## Join inverse categories and reversible recursion

- Robin Kaarsgaard, Holger Bock Axelsen, Robert Glück
- J. Log. Algebr. Meth. Program.
- 2017

1 Excerpt

- Published 2016 in FoSSaCS

Recently, a number of reversible functional programming languages have been proposed. Common to several of these is the assumption of totality, a property that is not necessarily desirable, and certainly not required in order to guarantee reversibility. In a categorical setting, however, faithfully capturing partiality requires handling it as additional structure. Recently, Giles studied inverse categories as a model of partial reversible (functional) programming. In this paper, we show how additionally assuming the existence of countable joins on such inverse categories leads to a number of properties that are desirable when modelling reversible functional programming, notably morphism schemes for reversible recursion, a †-trace, and algebraic ω-compactness. This gives a categorical account of reversible recursion, and, for the latter, provides an answer to the problem posed by Giles regarding the formulation of recursive data types at the inverse category level.

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@inproceedings{Axelsen2016JoinIC,
title={Join Inverse Categories as Models of Reversible Recursion},
author={Holger Bock Axelsen and Robin Kaarsgaard},
booktitle={FoSSaCS},
year={2016}
}