Haskell Language Lens Lens and Prism
Example
A Lens' s a means that you can always find an a within any s. A Prism' s a means that you can sometimes find that s actually just is a but sometimes it's something else.
To be more clear, we have _1 :: Lens' (a, b) a because any tuple always has a first element. We have _Just :: Prism' (Maybe a) a because sometimes Maybe a is actually an a value wrapped in Just but sometimes it's Nothing.
With this intuition, some standard combinators can be interpreted parallel to one another
view :: Lens' s a -> (s -> a)"gets" theaout of thesset :: Lens' s a -> (a -> s -> s)"sets" theaslot insreview :: Prism' s a -> (a -> s)"realizes" that anacould be anspreview :: Prism' s a -> (s -> Maybe a)"attempts" to turn ansinto ana.
Another way to think about it is that a value of type Lens' s a demonstrates that s has the same structure as (r, a) for some unknown r. On the other hand, Prism' s a demonstrates that s has the same structure as Either r a for some r. We can write those four functions above with this knowledge:
-- `Lens' s a` is no longer supplied, instead we just *know* that `s ~ (r, a)` view :: (r, a) -> a view (r, a) = a set :: a -> (r, a) -> (r, a) set a (r, _) = (r, a) -- `Prism' s a` is no longer supplied, instead we just *know* that `s ~ Either r a` review :: a -> Either r a review a = Right a preview :: Either r a -> Maybe a preview (Left _) = Nothing preview (Right a) = Just a
