msum package:lens

The sum of a collection of actions, generalizing concatOf.

>>> msumOf both ("hello","world")
"helloworld"

>>> msumOf each (Nothing, Just "hello", Nothing)
Just "hello"

msum ≡ msumOf folded

msumOf :: MonadPlus m => Getter s (m a)     -> s -> m a
msumOf :: MonadPlus m => Fold s (m a)       -> s -> m a
msumOf :: MonadPlus m => Lens' s (m a)      -> s -> m a
msumOf :: MonadPlus m => Iso' s (m a)       -> s -> m a
msumOf :: MonadPlus m => Traversal' s (m a) -> s -> m a
msumOf :: MonadPlus m => Prism' s (m a)     -> s -> m a

A dual of lensProduct: a prism sum. The law

preview l (review l b) ≡ Just b

breaks with

>>> let badPrism :: Prism' (Maybe Char) (Either Char Char); badPrism = prismSum _Just _Just

>>> preview badPrism (review badPrism (Right 'x'))
Just (Left 'x')

We put in Right value, but get back Left. Are you looking for without?