Natural Transformations as Rewrite Rules and Monad Composition
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Eklund et al. (2002) present a graphical technique aimed at simplifying the verification of various category-theoretic constructions, notably the composition of monads. In this note we take a different approach involving string rewriting. We show that a given tuple (T,mu,eta) is a monad if and only if T is a terminal object in a certain category of functors and natural transformations, and that this fact can be established by proving confluence of a certain string rewriting system. We illustrate the technique on the monad composition problem of Eklund et al.
computer science; technical report
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