How to Kill Epsilons with a Dagger

Abstract : We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or $\mathrm{ϵ<!--\; ϵ\; -->}$-transitions. Our approach employs monads with a parametrized fixpoint operator $†<!--\; †\; -->$ to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen as the unit of a free monoid. More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions. This allows to consider a wide range of other examples, including Mazurkiewicz traces for concurrent systems.