Continuity as a computational effect

TL;DR

This paper introduces a monadic encoding of continuous behavior as a computational effect, enabling the compositional development of hybrid systems that integrate physical processes with software components.

Contribution

It proposes a novel monad-based framework to model continuity as a computational effect within component calculi for hybrid systems.

Findings

The monad captures continuous behavior in a compositional manner.

The Kleisli category provides a setting for studying effects of continuity.

Analogies with other effect monads highlight its role in hybrid systems.

Abstract

The original purpose of component-based development was to provide techniques to master complex software, through composition, reuse and parametrisation. However, such systems are rapidly moving towards a level in which software becomes prevalently intertwined with (continuous) physical processes. A possible way to accommodate the latter in component calculi relies on a suitable encoding of continuous behaviour as (yet another) computational effect. This paper introduces such an encoding through a monad which, in the compositional development of hybrid systems, may play a role similar to the one played by the 1+, powerset, and distribution monads in the characterisation of partial, non deterministic and probabilistic components, respectively. This monad and its Kleisli category provide a setting in which the effects of continuity over (different forms of) composition can be suitably studied.