Home Arrows generalise monads and idioms Lindley, Wadler & Yallop, 2008. The Arrow Calculus, (Functional Pearl) (submitted to ICFP).

Lindley, Wadler & Yallop, 2008. Idioms are oblivious, arrows are meticulous, monads are promiscuous (submitted to MSFP) We revisit the connection between three notions of computation: Moggiâ€™s monads, Hughesâ€™s arrows and McBride and Patersonâ€™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 â†’ (1 ∼> B). Further, idioms embed into arrows and arrows embed into monads. The first paper introduce a reformulation of the Power/Thielecke/Paterson/McBride axiomatisation of arrows, which the authors argue is more natural, and shows that arrows generalise both monads and idioms. The second paper studies the relationships between the three formalisations in more formal depth; in particular the results about applicative functors struck me as significant. Two fresh papers from the Edinburgh theory stable:The first paper introduce a reformulation of the Power/Thielecke/Paterson/McBride axiomatisation of arrows, which the authors argue is more natural, and shows that arrows generalise both monads and idioms. The second paper studies the relationships between the three formalisations in more formal depth; in particular the results about applicative functors struck me as significant. Comment viewing options Flat list - collapsed Flat list - expanded Threaded list - collapsed Threaded list - expanded Date - newest first Date - oldest first Select your preferred way to display the comments and click "Save settings" to activate your changes.