Presenting Distributive Laws

Presenting Distributive Laws

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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 ORG KAMUT FLAKES 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 CAL/ MAG ORANGE apply this result to show the equivalence between two different representations of context-free languages.