Re: [Haskell-cafe] Why Kleisli composition is not in the Monad signature?

When I teach my students Haskell's monads, I never put "Kleisli" into my mouth. I tell them that monads are for sequencing effects; and the sequencing is visible clearly in (>>) :: IO a -> IO b -> IO b (>>=) :: IO a -> (a -> IO b) -> IO b but not in fmap :: (a -> b) -> IO a -> IO b join :: IO (IO a) -> IO a To me, print 1 >> print 2 looks natural, and print 1 >>= const (print 2) still understandable, but join $ fmap (const (print 2)) (print 1) rather not (I needed ghci to get this example right). I would not want to introduce category theory or Kleisli composition just to teach my students some effectful Haskell programming. Cheers, Andreas On 16.10.2012 21:45, Simon Thompson wrote:

Not sure I really have anything substantial to contribute, but it's certainly true that if you see

a -> m b

as a generalisation of the usual function type, a -> b, then return generalises the identity and kleisli generalises function composition. This makes the types pretty memorable (and often the definitions too).

Simon

On 16 Oct 2012, at 20:14, David Thomas wrote:

...

...

class Monad m where return :: a -> m a kleisli :: (a -> m b) -> (b -> m c) -> (a -> m c)

Simon Thompson | Professor of Logic and Computation School of Computing | University of Kent | Canterbury, CT2 7NF, UK s.j.thompson@kent.ac.uk | M +44 7986 085754 | W www.cs.kent.ac.uk/~sjt

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