Join Inverse Rig Categories for Reversible Functional Programming, and Beyond

Reversible computing is a computational paradigm in which computations are deterministic both the forward and backward direction, so that programs have well-defined semantics. We investigate formal semantics of reversible functional programming language Rfun. For this purpose, we introduce join inverse rig categories, natural marriage categories show can be used to model Rfun, under reasonable assumptions. These turn out particularly fit for as whole, they encompass models other languages, notably Theseus flowcharts. This suggests really categorical computing.