A coinductive calculus for asynchronous side-effecting processes

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 Moggiʼs monadic meta-language of effects. We establish soundness and completeness of a natural equational axiomatization of this calculus. Our main result is 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. Moreover, we present initial results on verification methods for generic side-effecting processes.