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

[Ben Franksen]

Brent Yorgey wrote:
> On Thu, Nov 29, 2012 at 03:52:58AM +0100, Ben Franksen wrote:
>> Tony Morris wrote:
>> > As a side note, I think a direct superclass of Functor for Monad is not
>> > a good idea, just sayin'
>> > 
>> > class Functor f where
>> >   fmap :: (a -> b) -> f a -> f b
>> > 
>> > class Functor f => Apply f where
>> >   (<*>) :: f (a -> b) -> f a -> f b
>> > 
>> > class Apply f => Bind f where
>> >   (=<<) :: (a -> f b) -> f a -> f b
>> > 
>> > class Apply f => Applicative f where
>> >   unit :: a -> f a
>> > 
>> > class (Applicative f, Bind f) => Monad f where
>> > 
>> > Same goes for Comonad (e.g. [] has (=<<) but not counit)
>> > ... and again for Monoid, Category, I could go on...
>> 
>> Hi Tony
>> 
>> even though I dismissed your mentioning this on the Haskell' list, I do 
have 
>> to admit that the proposal has a certain elegance. However, before I buy 
>> into this scheme, I'd like to see some striking examples for types with 
>> natural (or at least useful) Apply and Bind instances that cannot be made 
>> Applicative resp. Monad. 
> 
> Try writing an Applicative instances for (Data.Map.Map k).  It can't
> be done, but the Apply instance is (I would argue) both natural and 
useful.

I see. So there is one example. Are there more? I'd like to get a feeling 
for the abstraction and this is hard if there is only a single example.

>> Also, it is not clear to me what laws should hold 
>> for them.
> 
> http://hackage.haskell.org/package/semigroupoids defines all of these
> and specifies laws, presumably derived in a principled way.

Ok. I was not surprised to see that there are not many laws for the classes 
without unit.

Cheers
-- 
Ben Franksen
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