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Reversible computing is a computational paradigm in which computations are deterministic in both the forward and backward direction, so that programs have well-defined forward and backward semantics. We investigate the formal semantics of the reversible functional programming language Rfun. For this purpose we introduce join inverse rig categories, the natural marriage of join inverse categories and rig categories, which we show can be used to model the language Rfun, under reasonabledoi:10.4204/eptcs.351.10 fatcat:qhkblcncafd5dnolwfchgm46ry