This package comes \"Batteries Included\" with many useful lenses for the types
commonly used from the Haskell Platform, and with tools for automatically
generating lenses and isomorphisms for user-supplied data types.
The combinators in @Control.Lens@ provide a highly generic toolbox for composing
families of getters, folds, isomorphisms, traversals, setters and lenses and their
An overview, with a large number of examples can be found in the @README@: <https://github.com/ekmett/lens#lens-lenses-folds-and-traversals>
A video on how to use lenses and how they are constructed is available from youtube: <http://youtu.be/cefnmjtAolY?hd=1>
Slides can be obtained here: <http://comonad.com/haskell/Lenses-Folds-and-Traversals-NYC.pdf>
More information on the care and feeding of lenses, including a brief tutorial and motivation
for their types can be found on the lens wiki: <https://github.com/ekmett/lens/wiki>
A small game of @pong@ and other more complex examples that manage their state using lenses can be found in the example folder: <https://github.com/ekmett/lens/blob/master/examples/>
/Lenses, Folds and Traversals/
The core of the hierarchy of lens-like constructions looks like:
Local copy (<Hierarchy.png>)
You can compose any two elements of the hierarchy above using @(.)@ from the @Prelude@, and you can
use any element of the hierarchy as any type it linked to above it.
The result is their lowest upper bound in the hierarchy (or an error if that bound doesn't exist).
* You can use any 'Traversal' as a 'Fold' or as a 'Setter'.
* The composition of a 'Traversal' and a 'Getter' yields a 'Fold'.
If you want to provide lenses and traversals for your own types in your own libraries, then you
can do so without incurring a dependency on this (or any other) lens package at all.
/e.g./ for a data type:
> data Foo a = Foo Int Int a
You can define lenses such as
> -- bar :: Lens' (Foo a) Int
> bar :: Functor f => (Int -> f Int) -> Foo a -> f (Foo a)
> bar f (Foo a b c) = fmap (\a' -> Foo a' b c) (f a)
> -- baz :: Lens (Foo a) (Foo b) a b
> quux :: Functor f => (a -> f b) -> Foo a -> f (Foo b)
> quux f (Foo a b c) = fmap (Foo a b) (f c)
without the need to use any type that isn't already defined in the @Prelude@.
And you can define a traversal of multiple fields with 'Control.Applicative.Applicative':
> -- traverseBarAndBaz :: Traversal' (Foo a) Int
> traverseBarAndBaz :: Applicative f => (Int -> f Int) -> Foo a -> f (Foo a)
> traverseBarAndBaz f (Foo a b c) = Foo <$> f a <*> f b <*> pure c
What is provided in this library is a number of stock lenses and traversals for
common haskell types, a wide array of combinators for working them, and more
exotic functionality, (/e.g./ getters, setters, indexed folds, isomorphisms).