Dear HC,
Does AFunctor below have a standard name? It's a generalization of
the Functor class in terms of Arrow instead of (->):
fmap :: Functor f => (i -> o) -> f i -> f o
afmap :: Arrow a, AFunctor f => a i o -> a (f i) (f o)
It pops up in less general form (AFunctor = []) in iterated functions
(difference equations / state space models), where the arrow is the
update function parameterized by state type:
data Iter s i o = Iter ((s,i) -> (s,o))
instance Arrow (Iter s)
More concretely:
> afmap :: ((s,i) -> (s, o)) -> (s,[i]) -> (s,[o])
> afmap f (s,[]) = (s,[])
> afmap f (s0, i:is) = (sn, o:os) where
> (s1, o) = f (s0,i)
> (sn, os) = afmap f (s1, is)
> f (s,i) = (s', s') where s' = s + i
> is = [1,1,1,1,1]
> os = afmap f (0,is) -- (5,[1,2,3,4,5])
Cheers,
Tom
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