Rely-Guarantee Reasoning for Causally Consistent Shared Memory
Ori Lahav, Brijesh Dongol, Heike Wehrheim
Abstract
Abstract Rely-guarantee (RG) is a highly influential compositional proof technique for concurrent programs, which was originally developed assuming a sequentially consistent shared memory. In this paper, we first generalize RG to make it parametric with respect to the underlying memory model by introducing an RG framework that is applicable to any model axiomatically characterized by Hoare triples. Second, we instantiate this framework for reasoning about concurrent programs under causally consistent memory , which is formulated using a recently proposed potential-based operational semantics, thereby providing the first reasoning technique for such semantics. The proposed program logic, which we call $${\textsf{Piccolo}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Piccolo</mml:mi> </mml:math> , employs a novel assertion language allowing one to specify ordered sequences of states that each thread may reach. We employ $${\textsf{Piccolo}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Piccolo</mml:mi> </mml:math> for multiple litmus tests, as well as for an adaptation of Peterson’s algorithm for mutual exclusion to causally consistent memory.