Monad transformers as monoid transformers

The incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a preexisting 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 F. Here, we recast and extend those results in a -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. Key words: Monad, Monoid, Monoidal Category

• Type: Journal
• Year: 2010
• Where: TCS
• Authors: Mauro Jaskelioff, Eugenio Moggi
• Keywords: Monad Transformers, Monoid, Monoidal Category, TCS 2010, Theoretical Computer Science