Merging ST threads

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In the thread starting at http://www.haskell.org//pipermail/haskell/2004-January/013330.html there is a discussion about temporarily combining two independent monadic state threads. The problem is this: we have a computation that works with one bit of state, say a Bool, and another that works with another bit of state, say an Int, and we want to make one that works with both the Bool and the Int simultaneously for a while, and then go back to computations working on them individually.

So what we want is, given start1 and start2 computations that work with the Bool and the Int respectively, an intermediate computation that works with the pair (Bool,Int), and then computations end1 and end2 that work with the individual states, to construct the combined computation that does start1 and start2, then intermediate, then end1 and end2.

One solution is to define the individual computations using the StateT monad transformer, and then stack the two monad transformers on top of each other to make the combined one. This is a bit nasty and asymmetric, requiring one computation to be "lifted":

whole
    = do
        start1
        lift start2
        intermediate
        end1
        lift end2

Another option is to work with the normal State monad, and to define operations on this monad that "lifts" the state into a tuple:

embedState1 :: State s a -> State (s,t) a
embedState2 :: State t a -> State (s,t) a

embedState1 (State f) = State (\(s,t) -> let (s',a)=f s in ((s',t),a))
embedState2 (State f) = State (\(s,t) -> let (t',a)=f s in ((s,t'),a))

whole
    = do
         embedState1 start1
         embedState2 start2
         intermediate
         embedState1 end1
         embedState2 end2

This removes the asymmetry, but isn't really any nicer otherwise. However, what would be neat is if we could do this with ST threads too. ST is the extension present in at least GHC and Hugs that has an imperative implementation, and makes clever use of a forall in a type to guarantee purity. The key point is the operation

runST :: (forall s . ST s a) -> a

Which guarantees that state variables (STRef etc) cannot "escape" from one state thread to another. If we want to do the above with then ST, then we probably want operations like this:

embedST1 :: ST s a -> ST (s,t) a
embedST2 :: ST t a -> ST (s,t) a

Of course, we won't be able to run values of type ST (s,t) a, since they violate the forall restriction on runST. So we need some way to get rid of the tuple:

finishST1 :: (forall s . ST (s,t) a) -> ST t a
finishST2 :: (forall t . ST (s,t) a) -> ST s a

Does this make sense? Is it safe? I doubt it's very useful, but I think it's probably implementable with a bit of hacking inside the implementation of ST.

 -- GaneshSittampalam