Tom, On 19/02/2012, at 3:21 AM, Tom Schouten wrote:
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)
I think you can work with Arrow transformers instead. See: http://hackage.haskell.org/packages/archive/arrows/latest/doc/html/Control-A... It may be that you can generalise to arbitrary functors, but satisfying the Arrow laws may require some care. cheers peter -- http://peteg.org/