Idioms are oblivious, arrows are meticulous, monads are promiscuous

Sam Lindley; Philip Wadler; Jeremy Yallop

Idioms are oblivious, arrows are meticulous, monads are promiscuous

Sam Lindley, Philip Wadler, Jeremy Yallop

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 language	English
Title of host publication	Mathematically Structured Functional Programming 2008
Number of pages	19
Publication status	Published - 2008

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Lindley Wadler ET AL 2009 Idioms are oblivious, arrows are meticulous, monads are promiscuousSubmitted manuscript, 206 KB

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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 arrowsembed into monads..",

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AU - Wadler, Philip

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N2 - 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 arrowsembed into monads..

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 arrowsembed into monads..

M3 - Conference contribution

BT - Mathematically Structured Functional Programming 2008

ER -

Idioms are oblivious, arrows are meticulous, monads are promiscuous

Abstract

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