Composing functors using Data.Functor.Compose - thanks to Tony Morris for his presentation on Monad Transformers at http://vimeo.com/73648150

ComposeFunctors.hs

λ> import Data.Functor.Compose

-- List of lists
λ> getCompose $ fmap (+1) $ Compose [[],[1],[2,3],[4,5,6]]

[[],[2],[3,4],[5,6,7]]

-- List of Maybe
λ> getCompose $ fmap (+1) $ Compose [Just 1, Just 2, Nothing, Just 3]

[Just 2,Just 3,Nothing,Just 4]

-- Maybe of Lists
λ> getCompose $ fmap (+1) $ Compose $ Just [1,2,3]

Just [2,3,4]


-- the getCompose is needed because theres no Show instance for Compose
-- so we can map (fmap) an ordinary function over a nested structure of any two functors
-- rather than having to do:

λ> (fmap . fmap) (+1) [[],[1],[2,3],[4,5,6]]

[[],[2],[3,4],[5,6,7]]