[Haskell-beginners] Count with Writer asynchronously

[Baa]

Hello, Dear List!

There is package `async`
(https://hackage.haskell.org/package/async-2.1.1.1/docs/Control-Concurrent-Async.html).

Before, I had:

    import qualified Control.Concurent.Async as A
    ...
    runIt :: ... -> IO ()
    ...
      sequence [A.async $ runIt ...] >>= mapM_ A.wait

But now I want to count something inside `runIt`. I will use
`Writer` monad for it (sure, it can be `State` also, not in
principle to me). To do it synchronously, I done:

    module Main where

    import Control.Monad.Trans.Writer
    import Control.Monad.IO.Class
    import Data.Monoid

    runIt :: (Show a, Num a) => WriterT (Sum a) IO () -> a -> WriterT (Sum a) IO ()
    runIt w x = do
      censor (+1) w -- emulates conditional count of something
      liftIO $ print x

    main = do
      let l = [1,2,3,4]
          w = writer ((), 0) :: WriterT (Sum Int) IO ()
      z <- runWriterT $ sequence [runIt w i | i <- l]
      print $ snd z

but now my `runIt` changes it's signature:

    runIt :: Num a => WriterT (Sum a) IO () -> ... -> WriterT (Sum a) IO ()
    ...
      sequence [A.async $ runIt ...] >>= mapM_ A.wait
                ^^^^^^^^^^^
                     ` ERROR is here!

I get the error because `async`::IO () -> IO (A.Async ()) but I'm
trying to pass it `WriterT (Sum a) IO ()`!

To fix it I added `runWriterT` there:

    res <- sequence [A.async $ runWriterT (runIt ...) ...] >>= mapM A.wait

but now I will get list of counters, not one (res::[((), Sum Int)])!

How to solve this problem: to run several actions asyncronously and to count something
inside the action with `Writer` monad?


===
Best regards, Paul