nLab applicative functor




In computer science, applicative functors (also known as idioms) are the programming equivalent of lax monoidal functors with a tensorial strength in category theory.

A monad gives rise to an applicative functor, but not all applicative functors result from monads. Unlike monads, applicative functors are closed under composition.


  • Conor Mcbride, Ross Paterson, Applicative programming with effects, Journal of Functional Programming. 18 (01): 1–13. (doi:10.1017/S0956796807006326; author’s version)

  • Ross Paterson, Constructing Applicative Functors, in Mathematics of Program Construction, Madrid, 2012, Lecture Notes in Computer Science vol. 7342, pp. 300-323, Springer, 2012. (paper)

Last revised on November 15, 2021 at 14:27:42. See the history of this page for a list of all contributions to it.