[Haskell-cafe] Confusion on the third monad law when using lambda abstractions

[Sjoerd Visscher]

I had seen it before, and a bit of Googling turned up this:

   The monad laws can be written as
   return >=> g == g
   g >=> return == g
   (g >=> h) >=> k == g>=> (h >=> k)

   So, functions of type a -> m b are the arrows of a category with  
(>=>) as composition,
   and return as identity.

   http://sites.google.com/site/haskell/category-theory/thekleislicategory

Although I think I saw them somewhere else.

Sjoerd

On Jun 18, 2009, at 1:23 PM, Hans van Thiel wrote:

>
> On Wed, 2009-06-17 at 21:26 -0500, Jake McArthur wrote:
>> Jon Strait wrote:
>>> I'm reading the third (bind associativity) law for monads in this  
>>> form:
>>>
>>> m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h
>>
>> Arguably, that law would be better stated as:
>>
>>     (h <=< k) <=< m  =  h <=< (k <=< m)
>>
>> This wouldn't be so unintuitive.
> Hi,
> The only place I've ever seen Kleisli composition, or its flip, used  
> is
> in demonstrating the monad laws. Yet it is so elegant and, even having
> its own name, it must have some practical use. Do you, or anybody  
> else,
> have some pointers?
>
> Best Regards,
>
> Hans van Thiel
>>
>> - Jake
>>
>
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--
Sjoerd Visscher
sjoerd at w3future.com