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

Louis Wasserman wasserman.louis at gmail.com
Mon Feb 16 11:01:08 EST 2009

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

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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