How about using a read-write lock?

data Locked a = Locked { lockVar :: TVar Bool, valueVar :: TVar a }

new :: a -> IO (Locked a)
new val = Locked <$> newTVarIO False <*> newTVarIO val

-- lock blocks until unlocked
lock, unlock :: Locked a -> STM ()

-- never blocks
read :: Locked a -> STM a

-- blocks until unlocked
write :: Locked a -> a -> STM ()

When you want to apply your effectful state trasition `f :: s -> m s`:

l <- ask
s <- liftIO . atomically $ lock l *> read l
s' <- f s
liftIO . atomically $ write l s' *> unlock l

On Fri, 3 Sep 2021, 3:46 am Olaf Klinke, <olf@aatal-apotheke.de> wrote:
On Fri, 2021-09-03 at 00:00 +0800, YueCompl wrote:
> Um, I'm not sure I understand your case right, but if the "mutation" instead of the "mutated result" can be (might non-trivially) computed from a possibly outdated state, and the "mutation" can be trivially applied, I think `modifyTVar'` is the way to go. `readTVar` can be used to obtain an almost up-to-date state on demand, at low frequency.

To be concrete, my state is a collection of time stamped values, where
the monoid operation overwrites old values with new ones.
But I need to know the current state (x,t) to determine the "mutation",
because I'll be asking questions like "server, tell me if there is a
value of x newer than t."
Any observer whose initial state is synchronized with the worker thread
can in principle re-construct the worker's internal state by observing
the stream of emitted "mutations".

The most general abstraction would be that of a monoid action on a
type, but in my case the monoid (mutations) and the mutated type are
identical.

act :: m -> a -> a
act memtpy = id
act (x <> y) = act x . act y -- monoid homomorphism
act (x <> x) = act x         -- idempotent

Olaf

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