My favorite presentation of the monad laws is associativity of Kliesli composition: (a1 >=> a2) x = a1 x >>= a2 -- predefined in 6.8 control.monad -- The laws return >=> a = a a >=> return = a a >=> (b >=> c) = (a >=> b) >=> c
If you use this presentation you also need the following law: (a . b) >=> c = (a >=> c) . b that is, compatibility with ordinary function composition. I like to call this "naturality", since it's instrumental in proving return and bind to be natural transformations. The law looks less alien if we use a flipped version of (>=>): (<=<) = flip (>=>) {- Monad Laws in terms of (<=<) -} return <=< f = f <=< return = f -- Identity f <=< (g <=< h) = (f <=< g) <=< h -- Associativity f <=< (g . h) = (f <=< g) . h -- Naturality (which happens to be my favorite presentation of the laws, followed by the derivations that lead to the 'do' notation, which lead to various 'ah' moments from unsuspecting FP-challenged friends) ----- Ariel J. Birnbaum -- View this message in context: http://www.nabble.com/A-question-about-%22monad-laws%22-tp15411587p15975734.... Sent from the Haskell - Haskell-Cafe mailing list archive at Nabble.com.