This link might be what you are after:
http://okmij.org/ftp/Haskell/typecast.html#deepest-functor
On 3/1/07, Walter Potter
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
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