Embed?

[treeowl]

Control.Monad.Morph has a class

class MMonad t where
  embed :: Monad n => (forall a. m a -> t n a) -> t m a -> t n a

We can write a similar function with a stronger constraint:

embedSeq :: (Monad m, Monad n) => (forall a. m a -> SeqT n a) -> SeqT m a -> SeqT n a
embedSeq f s = f (toView s) >>= \r -> case r of
  Empty -> empty
  a :< s' -> pure a <|> embedSeq f s'

Is it lawful? I haven't checked yet, but I wouldn't be surprised.

The documentation doesn't indicate any restrictions on the function passed to embed, but I wonder if it's supposed to be a monad morphism (see Gabriella439/Haskell-MMorph-Library#68). If it is, we might be able to write an instance something like this inscrutable monstrosity:

instance MMonad SeqT where
  embed (f :: forall a. m a -> SeqT n a) (SeqT m0) = SeqT $ fmap go m0
    where
      go :: forall b. m (View m b) -> n (View n b)
      go m = toView (f m) >>= \r -> case r of
        Empty -> pure Empty
        Empty :< s -> toView (step s)
        (x :< q) :< s -> pure $ x :< (embed f q <|> step s)

      step :: forall b. SeqT n (View m b) -> SeqT n b
      step s = s >>= \r -> case r of
        Empty -> empty
        a :< s' -> pure a <|> embed f s'

Lawful? Sensible? No idea whatsoever.