I'm still getting to grips with defining and using Arrows in Haskell. While defining new arrows, it is much easier for me to think in terms of *** or &&& rather than first and second, as most of the time I want special processing for when two arrows are combined.
However the Arrow class does not allow defining the arrow in terms of arr and *** or &&&, and requires a definition of first to be included. This means that I am forced to write code like the following —
instance Arrow X where
arr f = ...
f (***) g = ...
first f = f *** arr id
It seems to me that there would have been no harm in including a default definition of first as well in the Control.Arrow module. That would have allowed us to choose between defining either first or ***.
Is there a good reason why a default definition of first was not included in the Arrow class? The only reason that I can think of is that the user may leave out the definition of first and *** both and then you would have circular definitions, but is that the only reason?
I actually believe it's the circularity that stopped someone from writing the default methods. But as @camccann pointed out, this should stop anyone. Suggest a change!