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.)

Dosh

For the same reason there is no runIO function (discounting unsafePerformIO of course)... – Meditate

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.) – Dosh

Yes - it was a bit gnomic. There is no runIO because you cannot run side-effecting code to get a pure answer. Similarly there is no justification for IOT because there is no monad which you can reasonably add IO effects to. In a monad stack IO has to be "innermost" monad - you can add the other monadic effects to it, but not the other way around. – Meditate

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) – Dosh

What should runIOT (launchMissiles >> lift []) evaluate to? – Cinchonidine

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. – Window

@Window - I think most people assume IO is side-effecting because the Haskell Report specifies that side-effecting functions happen in the IO monad. Aside from that, you might want to look at comonad.com/reader/2011/free-monads-for-less-3 – Rosannarosanne

@JohnL Yes, that's the sort of treatment I had in mind. It may be the case that side-effecting functions happen in the IO monad, but that doesn't imply that every conceivable semantics for IO is side-effecting. Now, the decision to keep IO abstract has the consequence that only the runtime system is able to provide a semantics for IO: programmers are stuck with it. But indeed, we might imagine a knock-off IO monad, offering the same interface interpretably, with a transformer variant. We might also imagine alternative runtimes which "do" IO by generating values in the knock-off IO type. – Window

My answer to the question at https://mcmap.net/q/282436/-is-access-to-the-internal-structure-of-a-monad-required-for-a-monad-transformer also explains why a IOT is not possible. – Sleeping

You say: "IOT Maybe can either do an IO action or nothing". However, in such a monad the values would be either IOT Just IO a i.e. an IO action wrapped inside Just and IOT or it could be IOT Nothing. In the latter case you don't have IO anymore and your can't really do anything anymore. Basically the behaviour would be that you do computations normally until some error producing Nothing occurs and the program can exit because there's no further work to do. This feels somewhat reasonable but probably not super useful since you can already use exitWith to similarly exit early. – Nonsuit

You said: "IOT [] can build a list that can later be sequenced". But you don't need transformer for IO in order to sequence a list of IO actions. The list monad in Haskell is for non-determinism where you have a computation that branches to multiple results. With IOT [] you'd have to be able to execute a list of IO actions based on the results of previous IO action lists. What would that mean? The most reasonable interpretation seems that the program would split into multiple threads or processes that run parallel. They'd still share "RealWorld" so I'm not sure if it's reasonable. – Nonsuit

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 magic pixie dust 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.

Romanesque

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? – Dosh

@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... – Romanesque

This is to mistake what it is to be an IO computation for one particular implementation of how to run one. – Window

What about IOT (Just m) >>= k = IOT $ Just $ m >>= maybe (fail "...") id . runIOT . k? It is bad because (>>=) can fail (when it shouldn't)? – Woodford

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? – Triphylite