Yes.
That's fantastic! This GADT is the missing piece of my puzzle. I transformed a bit your solution, polluting it with some classes instances and fleshing the functions:

data Player = Arrive | Leave deriving (Show, Typeable, Eq)
data Message m = Message String deriving (Show, Typeable, Eq)

data Data a where
  PlayerData  :: Int -> Data Player
  MessageData :: m -> Data (Message m)

data Handler where
  Handler :: (Typeable e) => e -> (Data e -> IO ()) -> Handler

instance forall e. (Typeable e) => Typeable (Data e) where
    typeOf _  = mkTyConApp (mkTyCon( ("Expression.EventData (" ++ (show $ typeOf (undefined::e))) ++ ")" )) []

addEvent :: (Typeable e) => e -> (Data e -> IO ()) -> [Handler] -> [Handler]
addEvent e h hs = (Handler e h) : hs

triggerEvent :: (Eq e, Typeable e) => e -> Data e -> [Handler] -> IO ()
triggerEvent e d hs = do
    let filtered = filter (\(Handler e1 _) -> e1 === e) hs
    mapM_ f filtered where
        f (Handler _ h) = case cast h of
            Just castedH -> do
                castedH d
            Nothing -> return ()

viewEvent :: (Typeable e) => e -> IO()
viewEvent event = do
    case cast event of
        Just (a :: Player) -> putStrLn $ "Player" ++ show a
        Nothing -> return ()
    case cast event of
        (Just (Message s)) -> putStrLn $ "Player" ++ s
        Nothing -> return ()


Unfortunately, I still cannot pattern match on the events to view them (viewEvent won't compile)...

Best,
Corentin


On Tue, Sep 11, 2012 at 4:10 PM, Sean Leather <leather@cs.uu.nl> wrote:
On Tue, Sep 11, 2012 at 3:39 PM, Corentin Dupontwrote:

@Oleg: Yes the set of events is closed and I would be much happier with a GADT! But no matter how hard I tried I couldn't manage.
Here is the full problem:

{-# LANGUAGE ExistentialQuantification, TypeFamilies, DeriveDataTypeable #-}

import Data.Typeable

-- | Define the events and their related data
class (Eq e, Typeable e, Show e) => Event e where
    data EventData e

-- | Groups of events
data PlayerEvent = Arrive | Leave deriving (Typeable, Show, Eq)

-- | events types
data Player          = Player PlayerEvent deriving (Typeable, Show, Eq)
data Message m  = Message String     deriving (Typeable, Show, Eq)

-- | event instances
instance Event Player                                      where data EventData Player             = PlayerData {playerData :: Int}
instance (Typeable m) => Event (Message m)   where data EventData (Message m)   = MessageData {messageData :: m}

-- | structure to store an event
data EventHandler = forall e . (Event e) =>
     EH {eventNumber :: Int,
         event :: e,
         handler :: (EventData e) -> IO ()} deriving Typeable

-- store a new event with its handler in the list
addEvent :: (Event e) => e -> (EventData e -> IO ()) -> [EventHandler] -> [EventHandler]
addEvent event handler ehs = undefined

-- trigger all the corresponding events in the list, passing the data to the handlers
triggerEvent :: (Event e) => e -> (EventData e) -> [EventHandler] -> IO ()
triggerEvent event edata ehs = undefined

--Examples:
msg :: Message Int
msg = Message "give me a number"
myList = addEvent msg (\(MessageData n) -> putStrLn $ "Your number is: " ++ show n) []
trigger = triggerEvent msg (MessageData 1) myList --Yelds "Your number is: 1"

Has you can see this allows me to associate an arbitrary data type to each event with the type family "EventData". Furthermore some events like "Message" let the user choose the data type using the type parameter. This way I have nice signatures for the functions "addEvent" and "triggerEvent". The right types for the handlers and the data passed is enforced at compilation time.
But I couldn't find any way to convert this into a GATD and get rid of the "Event" class......

Would this work?

data Player = Arrive | Leave
data Message m = Message String

data Data a where
  PlayerData  :: Int -> Data Player
  MessageData :: m -> Data (Message m)

data Handler where
  Handler :: Int -> e -> (Data e -> IO ()) -> Handler

addEvent :: e -> (Data e -> IO ()) -> [Handler] -> [Handler]
addEvent = undefined

triggerEvent :: e -> Data e -> [Handler] -> IO ()
triggerEvent = undefined

Regards,
Sean