Idioms are Oblivious, Arrows are Meticulous, Monads are Promiscuous

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.

• Type: Journal
• Year: 2011
• Where: ENTCS
• Authors: Sam Lindley, Philip Wadler, Jeremy Yallop
• Keywords: Arrows, ENTCS 2011, Moggi, Monads, Optimization