[Haskell-beginners] uses for Functor or Applicative?

[Johann Bach]

I'm wondering if the following problem might reveal a use for Functor
or Applicative, or just generally something cooler than I'm doing now.

I have a music document as type MusDoc. It has [Part]. Part has
[Note]. I have defined them using field names because I am
deliberating allowing for this to get more complicated later.

The question is about mapping functions over the individual parts. I
often find myself wanting to alter or
filter all the parts. In the following example I define filterDoc with
a couple of helper functions. What I
would like to know: is there a cooler way to do this using instances
of Functor or something? Defining
operators?

import Map(Map)
import qualified Map as M

type PartId = String   -- identification of a part in a music document
data PartInfo = ..     -- ancillary information about a part

-- the notes, markings, etc in a part
-- It is conceivable other fields could be added later.
data Part = Part { partNotes :: [Note] }

-- Main music document, consisting of parts.
data MusDoc = MusDoc { docParts :: Map PartId (PartInfo,Part) }


-- Helper function to map over parts
mapParts :: (Part -> Part) -> MusDoc -> MusDoc
mapParts g (MusDoc parts) = MusDoc $ M.map (second g) parts

-- Filter notes that meet a predicate
filterDoc :: (Note -> Bool) -> MusDoc -> MusDoc
filterDoc pred doc = mapParts (filterPart pred) doc

-- Helper function to filterDoc.
filterPart :: (Note -> Bool) -> Part -> Part
filterPart pred (Part notes) = Part (filter pred notes)