Idioms are oblivious, arrows are meticulous, monads are promiscuous

Sam Lindley, Philip Wadler, Jeremy Yallop

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

We revisit the connection between three notions of computation: Moggi s monads, Hughes s arrows and McBride and Paterson s idioms (also called applicative functors). We show that idioms are equivalent to arrows that satisfy the type isomorphism A→B 1→(A→B) and that monads are equivalent to arrows that satisfy the type isomorphism A→B←A→(1→B). Further, idioms embed into arrows and arrows embed into monads.

Original languageEnglish
Pages (from-to)97-117
Number of pages21
JournalElectronic Notes in Theoretical Computer Science
Volume229
Issue number5
DOIs
Publication statusPublished - 8 Mar 2011

Keywords

  • applicative functors
  • arrows
  • idioms
  • monads

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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