Stream processors and comodels

TL;DR

This paper provides a coalgebraic characterization of extensional stream processors, i.e., continuous functions from streams of inputs to outputs, using comodels for algebraic effects, bridging the gap with prior intensional characterizations.

Contribution

It introduces a coalgebraic framework for extensional stream processors, extending previous work on intensional characterizations and connecting to algebraic effects via comodels.

Findings

Characterizes extensional stream processors as continuous functions.

Links the distinction between intensional and extensional processors to bisimulation and trace equivalence.

Integrates comodels for algebraic effects into the coalgebraic framework.

Abstract

In 2009, Hancock, Pattinson and Ghani gave a coalgebraic characterisation of stream processors $A^\mathbb{N} \to B^\mathbb{N}$ drawing on ideas of Brouwerian constructivism. Their stream processors have an intensional character; in this paper, we give a corresponding coalgebraic characterisation of extensional stream processors, i.e., the set of continuous functions $A^\mathbb{N} \to B^\mathbb{N}$. Our account sites both our result and that of op. cit. within the apparatus of comodels for algebraic effects originating with Power-Shkaravska. Within this apparatus, the distinction between intensional and extensional equivalence for stream processors arises in the same way as the the distinction between bisimulation and trace equivalence for labelled transition systems and probabilistic generative systems.