Observation-Based Concurrent Program Logic for Relaxed Memory Consistency Models

Abstract

Concurrent program logics are frameworks for constructing proofs, which ensure that concurrent programs work correctly. However, most conventional concurrent program logics do not consider the complexities of modern memory structures, and the proofs in the logics do not ensure that programs will work correctly. To the best of our knowledge, Independent Reads Independent Writes (IRIW), which is known to have non-intuitive behavior under relaxed memory consistency models, has not been fully studied under the context of concurrent program logics. One reason is the gap between theoretical memory consistency models that program logics can handle and the realistic memory consistency models adopted by actual computer architectures. In this paper, we propose observation variables and invariants that fill this gap, releasing us from the need to construct operational semantics and logic for each specific memory consistency model. We describe general operational semantics for relaxed memory consistency models, define concurrent program logic sound to the operational semantics, show that observation invariants can be formalized as axioms of the logic, and verify IRIW under an observation invariant. We also obtain a novel insight through constructing the logic. To define logic that is sound to the operational semantics, we dismiss shared variables in programs from assertion languages, and adopt variables observed by threads. This suggests that the so-called bird’s-eye view of the whole computing system disturbs the soundness of the logic.