nLab monad transformer

Idea

In computer science and specifically in type theory, 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

Textbook account:

• Sergei Winitzki, Section 14 of: The Science of Functional Programming – A tutorial, with examples in Scala (leanpub:sofp)

See also

• Bryan O’Sullivan, 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)