This is the main module for end-users of lens-families. If you are not building your own lenses, but just using top-level defined lenses made by others, this is the only module you need. It provides ^. for accessing fields and ^= and ^%= for setting and modifying fields. Lenses are composed with . from the Prelude and id is the identity lens.

Warning: Lenses are composed in the opposite order than most lens packages. Lenses in this library enjoy the following identities.

• x ^. l1 . l2 === x ^. l1 ^. l2

• l1 . l2 ^%= f === l1 ^%= l2 ^%= f

The identity lens behaves as follows.

• x ^. id === x

• id ^%= f === f

Lenses are implemented in van Laarhoven style. Lenses have type Functor f => (b -> f b) -> a -> f a and lens families have type Functor f => (b x -> f (b x')) -> a x -> f (a x').

Remember that lenses and lens families can be used directly for functorial updates. For example, sndL id gives you strength.

 sndL id :: Functor f => (a, f b) -> f (a, b)

Here is an example of code that uses the Maybe functor to preserves sharing during update when possible.

 -- | 'sharedUpdate' returns the *identical* object if the update doesn't change anything.
 -- This is useful for preserving sharing.
 sharedUpdate :: Eq b => Lens Maybe a b -> (b -> b) -> a -> a
 sharedUpdate lens f a = fromMaybe a (lens f' a)
  where
   f' b | fb == b  = Nothing
        | otherwise = Just fb
    where
     fb = f b

For stock lenses, see Lens.Family.Stock.

To build your own lenses, see Lens.Family.Unchecked.

References:

• http://www.twanvl.nl/blog/haskell/cps-functional-references
• http://r6.ca/blog/20120623T104901Z.html
• http://comonad.com/reader/2012/mirrored-lenses/
• http://conal.net/blog/posts/semantic-editor-combinators