Proof Pearl: A Verified Bignum Implementation in x86-64 Machine Code

Verification of machine code can easily deteriorate into an endless clutter of low-level details. This paper presents a case study which shows that machine-code verification does not necessitate ghastly lowlevel proofs. The case study we describe is the construction of an x86-64 implementation of arbitrary-precision integer arithmetic. Compared with closely related work, our proofs are shorter and, more importantly, the reasoning is at a more convenient high level of abstraction, e.g. pointer reasoning is largely avoided. We achieve this improvement as a result of using an abstraction for arrays and previously developed tools, namely, a proof-producing decompiler and compiler. The work presented in this paper has been developed in the HOL4 theorem prover. The case study resulted in 800 lines of verified 64-bit x86 machine code.