On Thu, 10 Dec, 2015 at 6:43 PM, Kim-Ee Yeoh
The wrong way is to try to write:
neededLift :: (Monad m) => ((b -> b) -> a -> a) -> (m b -> m b) -> m a -> m a
which, as Daniel pointed out, is impossible.
So we start with the isomorphisms:
isoL :: (f -> a) -> (a -> f -> f) -> ((a -> a) -> (f -> f)) isoL g s m f = s (m (g f)) f isoR :: (f -> a) -> ((a -> a) -> (f -> f)) -> (a -> f -> f) isoR _ m a = m (const a)
It turns out we really only need isoL, but isoR is there for completeness.
Then we write:
liftALabel :: Applicative f => a :-> b -> f a :-> f b liftALabel l0 = lens g1 m1 where g1 = fmap (get l0) s1 = liftA2 (set l0) m1 = isoL g1 s1
Naturally, monad has been effect-reduced to applicative to admit more legal programs.
-- Kim-Ee
Thanks guys, I appreciate your help. You've given me a lot of food for thought here, Kim-Ee, and I'll spin off a new project to explore this in isolation. Si