View source for Merging ST threads

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 <hask>Bool</hask>, and another that 
works with another bit of state, say an <hask>Int</hask>, and we want to make one that works with both the <hask>Bool</hask> and the <hask>Int</hask> simultaneously for a while, and then go back to computations working on them individually.

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

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":

<haskell>
whole
    = do
        start1
        lift start2
        intermediate
        end1
        lift end2
</haskell>

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

<haskell>
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
</haskell>

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 <hask>forall</hask> in a type to guarantee purity.
The key point is the operation

<haskell>
runST :: (forall s . ST s a) -> a
</haskell>

Which guarantees that state variables (<hask>STRef</hask> 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:

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

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

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

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

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