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

[Benjamin Franksen]

Ertugrul Söylemez wrote:
> damodar kulkarni <kdamodar2000 at gmail.com> wrote:
>> The Monad class makes us define bind (>>=) and unit (return) for our
>> monads.
>>
>> Why the Kleisli composition (>=>) or (<=<) is not made a part of Monad
>> class instead of bind (>>=)?
>>
>> Is there any historical reason behind this?
>>
>> The bind (>>=) is not as elegant as (>=>), at least as I find it.
>>
>> Am I missing something?
> 
> Try to express
> 
>     do x <- getLine
>        y <- getLine
>        print (x, y)
> 
> using only Kleisli composition (without cheating).  Through cheating
> (doing non-categorical stuff) it's possible to implement (>>=) in terms
> of (<=<), but as said that's basically breaking the abstraction.

What do you mean with "cheating" / "doing non-categorical stuff"?

m >>= f = (const m >=> f) ()

f >=> g = \x -> f x >>= g

How does the first definition "break the abstraction" while the second does 
not?

Cheers
-- 
Ben Franksen
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