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Categorical Semantics of Reversible Pattern-Matching (2109.05837v3)
Published 13 Sep 2021 in cs.LO and cs.CL
Abstract: 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.