Use an abstract monad in the linear interfaces

[facundominguez]

The linear interfaces were using Linear.IO, that might not be particularly easy to integrate in applications which use other monads.

I propose here a class to lift non-linear monads into linear monads. jni uses this to offer operations that run on any linear monad that can lift the non-linear IO.

class (Linear.Monad m, NonLinear.Monad (LiftedM m)) => MonadLift m where
  type LiftedM m :: * -> *
  lift :: LiftedM m a -> m a
  liftU :: LiftedM m a -> m (Unrestricted a)

Thus, an application can provide an instance of Linear.Monad for any wrapper of a regularly looking monadic stack. e.g.

data App a = App (ReaderT Env IO a)
  deriving (Monad, Functor, Applicative, MonadIO)

data LinearApp a = LinearApp (App a)

instance Linear.Monad LinearApp where
  ...

instance Linear.MonadLift LinearApp where
  type LiftedM LinearApp = App
  lift = LinearApp
  liftU = LinearApp . fmap Unrestricted

[b-mehta]

This proposal sounds good to me. I think Control.Monad.Lift.Linear in linear-base would be an appropriate place for the MonadLift class, and MonadIO can live in Control.Monad.IO.Class.

[facundominguez]

I have moved the Extra modules for linear-base to tweag/linear-base#64