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Reversible computing is a computational paradigm in which computations aredeterministic in both the forward and backward direction, so that programs havewell-defined forward and backward semantics. We investigate the formalsemantics of the reversible functional programming language Rfun. For thispurpose, we introduce join inverse rig categories, the natural marriage of joininverse categories and rig categories, which we show can be used to model thelanguage Rfun, under reasonable assumptions. These categories turn out to be aparticularly natural fit for reversible computing as a whole, as they encompassmodels for other reversible programming languages, notably Theseus andreversible flowcharts. This suggests that join inverse rig categories reallyare the categorical models of reversible computing.

Join Inverse Rig Categories for Reversible Functional Programming, and Beyond