Idioms are oblivious, arrows are meticulous, monads are promiscuous

Sam Lindley; Philip Wadler; Jeremy Yallop

doi:10.1016/j.entcs.2011.02.018

Idioms are oblivious, arrows are meticulous, monads are promiscuous

Sam Lindley^*
, Philip Wadler
, Jeremy Yallop

^*Corresponding author for this work

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

38 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 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 - 8 Mar 2011

Keywords

applicative functors
arrows
idioms
monads

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1016/j.entcs.2011.02.018Licence: CC BY-NC-ND

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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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AU - Yallop, Jeremy

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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.

KW - applicative functors

KW - arrows

KW - idioms

KW - monads

UR - https://www.scopus.com/pages/publications/79952374884

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M3 - Article

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ER -

Idioms are oblivious, arrows are meticulous, monads are promiscuous

Abstract

Keywords

ASJC Scopus subject areas

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