[Haskell-cafe] Type famillies & Lifting IO

[oleg at okmij.org]

Maciej Piechotka wrote:
> class (Monad m, Monad (IO' m)) => MonadIO m where
>     type IO' m :: * -> *
>     liftIO :: IO a -> IO' m a
>     liftM :: m a -> IO' m a

The signature for liftIO betrays a problem. Since liftIO is a member
of a type class, when liftIO is used in code, the type checker has to
find the appropriate instance (i.e., resolve the overloading). Suppose
we have this piece of code:

	tt :: FooIO ()
	tt = liftIO (return () :: IO ())

How to find the appropriate instance of MonadIO and resolve the liftIO
overloading? The argument type of liftIO does not mention the type
class parameter m at all, and so it is of no guidance for overloading
resolution. We know that the return type of liftIO in the tt code is
FooIO (). Thus we have to find such instance of the MonadIO class that
its associated type IO' m is equal to FooIO. In other words, we have
to find m as a solution of the equation
	IO' m = FooIO
Or, we have to invert the type function IO' m. Alas, type functions
are not generally injective and hence not invertible. Indeed, nothing
prevents the user from defining two instances of MonadIO, for types m1
and m2, such that IO' m1 = IO' m2 = FooIO.