Idioms are oblivious, arrows are meticulous, monads are promiscuous

Philip Wadler; Sam Lindley; Jeremy Yallop

doi:10.1016/j.entcs.2011.02.018

Idioms are oblivious, arrows are meticulous, monads are promiscuous

Philip Wadler, Sam Lindley, Jeremy Yallop

Research output: Contribution to journal › Article › peer-review

Abstract / Description of output

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 language	English
Pages (from-to)	97-117
Number of pages	21
Journal	Electronic Notes in Theoretical Computer Science
Volume	229
Issue number	5
DOIs	https://doi.org/10.1016/j.entcs.2011.02.018
Publication status	Published - 2011

Keywords / Materials (for Non-textual outputs)

applicative functors
idioms
arrows
monads

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10.1016/j.entcs.2011.02.018

Lindley Wadler ET AL 2011 Idioms are Oblivious, Arrows are Meticulous, Monads are PromiscuousAccepted author manuscript, 241 KB

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title = "Idioms are oblivious, arrows are meticulous, monads are promiscuous",

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.",

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AB - 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.

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KW - monads

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Idioms are oblivious, arrows are meticulous, monads are promiscuous

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