I recently discovered the lens package on Hackage and have been trying to make use of it now in a small test project that might turn into a MUD/MUSH server one very distant day if I keep working on it.

Here is a minimized version of my code illustrating the problem I am facing right now with the at lenses used to access Key/Value containers (Data.Map.Strict in my case)

{-# LANGUAGE OverloadedStrings, GeneralizedNewtypeDeriving, TemplateHaskell #-}
module World where
import Control.Applicative ((<$>),(<*>), pure)
import Control.Lens
import Data.Map.Strict (Map)
import qualified Data.Map.Strict as DM
import Data.Maybe
import Data.UUID
import Data.Text (Text)
import qualified Data.Text as T
import System.Random (Random, randomIO)

newtype RoomId = RoomId UUID deriving (Eq, Ord, Show, Read, Random)
newtype PlayerId = PlayerId UUID deriving (Eq, Ord, Show, Read, Random)

data Room =
  Room { _roomId :: RoomId 
       , _roomName :: Text
       , _roomDescription :: Text
       , _roomPlayers :: [PlayerId]
       } deriving (Eq, Ord, Show, Read)

makeLenses ''Room

data Player =
  Player { _playerId :: PlayerId
         , _playerDisplayName :: Text
         , _playerLocation :: RoomId
         } deriving (Eq, Ord, Show, Read)

makeLenses ''Player

data World =
  World { _worldRooms :: Map RoomId Room
        , _worldPlayers :: Map PlayerId Player
        } deriving (Eq, Ord, Show, Read)

makeLenses ''World

mkWorld :: IO World
mkWorld = do
  r1 <- Room <$> randomIO <*> (pure "The Singularity") <*> (pure "You are standing in the only place in the whole world") <*> (pure [])
  p1 <- Player <$> randomIO <*> (pure "testplayer1") <*> (pure $ r1^.roomId)
  let rooms = at (r1^.roomId) ?~ (set roomPlayers [p1^.playerId] r1) $ DM.empty
      players = at (p1^.playerId) ?~ p1 $ DM.empty in do
    return $ World rooms players

viewPlayerLocation :: World -> PlayerId -> RoomId
viewPlayerLocation world playerId=
  view (worldPlayers.at playerId.traverse.playerLocation) world  

Since rooms, players and similar objects are referenced all over the code I store them in my World state type as maps of Ids (newtyped UUIDs) to their data objects.

To retrieve those with lenses I need to handle the Maybe returned by the at lens (in case the key is not in the map this is Nothing) somehow. In my last line I tried to do this via traverse which does typecheck as long as the final result is an instance of Monoid but this is not generally the case. Right here it is not because playerLocation returns a RoomId which has no Monoid instance.

No instance for (Data.Monoid.Monoid RoomId)
  arising from a use of `traverse'
Possible fix:
  add an instance declaration for (Data.Monoid.Monoid RoomId)
In the first argument of `(.)', namely `traverse'
In the second argument of `(.)', namely `traverse . playerLocation'
In the second argument of `(.)', namely
  `at playerId . traverse . playerLocation'

Since the Monoid is required by traverse only because traverse generalizes to containers of sizes greater than one I was now wondering if there is a better way to handle this that does not require semantically nonsensical Monoid instances on all types possibly contained in one my objects I want to store in the map.

Or maybe I misunderstood the issue here completely and I need to use a completely different bit of the rather large lens package?