Interaction and observation, categorically

TL;DR

This paper introduces dialgebras as a categorical framework to model the semantics of interactive systems, clearly distinguishing between observation and interaction, and demonstrates its application to asynchronous CCS semantics.

Contribution

It presents dialgebras as a natural extension of coalgebras for specifying interactive system semantics, emphasizing the separation of observation and interaction.

Findings

Dialgebras effectively model interactive system semantics.

The framework distinguishes observation from interaction.

Application to asynchronous CCS semantics demonstrates practicality.

Abstract

This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras. In this categorical model, from the point of view that we provide, the notions of observation and interaction are separate features. This is useful, for example, in the specification of process equivalences, which are obtained as kernels of the homomorphisms of dialgebras. As an example we present the asynchronous semantics of the CCS.