nLab
monad transformer

Contents

Idea

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 MTM T of a monad MM is equivalent to MM.

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‚ÄôSullivan, Don Stewart, and John Goerzen, Monad transformers, Chapter 18 of Real World Haskell.

  • Chung-Chieh Shan, Monad transformers, blog post

  • 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. See the history of this page for a list of all contributions to it.