[Haskell-beginners] Arrow vs. function

[martin]

Am 03/23/2015 um 09:57 PM schrieb John Wiegley:
>>>>>> martin  <martin.drautzburg at web.de> writes:
> 
>> But that's what a function does. So what's the fundamental difference
>> between an arrow and a fuction?
> 
> Arrows abstract functions, allowing you to have constructions like Kleisli,
> which are Arrows, but compose in the presence of effects using (<=<) rather
> than (.).

I recall reading something like "under composition an arrow returns a new version of itself". It this correct? This
would indeed be something a function does not do.