[Haskell-cafe] Are all arrows functors?

Andrew Coppin andrewcoppin at btinternet.com
Thu Nov 5 16:34:57 EST 2009

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...

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