[Haskell-cafe] ANNOUNCE: pqueue-mtl, stateful-mtl

Mon Feb 16 11:04:15 EST 2009

I don't think this can be right, because the m -> s dependency will
contradict the universal quantification of s required by runST. In other
words, unwrapping the transformers will leave you with an ST computation
for a specific s, which runST will reject.

________________________________

From: Louis Wasserman [mailto:wasserman.louis at gmail.com] 
Sent: 16 February 2009 16:01
To: Sittampalam, Ganesh
Cc: Dan Doel; Henning Thielemann; haskell-cafe at haskell.org
Subject: Re: [Haskell-cafe] ANNOUNCE: pqueue-mtl, stateful-mtl

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 at gmail.com

On Mon, Feb 16, 2009 at 3:07 AM, Sittampalam, Ganesh
<ganesh.sittampalam at 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 at haskell.org
[mailto:haskell-cafe-bounces at haskell.org] On Behalf Of Louis Wasserman
	Sent: 16 February 2009 03:31
	To: Dan Doel
	Cc: Henning Thielemann; haskell-cafe at 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 at gmail.com

	On Sun, Feb 15, 2009 at 9:20 PM, Dan Doel <dan.doel at 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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