Presenting Distributive Laws

Abstract

Distributive laws of a monad T over a functor F are categorical tools forspecifying algebra-coalgebra interaction. They proved to be important forsolving systems of corecursive equations, for the specification of well-behavedstructural operational semantics and, more recently, also for enhancements ofthe bisimulation proof method. If T is a free monad, then such distributivelaws correspond to simple natural transformations. However, when T is not freeit 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 anequational presentation from a distributive law for the underlying free monad.We apply this result to show the equivalence between two differentrepresentations of context-free languages