Distributive laws of a monad T over a functor F are categorical tools for specifying algebra-coalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of well-behaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of context-free languages.
M. Bonsangue, H. Hansen, A. Kurz, and J. Rot, “Presenting Distributive Laws,” Logical Methods in Computer Science, vol. 11, no. 3, Aug. 2015. DOI: 10.2168/LMCS-11(3:2)2015
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