Categorical Semantics for Functional Reactive Programming with Temporal Recursion and Corecursion

TL;DR

This paper extends categorical models of functional reactive programming to include recursion and corecursion related to time, generalizing previous models and excluding Zeno-like supertasks.

Contribution

It introduces an extended categorical framework for FRP that models temporal recursion and corecursion, broadening the applicability of existing models.

Findings

Models generalize previous CPCs by including recursion and corecursion.

Excludes Zeno's paradox related supertasks from the models.

Provides a unified categorical semantics for temporal aspects in FRP.

Abstract

Functional reactive programming (FRP) makes it possible to express temporal aspects of computations in a declarative way. Recently we developed two kinds of categorical models of FRP: abstract process categories (APCs) and concrete process categories (CPCs). Furthermore we showed that APCs generalize CPCs. In this paper, we extend APCs with additional structure. This structure models recursion and corecursion operators that are related to time. We show that the resulting categorical models generalize those CPCs that impose an additional constraint on time scales. This constraint boils down to ruling out $\omega$-supertasks, which are closely related to Zeno's paradox of Achilles and the tortoise.