I think monad-control is what I was looking for but was missing when trying
to come up with a solution involving lift. Thanks!
Paul
On Tue, May 29, 2018 at 11:15 PM Li-yao Xia
Hi Paul,
We can use Data.Coerce.coerce to do the (un)wrapping and defer to the Alternative/MonadPlus instance at the right level.
(MyMonad a) is representationally equivalent to (Stack (Either String a)), where Stack is defined as
type Stack = ReaderT Env (StateT Store (ListT Identity))
Thus, we can coerce Stack's MonadPlus methods (which lift ListT's methods) as follows:
import Data.Coerce
instance MonadPlus MyMonad where mzero :: forall a. MyMonad a mzero = coerce (mzero @Stack @(Either String a))
mplus :: forall a. MyMonad a -> MyMonad a -> MyMonad a mplus = coerce (mplus @Stack @(Either String a))
The upcoming DerivingVia generalizes this pattern somewhat, although it will be necessary to pick a different equivalent type than above.
newtype MyMonad = MyMonad { runMyMonad :: ((ReaderT Env (ExceptT String (StateT Store (ListT Identity)))) a) } deriving (Functor, Applicative, Monad) deriving (Alternative, MonadPlus) via (ReaderT Env (ExceptT' String (StateT Store (ListT Identity))))
where ExceptT' is a transformer identical to ExceptT, but it lifts the transformed monad's MonadPlus instance instead of providing its own.
A different solution is monad-control, which generalizes MonadTrans. Like `lift`, `liftWith` moves an action "up" one level in a transformer stack, but in addition, it provides a way to move "down" as well, as a continuation given to the wrapped action.
Although powerful, it is certainly not an easy interface to grasp, but my point here is to demonstrate one use of it.
liftControl :: (MonadTransControl t, Monad m, Monad (t m)) => (Run t -> m (StT t a)) -> t m a liftControl f = liftWith f >>= restoreT . return
instance Alternative MyMonad where empty = MyMonad ((lift . lift) empty) MyMonad a <|> MyMonad b = MyMonad $ liftControl $ \run1 -> liftControl $ \run2 -> (run2 . run1) a <|> (run2 . run1) b
It's also not quite obvious this does the right thing so here are some QuickCheck tests that these two implementations are equivalent to the original one:
https://lpaste.net/2697355636458389504
Cheers, Li-yao _______________________________________________ Haskell-Cafe mailing list To (un)subscribe, modify options or view archives go to: http://mail.haskell.org/cgi-bin/mailman/listinfo/haskell-cafe Only members subscribed via the mailman list are allowed to post.