Folks, Given f:: a -> b it is very natural to lift f to P f :: P a -> P b where P is the power set functor. Or L f :: [a] -> [b]. We are modeling structures using repeated application of the power functor, via repeated application of [ ]. It would be very nice if Haskell would recognize this lifting. That is, if f :: a -> b then one automatically has f :: [a] -> [b] without using fMap. We can do something similar with classes in the following way: Given class Addy a where (+.) :: a -> a -> a instance(Addy a) => Addy [ a] (+.) w [ ] = w (+.) [ ] w = w (+.) (a:as) (b:bs) = (a+b) :(as + bs) Now given instance Addy Int (+.) x y = x+y One can compute [[1,2],[3,4]] +. [ [2,3],[1,2,.3]]. I know I'm asking for a bit more here. I might need to use fMap f : [ a] -> [ b]. But I can't seem to get by with fMap f [[1,2],[3,4]] when f :: Int -> Int We often need to lift functions to higher power maps. It would be nice to have a way to do this with ease. Suggestions are welcome. Walt