Could someone explain functional lenses to me? It's a surprisingly difficult subject to google for and I haven't made any progress. All I know is that they provide similar get/set functionality than in OO.
A lens consists of two functions, a getter and a setter:
data Lens a b = Lens { getter :: a -> b, setter :: b -> a -> a }
For example, we might have lenses for the first and second parts of a pair:
fstLens :: Lens (a, b) a
fstLens = Lens fst $ \x (a, b) -> (x, b)
sndLens :: Lens (a, b) b
sndLens = Lens snd $ \x (a, b) -> (a, x)
The real convenience of lenses is that they compose:
compose :: Lens b c -> Lens a b -> Lens a c
compose f g = Lens (getter f . getter g) $
\c a -> setter g (setter f c (getter g a)) a
And they mechanically convert to State
transitions:
lensGet :: MonadState s m => Lens s a -> m a
lensGet = gets . getter
lensSet :: MonadState s m => Lens s b -> b -> m ()
lensSet f = modify . setter f
lensMod :: MonadState s m => Lens s b -> (b -> b) -> m ()
lensMod f g = modify $ setter f =<< g . getter f
(+=) :: (MonadState s m, Num b) => Lens s b -> b -> m ()
f += x = lensMod f (+ x)