Idioms are oblivious, arrows are meticulous, monads are promiscuous

Sam Lindley, Philip Wadler, Jeremy Yallop

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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
Title of host publicationMathematically Structured Functional Programming 2008
Number of pages19
Publication statusPublished - 2008

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