A Coinductive Calculus for Asynchronous Side-effecting Processes

TL;DR

This paper introduces a coinductive calculus for modeling asynchronous processes with side effects, providing a formal framework with sound axioms and expressive corecursion, demonstrated through a mutual exclusion example.

Contribution

It develops a novel coinductive calculus for asynchronous side-effecting processes, extending Moggi's monadic effects with corecursion and equational reasoning.

Findings

Established soundness and completeness of the calculus.

Defined a corecursion scheme for process operators.

Proved safety of a mutual exclusion protocol.

Abstract

We present an abstract framework for concurrent processes in which atomic steps have generic side effects, handled according to the principle of monadic encapsulation of effects. Processes in this framework are potentially infinite resumptions, modelled using final coalgebras over the monadic base. As a calculus for such processes, we introduce a concurrent extension of Moggi's monadic metalanguage of effects. We establish soundness and completeness of a natural equational axiomatisation of this calculus. Moreover, we identify a corecursion scheme that is explicitly definable over the base language and provides flexible expressive means for the definition of new operators on processes, such as parallel composition. As a worked example, we prove the safety of a generic mutual exclusion scheme using a verification logic built on top of the equational calculus.