[Haskell-cafe] Selecting a transformer in a monad transformer stack
Li-yao Xia
lysxia at gmail.com
Tue May 29 21:14:47 UTC 2018
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
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