Arrows are strong monads

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Citations (Scopus)


Hughes' arrows were shown, by Jacobs et al., to be roughly monads in the bicategory Prof of profunctors (distributors, modules). However in their work as well as others', the categorical nature of the first operator was not pursued and its formulation remained rather ad hoc. In this paper, we identify first with strength for a monad, therefore: arrows are strong monads in Prof. Strong monads have been widely used in the semantics of functional programming after Moggi's seminal work, therefore our observation establishes categorical canonicity of the notion of arrow.

Original languageEnglish
Title of host publicationMSFP'10 - Proceedings of the 2010 ACM SIGPLAN Workshop on Mathematically Structured Functional Programming, Co-located with ICFP'10
Number of pages9
Publication statusPublished - 2010
Event3rd Workshop on Mathematically Structured Functional Programming, MSFP 2010 - Baltimore, MD, United States
Duration: 2010 Sept 252010 Sept 25

Publication series

NameProceedings of the ACM SIGPLAN International Conference on Functional Programming, ICFP


Conference3rd Workshop on Mathematically Structured Functional Programming, MSFP 2010
Country/TerritoryUnited States
CityBaltimore, MD


  • arrow
  • computational effect
  • freyd category
  • profunctor
  • strong monad


Dive into the research topics of 'Arrows are strong monads'. Together they form a unique fingerprint.

Cite this