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Idioms are oblivious, arrows are meticulous, monads are promiscuous

By Sam Lindley, Philip Wadler and Jeremy Yallop

Abstract

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

Topics: applicative functors, idioms, arrows, monads
Publisher: Elsevier
Year: 2008
OAI identifier: oai:www.era.lib.ed.ac.uk:1842/3800
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Citations

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