Formalization of Phase Ordering

TL;DR

This paper formalizes the synchronization mechanism of phasers in parallel programming, providing a rigorous theoretical foundation and mechanized proofs for their semantics using Coq.

Contribution

It introduces a formal model of phasers, including May-Happen-In-Parallel and Happens-Before relations, with fully mechanized proofs in Coq.

Findings

Formalization of phaser semantics

Proofs of correctness using Coq

Relation to existing synchronization patterns

Abstract

Phasers pose an interesting synchronization mechanism that generalizes many collective synchronization patterns seen in parallel programming languages, including barriers, clocks, and point-to-point synchronization using latches or semaphores. This work characterizes scheduling constraints on phaser operations, by relating the execution state of two tasks that operate on the same phaser. We propose a formalization of Habanero phasers, May-Happen-In-Parallel, and Happens-Before relations for phaser operations, and show that these relations conform with the semantics. Our formalization and proofs are fully mechanized using the Coq proof assistant, and are available online.