Monad Transformers as Monoid Transformers

with Eugenio Moggi. TCS 2010.PDF


The incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a pre-existing monad. A complication of this approach is that the operations associated to the pre-existing monad need to be lifted to the new monad. In a companion paper by Jaskelioff, the lifting problem has been addressed in the setting of system Fw. Here, we recast and extend those results in a category-theoretic setting. We abstract and generalize from monads to monoids (in a monoidal category), and from monad transformers to monoid transformers. The generalization brings more simplicity and clarity, and opens the way for lifting of operations with applicability beyond monads.


	Author = {Mauro Jaskelioff and Eugenio Moggi},
	Journal = {Theoretical Computer Science},
	Number = {51-52},
	Pages = {4441 - 4466},
	Title = {Monad transformers as monoid transformers},
	Volume = {411},
	Year = {2010}}