Interaction and observation: categorical semantics of reactive systems trough dialgebras

TL;DR

This paper introduces dialgebras as a new semantic framework for reactive systems, emphasizing interaction-based equivalence over traditional side-effect analysis, and demonstrates its application to CCS and pi-calculus.

Contribution

It develops a novel dialgebraic approach to semantics, allowing comparison with coalgebraic models and simplifying the semantics of pi-calculus without presheaf categories.

Findings

Dialgebras generalize algebras and coalgebras for reactive systems.

Semantic equivalence is based on interaction and observations.

Application to CCS and pi-calculus demonstrates the framework's effectiveness.

Abstract

We use dialgebras, generalising both algebras and coalgebras, as a complement of the standard coalgebraic framework, aimed at describing the semantics of an interactive system by the means of reaction rules. In this model, interaction is built-in, and semantic equivalence arises from it, instead of being determined by a (possibly difficult) understanding of the side effects of a component in isolation. Behavioural equivalence in dialgebras is determined by how a given process interacts with the others, and the obtained observations. We develop a technique to inter-define categories of dialgebras of different functors, that in particular permits us to compare a standard coalgebraic semantics and its dialgebraic counterpart. We exemplify the framework using the CCS and the pi-calculus. Remarkably, the dialgebra giving semantics to the pi-calculus does not require the use of presheaf categories.