Authors: Marcello M. Bonsangue ; Helle Hvid Hansen ; Alexander Kurz ; Jurriaan Rot

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.

• 18C15 - Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
• 68Q45 - Formal languages and automata
• 68Q55 - Semantics in the theory of computing
• 68Q65 - Abstract data types; algebraic specification