This paper is concerned with categorical structures for reversible computation. In particular, we focus on a typed, functional reversible language based on Theseus. We discuss how join inverse rig categories do not in general capture pattern-matching, the core construct Theseus uses to enforce reversibility. We then derive a categorical structure to add to join inverse rig categories in order to capture pattern-matching. We show how such a structure makes an adequate model for reversible pattern-matching.

中文翻译：

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可逆模式匹配的分类语义

本文涉及可逆计算的分类结构。特别是，我们专注于基于忒修斯的类型化、函数式可逆语言。我们讨论了加入逆钻机类别通常如何不捕获模式匹配，这是忒修斯用来强制可逆性的核心构造。然后我们推导出一个分类结构来添加加入逆钻机类别，以捕获模式匹配。我们展示了这种结构如何为可逆模式匹配建立一个合适的模型。