[Haskell-cafe] Are all arrows functors?

[Andrew Coppin]

Nicolas Pouillard wrote:
> Excerpts from Neil Brown's message of Tue Nov 03 13:45:42 +0100 2009:
>   
>> Hi,
>>
>> I was thinking about some of my code today, and I realised that where I 
>> have an arrow in my code, A b c, the type (A b) is also a functor.  The 
>> definition is (see 
>> http://www.haskell.org/ghc/docs/latest/html/libraries/base/Control-Arrow.html):
>>
>> fmap = (^<<)
>> -- Or, in long form:
>> fmap f x = arr f <<< x
>>
>> Out of curiosity, and since this is a typical haskell-cafe question, 
>> does this definition of fmap hold for all arrows?
>>     
>
> Yes, as shown by the 'WrappedArrow' newtype:
>
> http://www.haskell.org/ghc/docs/latest/html/libraries/base/Control-Applicative.html#t%3AWrappedMonad
>   

While I don't wish to suggest that "all arrows are functors" is false, I 
think the argument "yes, because this library says so" is not too 
strong. Let us not forget, according to *the libraries*, Double is in 
Enum - which, I think you'll agree, is just weird...