Summary: Systems code is almost universally written in the C programming language or a variant. C has a very low level of type and memory abstraction and formal reasoning about C systems code requires a memory model that is able to capture the semantics of C pointers and types. At the same time, proof-based verification demands abstraction, in particular from the aliasing and frame problems. In this paper we present a study in the mechanisation of two proof abstractions for pointer program verification in the Isabelle/HOL theorem prover, based on a low-level memory model for C. The language’s type system presents challenges for the multiple independent typed heaps (Burstall-Bornat) and separation logic proof techniques.
In addition to issues arising from explicit value size/alignment, padding, type-unsafe casts and pointer address arithmetic, structured types such as C’s arrays and structs are problematic due to the non-monotonic nature of pointer and lvalue validity in the presence of the unary &-operator. For example, type-safe updates through pointers to fields of a struct break the independence of updates across typed heaps or \(\land^{*}\)-conjuncts. We provide models and rules that are able to cope with these language features and types, eschewing common over-simplifications and utilising expressive shallow embeddings in higher-order logic. Two case studies are provided that demonstrate the applicability of the mechanised models to real-world systems code; a working of the standard in-place list reversal example and an overview of the verification of the L4 microkernel’s memory allocator.