lens is:exact

Lenses, Folds and Traversals 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 indexed variants. An overview, with a large number of examples can be found in the README. An introductory video on the style of code used in this library by Simon Peyton Jones is available from Internet Archive. A video on how to use lenses and how they are constructed is available on youtube. Slides for that second talk can be obtained from comonad.com. 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. A small game of pong and other more complex examples that manage their state using lenses can be found in the example folder. Lenses, Folds and Traversals With some signatures simplified, the core of the hierarchy of lens-like constructions looks like: (Local Copy) 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). For instance:

• You can use any Traversal as a Fold or as a Setter.
• The composition of a Traversal and a Getter yields a Fold.

Minimizing Dependencies 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)

-- quux :: 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).

Build a Lens from a getter and a setter.

lens :: Functor f => (s -> a) -> (s -> b -> t) -> (a -> f b) -> s -> f t

>>> s ^. lens getter setter
getter s

>>> s & lens getter setter .~ b
setter s b

>>> s & lens getter setter %~ f
setter s (f (getter s))

lens :: (s -> a) -> (s -> a -> s) -> Lens' s a

lens creates a Lens from a getter and a setter. The resulting lens isn't the most effective one (because of having to traverse the structure twice when modifying), but it shouldn't matter much. A (partial) lens for list indexing:

ix :: Int -> Lens' [a] a
ix i = lens (!! i)                                   -- getter
(\s b -> take i s ++ b : drop (i+1) s)   -- setter

Usage:

>>> [1..9] ^. ix 3
4

>>> [1..9] & ix 3 %~ negate
[1,2,3,-4,5,6,7,8,9]

When getting, the setter is completely unused; when setting, the getter is unused. Both are used only when the value is being modified. For instance, here we define a lens for the 1st element of a list, but instead of a legitimate getter we use undefined. Then we use the resulting lens for setting and it works, which proves that the getter wasn't used:

>>> [1,2,3] & lens undefined (\s b -> b : tail s) .~ 10
[10,2,3]

Creates Lens' from the getter and setter.

Build a lens from a getter and a setter, which must respect the well-formedness laws. If you want to build a Lens from the van Laarhoven representation, use lensVL.

Build a lens from a getter and setter family. Caution: In order for the generated lens family to be well-defined, you must ensure that the three lens laws hold:

• getter (setter s a) === a

• setter s (getter s) === s

• setter (setter s a1) a2 === setter s a2

My lens creation function to avoid a dependency on lens.

lens :: (s -> a) -> (s -> b -> t) -> Lens s t a b

Build a lens from a getter and setter family. Caution: In order for the generated lens family to be well-defined, you must ensure that the three lens laws hold:

• getter (setter s a) === a

• setter s (getter s) === s

• setter (setter s a1) a2 === setter s a2

Build a lens from a getter and a setter.

Build a lens out of a getter and setter

Make a lens out of the label. Example: over (lens #salary) (* 1.1) employee