Recent years have seen great advances towards verifying large-scale systems code. However, these verifications are usually based on hand-written assembly or machine-code semantics for the underlying architecture that only cover a small part of the instruction set architecture (ISA). In contrast, other recent work has used Sail to establish formal models for large real-world architectures, including Armv8-A and RISC-V, that are comprehensive (complete enough to boot an operating system or hypervisor) and authoritative (automatically derived from the Arm internal model and validated against the Arm validation suite, and adopted as the official formal specification by RISC-V International, respectively). But the scale and complexity of these models makes them challenging to use as a basis for verification.

Systems code often requires fine-grained control over memory layout and pointers, expressed using low-level ( e.g. , bitwise) operations on pointer values. Since these operations go beyond what basic pointer arithmetic in C allows, they are performed with the help of integer-pointer casts . Prior work has explored increasingly realistic memory object models for C that account for the desired semantics of integer-pointer casts while also being sound w.r.t. compiler optimisations, culminating in PNVI, the preferred memory object model in ongoing discussions within the ISO WG14 C standards committee. However, its complexity makes it an unappealing target for verification, and no tools currently exist to verify C programs under PNVI. In this paper, we introduce VIP, a new memory object model aimed at supporting C verification. VIP sidesteps the complexities of PNVI with a simple but effective idea: a new construct that lets programmers express the intended provenances of integer-pointer casts explicitly. At the same time, we prove VIP compatible with PNVI, thus enabling verification on top of VIP to benefit from PNVI’s validation with respect to practice. In particular, we build a verification tool, RefinedC-VIP, for verifying programs under VIP semantics. As the name suggests, RefinedC-VIP extends the recently developed RefinedC tool, which is automated yet also produces foundational proofs in Coq. We evaluate RefinedC-VIP on a range of systems-code idioms, and validate VIP’s expressiveness via an implementation in the Cerberus C semantics.

Low-level systems code often needs to interact with data, such as page table entries or network packet headers, in which multiple pieces of information are packaged together as bitfield components of a single machine integer and accessed via bitfield manipulations (e.g., shifts and masking). Most existing approaches to verifying such code employ SMT solvers, instantiated with theories for bit vector reasoning: these provide a powerful hammer, but also significantly increase the trusted computing base of the verification toolchain. In this work, we propose an alternative approach to the verification of bitfield-manipulating systems code, which we call BFF. Building on the RefinedC framework, BFF is not only highly automated (as SMT-based approaches are) but also foundational---i.e., it produces a machine-checked proof of program correctness against a formal semantics for C programs, fully mechanized in Coq. Unlike SMT-based approaches, we do not try to solve the general problem of arbitrary bit vector reasoning, but rather observe that real systems code typically accesses bitfields using simple, well-understood programming patterns: the layout of a bit vector is known up front, and its bitfields are accessed in predictable ways through a handful of bitwise operations involving bit masks. Correspondingly, we center our approach around the concept of a structured bit vector---i.e., a bit vector with a known bitfield layout---which we use to drive simple and predictable automation. We validate the BFF approach by verifying a range of bitfield-manipulating C functions drawn from real systems code, including page table manipulation code from the Linux kernel and the pKVM hypervisor.

Given the central role that C continues to play in systems software, and the difficulty of writing safe and correct C code, it remains a grand challenge to develop effective formal methods for verifying C programs. In this paper, we propose a new approach to this problem: a type system we call RefinedC, which combines ownership types (for modular reasoning about shared state and concurrency) with refinement types (for encoding precise invariants on C data types and Hoare-style specifications for C functions).

Early in the development of Hoare logic, Owicki and Gries introduced auxiliary variables as a way of encoding information about the history of a program’s execution that is useful for verifying its correctness. Over a decade later, Abadi and Lamport observed that it is sometimes also necessary to know in advance what a program will do in the future . To address this need, they proposed prophecy variables , originally as a proof technique for refinement mappings between state machines. However, despite the fact that prophecy variables are a clearly useful reasoning mechanism, there is (surprisingly) almost no work that attempts to integrate them into Hoare logic. In this paper, we present the first account of prophecy variables in a Hoare-style program logic that is flexible enough to verify logical atomicity (a relative of linearizability) for classic examples from the concurrency literature like RDCSS and the Herlihy-Wing queue. Our account is formalized in the Iris framework for separation logic in Coq. It makes essential use of ownership to encode the exclusive right to resolve a prophecy, which in turn enables us to enforce soundness of prophecies with a very simple set of proof rules.

We present a new, syntax-directed framework for Curry-style type systems with subtyping. It supports a rich set of features, and allows for a reasonably simple theory and implementation. The system we consider has sum and product types, universal and existential quantifiers, and inductive and coinductive types. The latter two may carry size invariants that can be used to establish the termination of recursive programs. For example, the termination of quicksort can be derived by showing that partitioning a list does not increase its size. The system deals with complex programs involving mixed induction and coinduction, or even mixed polymorphism and (co-)induction. One of the key ideas is to separate the notion of size from recursion. We do not check the termination of programs directly, but rather show that their (circular) typing proofs are well-founded. Termination is then obtained using a standard (semantic) normalisation proof. To demonstrate the practicality of the system, we provide an implementation accepting all the examples discussed in the article.