A monad transformer is a type constructor which takes a monad as an argument and returns a monad as a result. The concept is typically treated in the literature on monads in computer science.

Monad transformers generally derive from ordinary monads and allow a modular composition, so that the action on the identity monad of the associated transform $M T$ of a monad $M$ is equivalent to $M$.

This construction is sometimes viewed (see HP07, Eff) as a complication resulting from passing to monads from the setting of Lawvere theories, where any two theories may be naturally combined.

References

Bryan O’Sullivan, Don Stewart, and John Goerzen, Monad transformers, Chapter 18 of Real World Haskell.

Mauro Jaskelioff, Eugenio Moggi, Monad Transformers as Monoid Transformers, pdf

Oleksandr Manzyuk, Calculating monad transformers with category theory, pdf

Martin Hyland, John Power, The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads, Electronic Notes in Theoretical Computer Science (ENTCS) archive Volume 172, April, 2007 Pages 437-458 (pdf)

Last revised on October 10, 2016 at 05:17:36.
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