Presenting Distributive Laws

Abstract

Distributive laws of a monad T over a functor F are categorical tools for \nspecifying algebra-coalgebra interaction. They proved to be important for solving systems \nof corecursive equations, for the specication of well-behaved structural operational se- \nmantics and, more recently, also for enhancements of the bisimulation proof method. If T \nis a free monad, then such distributive laws correspond to simple natural transformations. \nHowever, when T is not free it can be rather dicult to prove the dening axioms of a \ndistributive law. In this paper we describe how to obtain a distributive law for a monad \nwith an equational presentation from a distributive law for the underlying free monad. \nWe apply this result to show the equivalence between two dierent representations of \ncontext-free languages