[Haskell-cafe] Are all arrows functors?

[Nicolas Pouillard]

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

-- 
Nicolas Pouillard
http://nicolaspouillard.fr