Overnight I had the following thought, which I think could work rather well.  The most basic implementation of the idea is as follows:

class MonadST s m | m -> s where
liftST :: ST s a -> m a

instance MonadST s (ST s) where ...
instance MonadST s m => MonadST ...

newtype FooT m e = FooT (StateT Foo m e)

instance (Monad m, MonadST s m) => Monad (FooT m) where ...

instance (Monad m, MonadST s m) => MonadBar (FooT m) where
<operations using an ST state>

instance (Monad m, MonadST s m)  => MonadST s (FooT m) where ...

The point here is that a MonadST instance guarantees that the bottom monad is an ST -- and therefore single-threaded of necessity -- and grants any ST-based monad transformers on top of it access to its single state thread.

The more fully general approach to guaranteeing an underlying monad is single-threaded would be to create a dummy state parameter version of each single-threaded monad -- State, Writer, and Reader -- and add a typeclass called MonadThreaded or something.

The real question with this approach would be how to go about unwrapping ST-based monad transformers in this fashion: I'm thinking that you would essentially perform unwrapping of the outer monad using an ST computation which gets lifted to the next-higher monad.  So, say, for example:

newtype MonadST s m => ArrayT e m a = ArrayT {execArrayT :: StateT (STArray s Int e) m a}

runArrayT :: (Monad m, MonadST s m) => Int -> ArrayT e m a -> m a
runArrayT n m = liftST (newArray_ (0, n-1)) >>= evalStateT (execArrayT m)

Key points:
- A MonadST s m instance should always imply that the bottom-level monad is of type ST s, preferably a bottom level provided when defining a monad by stacking transformers.  The fact that the bottom monad is in ST should guarantee single-threaded, referentially transparent behavior.
- A non-transformer implementation of an ST-bound monad transformer would simply involve setting the bottom monad to ST, rather than Identity as for most monad transformers.
- Unwrapping an ST-bound monad transformer involves no universal quantification on the state type.  After all transformers have been unwrapped, it should be possible to invoke runST on the final ST s a.
- Both normal transformers and ST-bound transformers should propagate MonadST.

I'm going to go try implementing this idea in stateful-mtl now...

Louis Wasserman
wasserman.louis@gmail.com


On Mon, Feb 16, 2009 at 3:07 AM, Sittampalam, Ganesh <ganesh.sittampalam@credit-suisse.com> wrote:
Well, I think a type system like Clean's that had linear/uniqueness types could "fix" the issue by actually checking that the state is single-threaded (and thus stop you from applying it to a "forking" monad). But there's a fundamental operational problem that ST makes destructive updates, so to support it as a monad transformer in general you'd need a type system that actually introduced fork operations (which "linear implicit parameters" used to do in GHC , but they were removed because they were quite complicated semantically and noone really used them).

From: haskell-cafe-bounces@haskell.org [mailto:haskell-cafe-bounces@haskell.org] On Behalf Of Louis Wasserman
Sent: 16 February 2009 03:31
To: Dan Doel
Cc: Henning Thielemann; haskell-cafe@haskell.org
Subject: Re: [Haskell-cafe] ANNOUNCE: pqueue-mtl, stateful-mtl

Okay, I tested it out and the arrow transformer has the same problem.  I realized this after I sent the last message -- the point is that at any particular point, intuitively there should be exactly one copy of a State# s for each state thread, and it should never get duplicated; allowing other monads or arrows to hold a State# s in any form allows them to hold more than one, violating that goal.

I'm not entirely convinced yet that there isn't some really gorgeous type system magic to fix this issue, like the type-system magic that motivates the type of runST in the first place, but that's not an argument that such magic exists...it's certainly an interesting topic to mull.

Louis Wasserman
wasserman.louis@gmail.com


On Sun, Feb 15, 2009 at 9:20 PM, Dan Doel <dan.doel@gmail.com> wrote:
On Sunday 15 February 2009 9:44:42 pm Louis Wasserman wrote:
> Hello all,
>
> I just uploaded stateful-mtl and pqueue-mtl 1.0.1.  The ST monad
> transformer and array transformer have been removed -- I've convinced
> myself that a heap transformer backed by an ST array cannot be
> referentially transparent -- and the heap monad is now available only as a
> basic monad and not a transformer, though it still provides priority queue
> functionality to any of the mtl wrappers around it.  stateful-mtl retains a
> MonadST typeclass which is implemented by ST and monad transformers around
> it, allowing computations in the the ST-bound heap monad to perform ST
> operations in its thread.
>
> Since this discussion had largely led to the conclusion that ST can only be
> used as a bottom-level monad, it would be pretty uncool if ST computations
> couldn't be performed in a monad using ST internally because the ST thread
> was hidden and there was no way to place ST computations 'under' the outer
> monad.  Anyway, it's essentially just like the MonadIO typeclass, except
> with a functional dependency on the state type.
>
> There was a question I asked that never got answered, and I'm still
> curious: would an ST *arrow* transformer be valid?  Arrows impose
> sequencing on their operations that monads don't...  I'm going to test out
> some ideas, I think.

Your proposed type:

 State (Kleisli []) x y = (s, x) -> [(s, y)]

is (roughly) isomorphic to:

 x -> StateT s [] y = x -> s -> [(s, y)]

The problem with an ST transformer is that the state parameter needs to be
used linearly, because that's the only condition under which the optimization
of mutable update is safe. ST ensures this by construction, as opposed to
other languages (Clean) that have type systems that can express this kind of
constraint directly. However, with STT, whether the state parameter is used
linearly is a function of the wrapped monad. You'd have to give a more fleshed
out version of your proposed state arrow transformer, but off the top of my
head, I'm not sure it'd be any better.

-- Dan

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