Feb. 6th, 2011
arrows and idioms
Feb. 6th, 2011 09:38 pmIdioms are oblivious, arrows are meticulous,
monads are promiscuous
Sam Lindley, Philip Wadler and Jeremy Yallop
"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.
Keywords: applicative functors, idioms, arrows, monads"
monads are promiscuous
Sam Lindley, Philip Wadler and Jeremy Yallop
"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.
Keywords: applicative functors, idioms, arrows, monads"