Why is there no IO transformer in Haskell?

Question

Every other monad comes with a transformer version, and from what I know the idea of a transformer is a generic extension of monads. Following how the other transformers are build, IOT would be something like

newtype IOT m a = IOT { runIOT :: m (IO a) }

for which I could make up useful applications on the spot: IOT Maybe can either do an IO action or nothing, IOT [] can build a list that can later be sequenced.

So why is there no IO transformer in Haskell?

(Notes: I've seen this post on Haskell Cafe, but can't make much sense of it. Also, the Hackage page for the ST transformer mentions a possibly related issue in its description, but doesn't offer any details.)

• stephen tetley: For the same reason there is no runIO function (discounting unsafePerformIO of course)...
• David: 1. that doesn't explain anything, 2. there is no function m a -> a in the monad interface so I don't see how it is related in the first place. (The internals of bind can be as unsafe as they want as long as the interface is pure.)
• David: Do you mean that there is no IOT without (sensibly) unwrapping internally every time you use bind, which leads to unpredictable behavior? (If yes, maybe make it into a full answer)
• is7s: What should runIOT (launchMissiles >> lift []) evaluate to?
• pigworker: If I could upvote this question more than once, I would. Consider how one might give an alternative semantics to IO, how one might interpret it purely in terms of a datatype. What makes anyone think that IO code is "side-effecting"? Only one particular runtime interpretation.

Answer 1

Consider the specific example of IOT Maybe. How would you write a Monad instance for that? You could start with something like this:

instance Monad (IOT Maybe) where
 return x = IOT (Just (return x))
 IOT Nothing >>= _ = IOT Nothing
 IOT (Just m) >>= k = IOT $ error "what now?"
 where m' = liftM (runIOT . k) m

Now you have m' :: IO (Maybe (IO b)), but you need something of type Maybe (IO b), where--most importantly--the choice between Just and Nothing should be determined by m'. How would that be implemented?

The answer, of course, is that it wouldn't, because it can't. Nor can you justify an unsafePerformIO in there, hidden behind a pure interface, because fundamentally you're asking for a pure value--the choice of Maybe constructor--to depend on the result of something in IO. Nnnnnope, not gonna happen.

The situation is even worse in the general case, because an arbitrary (universally quantified) Monad is even more impossible to unwrap than IO is.

---

Incidentally, the ST transformer you mention is implemented differently from your suggested IOT. It uses the internal implementation of ST as a State-like monad using (削除) magic pixie dust (削除ここまで) special primitives provided by the compiler, and defines a StateT-like transformer based on that. IO is implemented internally as an even more magical ST, and so a hypothetical IOT could be defined in a similar way.

Not that this really changes anything, other than possibly giving you better control over the relative ordering of impure side effects caused by IOT.

• David: Good answer! Concerning the last sentence: does that mean transformers are not universal even if we leave away the quirky RealWorld? Is it a nice coincidence that there are (as in exist) transformers of all the other monads we commonly use?
• C. A. McCann: @David: Depends on how you look at it. If IO was really truly a State monad whose state value was the entire outside universe, then an IOT defined as such would work correctly, where "correctly" means that a Nothing in IOT Maybe would discard the universe and thus end all existence. Personally, I'd stick with the current situation instead...
• pigworker: This is to mistake what it is to be an IO computation for one particular implementation of how to run one.
• JJJ: What about IOT (Just m) >>= k = IOT $ Just $ m >>= maybe (fail "...") id . runIOT . k? It is bad because (>>=) can fail (when it shouldn't)?
• Sebastian Graf: Soo... The actual root of the problem is that we can't conjure an a out of a Nothing :: Maybe a which we could return and then join, right? Obviously, this would work then for Identity, but are there even other monads for which it could possibly work?