a small core such that only the core needs to be verified to ensure KVM's security guarantees. Using layers, we model hardware features at different levels of abstraction tailored to each layer of software. Lower hypervisor layers that configure and control hardware are verified using a novel machine model that includes multiprocessor memory management hardware such as multi-level shared page tables, tagged TLBs, and a coherent cache hierarchy with cache bypass support. Higher hypervisor layers that build on the lower layers are then verified using a more abstract and simplified model, taking advantage of layer encapsulation to reduce proof burden. Furthermore, layers provide modularity to reduce verification effort across multiple implementation versions. We have retrofitted and verified multiple versions of KVM on Arm multiprocessor hardware, proving the correctness of the implementations and that they contain no vulnerabilities that can affect KVM's security guarantees. Our work is the first machine-checked proof for a commodity hypervisor using multiprocessor memory management hardware. SeKVM requires only modest KVM modifications and incurs only modest performance overhead versus unmodified KVM on real application workloads. 

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