Lenses, Folds, and Traversals
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Lens: Lenses, Folds, and Traversals

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This package provides families of lenses, isomorphisms, folds, traversals, getters and setters.

An overview of the derivation of these types can be found on the Lens Wiki along with a brief Overview.

Documentation is available through github or hackage.

Field Guide

Lens Hierarchy


(See wiki/Examples)

First, import Control.Lens.

ghci> import Control.Lens

Now, you can read from lenses

ghci> ("hello","world")^._2

and you can write to lenses.

ghci> set _2 42 ("hello","world")

Composing lenses for reading (or writing) goes in the order an imperative programmer would expect, and just uses (.) from the Prelude.

ghci> ("hello",("world","!!!"))^._2._1
ghci> set (_2._1) 42 ("hello",("world","!!!"))

You can make a Getter out of a pure functions with to.

ghci> "hello"^.to length

You can easily compose a Getter with a Lens just using (.). No explicit coercion is necessary.

ghci> ("hello",("world","!!!"))^._2._2.to length

As we saw above, you can write to lenses and these writes can change the type of the container. (.~) is an infix alias for set.

ghci> _1 .~ "hello" $ ((),"world")

Conversely view, can be used as a prefix alias for (^.).

ghci> view _2 (10,20)

There are a large number of other lens variants provided by the library, in particular a Traversal generalizes traverse from Data.Traversable.

We'll come back to those later, but continuing with just lenses:

You can let the library automatically derive lenses for fields of your data type

import Control.Lens

data Foo a = Foo { _bar :: Int, _baz :: Int, _quux :: a }
makeLenses ''Foo

This will automatically generate the following lenses:

bar, baz :: Simple Lens (Foo a) Int
quux :: Lens (Foo a) (Foo b) a b

A Lens takes 4 parameters because it can change the types of the whole when you change the type of the part.

Often you won't need this flexibility, a Simple Lens takes 2 parameters, and can be used directly as a Lens.

You can also write to setters that target multiple parts of a structure, or their composition with other lenses or setters. The canonical example of a setter is 'mapped':

mapped :: Functor f => Setter (f a) (f b) a b

over is then analogous to fmap, but parameterized on the Setter.

ghci> fmap succ [1,2,3]
ghci> over mapped succ [1,2,3]

The benefit is that you can use any Lens as a Setter, and the composition of setters with other setters or lenses using (.) yields a Setter.

ghci> over (mapped._2) succ [(1,2),(3,4)]

(%~) is an infix alias for 'over', and the precedence lets you avoid swimming in parentheses:

ghci> _1.mapped._2.mapped %~ succ $ ([(42, "hello")],"world")
([(42, "ifmmp")],"world")

There are a number of combinators that resemble the +=, *=, etc. operators from C/C++ for working with the monad transformers.

There are +~, *~, etc. analogues to those combinators that work functionally, returning the modified version of the structure.

ghci> both *~ 2 $ (1,2)

There are combinators for manipulating the current state in a state monad as well

fresh :: MonadState Int m => m Int
fresh = id <+= 1

Anything you know how to do with a Foldable container, you can do with a Fold

ghci> :m + Data.Char Data.Text.Lens
ghci> allOf (folded.text) isLower ["hello"^.packed, "goodbye"^.packed]

You can also use this for generic programming. Combinators are included that are based on Neil Mitchell's uniplate, but which have been generalized to work on or as lenses, folds, and traversals.

ghci> :m + Data.Data.Lens
ghci> anyOf biplate (=="world") ("hello",(),[(2::Int,"world")])

As alluded to above, anything you know how to do with a Traversable you can do with a Traversal.

ghci> mapMOf (traverse._2) (\xs -> length xs <$ putStrLn xs) [(42,"hello"),(56,"world")]

Moreover, many of the lenses supplied are actually isomorphisms, that means you can use them directly as a lens or getter:

ghci> let hello = "hello"^.packed
ghci> :t hello
hello :: Text

but you can also flip them around and use them as a lens the other way with from!

ghci> hello^.from packed.to length

You can automatically derive isomorphisms for your own newtypes with makeIso. e.g.

newtype Neither a b = Neither { _nor :: Either a b } deriving (Show)
makeIso ''Neither

will automatically derive

neither :: Iso (Neither a b) (Neither c d) (Either a b) (Either c d)
nor :: Iso (Either a b) (Either c d) (Neither a b) (Neither c d)

such that

from neither = nor
from nor = neither
neither.nor = id
nor.neither = id

There is also a fully operational, but simple game of Pong in the examples/ folder.

There are also a couple of hundred examples distributed throughout the haddock documentation.


(See wiki/Operators)

Combinator(s) w/ Result Stateful w/ Result Notes
view,views,^. use,uses View target(s). query works like use over a MonadReader
set, .~ <.~ .= assign,<.= Replace target(s). <<.~ and <<.= return the old value
over,mapOf,%~ <%~ %= <%= Update target(s). <<%~ and <<%= return the old value
id,traverseOf,%%~ %%= Update target(s) with an Applicative or auxillary result
+~ <+~ += <+= Add to target(s)
-~ <-~ -= <-= Subtract from target(s)
*~ <*~ *= <*= Multiply target(s)
//~ <//~ //= <//= Divide target(s)
^~ <^~ ^= <^= Raise target(s) to a non-negative Integral power
^^~ <^^~ ^^= <^^= Raise target(s) to an Integral power
**~ <**~ **= <**= Raise target(s) to an arbitrary power
||~ <||~ ||= <||= Logically or target(s)
&&~ <&&~ &&= <&&= Logically and target(s)
headOf,^? Return Just the first target or Nothing
toListOf,^.. Return a list of the target(s)
perform,performs^! Perform monadic action(s)
Control.Lens (Indexed)
iover,imapOf,%@~ <%@~ %@= <%@= Update target(s) with access to the index.
withIndex,itraverseOf,%%@~ %%@= Update target(s) with an Applicative or auxillary result with access to the index.
.|.~ <.|.~ .|.= <.|.= Bitwise or target(s)
.&.~ <.&.~ .&.= <.&.= Bitwise and target(s)
<>~ <<>~ <>= <<>= mappend to the target monoidal value(s)
</>~ <</>~ </>= <</>= Append a relative path to a FilePath
<.>~ <<.>~ <.>= <<.>= Append a file extension to a FilePath

Contact Information

Contributions and bug reports are welcome!

Please feel free to contact me through github or on the #haskell IRC channel on irc.freenode.net.

-Edward Kmett