Mechanized Theory of Event Structures: A Case of Parallel Register Machine

Vladimir Gladstein,Dmitrii Mikhailovskii,Anton Trunov,Evgenii Moiseenko

doi:10.15514/ispras-2021-33(3)-11

Abstract

The true concurrency models, and in particular event structures, have been introduced in the 1980s as an alternative to operational interleaving semantics of concurrency, and nowadays they are regaining popularity. Event structures represent the causal dependency and conflict between the individual atomic actions of the system directly. This property leads to a more compact and concise representation of semantics. In this work-in-progress report, we present a theory of event structures mechanized in the COQ proof assistant and demonstrate how it can be applied to define certified executable semantics of a simple parallel register machine with shared memory.

Highlights

Event structures is a mathematical formalism introduced by Winskel [1] as a semantic domain of concurrent programs
In recent years there has been renewed interest in event structures, with the applications of the theory ranging from relaxed memory models [2,3,4] to model-based mutation testing [5]
Event structures were applied in the context of relaxed memory models [2,3,4], [16]. Among this line of work, we are aware of only one paper [16] that was accompanied by a mechanization in a proof assistant

Summary

Introduction

Event structures is a mathematical formalism introduced by Winskel [1] as a semantic domain of concurrent programs. In this work-in-progress report, we sketch the common design principles behind our library and give a concrete example of its usage by developing a formal mechanized semantics of a simple register machine with shared memory. Event structures were applied in the context of relaxed memory models [2,3,4], [16] Among this line of work, we are aware of only one paper [16] that was accompanied by a mechanization in a proof assistant. This memory model uses a custom variant of event structures, that does not obey the axioms of any conventional class of event structures [13–15] This fact makes it harder to reuse and adapt it to other applications of the theory

Background

Overview of Our Library

Event Structure of Register Machine