Categorical Semantics of Reversible Pattern-Matching

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.