The lens package
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.
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 that manages its state using lenses can be found in the example folder.
Lenses, Folds and Traversals
The core of this hierarchy looks like:
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 links 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 :: Simple 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 :: Simple 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).
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