A Rely-Guarantee Proof System for x86-TSO

Current multiprocessors provide weak or relaxed memory models. Existing program logics assume sequential consistency, and are therefore typically unsound for weak memory. We introduce a novel RelyGuarantee style proof system for reasoning about x86 assembly programs running against the weak x86-TSO memory model. Interesting features of the logic include processor assertions which can refer to the local state of other processors (including their program counters), and a syntactic operation of closing an assertion under write buffer interference. We use the expressivity of the proof system to construct a new correctness proof for an x86-TSO version of Simpson’s four slot algorithm. Mechanization in the Hol theorem prover provides a flexible tool to support semi-automated verification.