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 reasonable assumptions. These categories turn out to be a particularly natural fit for reversible computing as a whole, as they encompass models for other reversible programming languages, notably Theseus and reversible flowcharts. This suggests that join inverse rig categories really are the categorical models of reversible computing.

中文翻译：

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加入逆向钻机类别以进行可逆的函数式编程

可逆计算是一种计算范例，其中计算在向前和向后方向都是确定性的，因此程序具有明确定义的向前和向后语义。我们研究可逆功能编程语言Rfun的形式语义。为此，我们介绍了联接反钻机类别，联接反钻机类别和钻机类别的自然联结，在合理的假设下，我们显示了这些联接可用于对Rfun语言进行建模。这些类别特别适合于整个可逆计算，因为它们涵盖了其他可逆编程语言的模型，尤其是us修斯和可逆流程图。这表明联接逆向钻机类别确实是可逆计算的分类模型。