3. I believe the documentation stating that Haskell arrows are a generalization of Haskell monads, but arrows are a categorical thing too and in that context bear a much more distant relationship to monads. Does a Haskell arrow have Hask as domain and codomain? Or is one particular element in Hask its domain and possibly another its codomain? Those are not at all the same thing.
Without being able to dive into this matter now,
I just want to say that both the Haskell monads
and arrows can be generalized to something
I call a "thrist", which appears to be the moral
equivalent of a free category. The underlying
category is obtained by a two-parameter GADT
(defining the morphisms) and the domains and
codomains of its members (which are Haskell types)
being the objects.
Here is my blog entry that motivates the concept
a bit:
Cheers,
Gabor