Lens: Lenses, Folds, and Traversals

This package provides families of lenses, isomorphisms, folds, traversals, getters and setters.
The FAQ, which provides links to a large number of different resources for learning about lenses and an overview of the derivation of these types can be found on the Lens Wiki along with a brief overview and some examples.
Documentation is available through github (for HEAD) or hackage for the current and preceding releases.
Field Guide

Examples
(See wiki/Examples
)
First, import Control.Lens
.
ghci> import Control.Lens
Now, you can read from lenses
ghci> ("hello","world")^._2
"world"
and you can write to lenses.
ghci> set _2 42 ("hello","world")
("hello",42)
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
"world"
ghci> set (_2._1) 42 ("hello",("world","!!!"))
("hello",(42,"!!!"))
You can make a Getter
out of a pure functions with to
.
ghci> "hello"^.to length
5
You can easily compose a Getter
with a Lens
just using (.)
. No explicit coercion is necessary.
ghci> ("hello",("world","!!!"))^._2._2.to length
3
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")
("hello","world)
Conversely view
, can be used as a prefix alias for (^.)
.
ghci> view _2 (10,20)
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
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]
[2,3,4]
ghci> over mapped succ [1,2,3]
[2,3,4]
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)]
[(1,3),(3,5)]
(%~)
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)
(2,4)
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]
True
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")])
True
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")]
"hello"
"world"
[(42,5),(56,5)]
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
"hello"
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
5
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.
Operators
(See wiki/Operators
)
<table>
<thead>
<tr>
<th>Combinator(s)</th>
<th>w/ Result</th>
<th>Stateful</th>
<th>w/ Result</th>
<th>Notes</th>
</tr>
</thead>
<tbody>
<tr><th colspan=5><a href="http://ekmett.github.com/lens/Control-Lens.html">Control.Lens</a></th></tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Getter.html#v:view"><code>view</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-Getter.html#v:views"><code>views</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-Getter.html#v:-94-."><code>^.</code></a></td>
<td/>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Getter.html#v:use"><code>use</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-Getter.html#v:uses"><code>uses</code></a></td>
<td/>
<td>View target(s). <a href="http://ekmett.github.com/lens/Control-Lens-Getter.html#v:query"><code>query</code></a> works like <a href="http://ekmett.github.com/lens/Control-Lens-Getter.html#v:use"><code>use</code></a> over a <code>MonadReader</code></td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:set"><code>set</code></a>, <a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:.-126-"><code>.~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-60-.-126-"><code><.~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:.-61-"><code>.=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:assign"><code>assign</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-60-.-61-"><code><.=</code></a></td>
<td>Replace target(s). <a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--60-.-126-"><code><<.~</code> and
<a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--60-.-61-"><code><<.=</code></a>
return the old value</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:over"><code>over</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:mapOf"><code>mapOf</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-37--126-"><code>%~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--37--126-"><code><%~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-37--61-"><code>%=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--37--61-"><code><%=</code></td>
<td>Update target(s). <a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--60--37--126-"><code><<%~</code> and
<a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--60--37--61-"><code><<%=</code></a>
return the old value</td>
</tr>
<tr>
<td><code>id</code>,<a href="http://ekmett.github.com/lens/Control-Lens-Traversal.html#v:traverseOf"><code>traverseOf</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-37--37--126-"><code>%%~</code></a></td>
<td/>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-37--37--61-"><code>%%=</code></a></td>
<td/>
<td>Update target(s) with an <code>Applicative</code> or auxiliary result</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-43--126-"><code>+~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--43--126-"><code><+~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-43--61-"><code>+=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--43--61-"><code><+=</code></td>
<td>Add to target(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-45--126-"><code>-~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--45--126-"><code><-~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-45--61-"><code>-=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--45--61-"><code><-=</code></td>
<td>Subtract from target(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-42--126-"><code>*~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--42--126-"><code><*~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-42--61-"><code>*=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--42--61-"><code><*=</code></td>
<td>Multiply target(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-47--47--126-"><code>//~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--47--47--126-"><code><//~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-47--47--61-"><code>//=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--47--47--61-"><code><//=</code></td>
<td>Divide target(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-94--126-"><code>^~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--94--126-"><code><^~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-94--61-"><code>^=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--94--61-"><code><^=</code></td>
<td>Raise target(s) to a non-negative <code>Integral</code> power</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-94--94--126-"><code>^^~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--94--94--126-"><code><^^~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-94--94--61-"><code>^^=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--94--94--61-"><code><^^=</code></td>
<td>Raise target(s) to an <code>Integral</code> power</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-42--42--126-"><code>**~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--42--42--126-"><code><**~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-42--42--61-"><code>**=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--42--42--61-"><code><**=</code></td>
<td>Raise target(s) to an arbitrary power</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-124--124--126-"><code>||~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--124--124--126-"><code><||~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-124--124--61-"><code>||=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--124--124--61-"><code><||=</code></td>
<td>Logically or target(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-38--38--126-"><code>&&~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--38--38--126-"><code><&&~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-38--38--61-"><code>&&=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--38--38--61-"><code><&&=</code></td>
<td>Logically and target(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-60--62--126-"><code><>~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--60--62--126-"><code><<>~</code></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Setter.html#v:-60--62--61-"><code><>=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Type.html#v:-60--60--62--61-"><code><<>=</code></td>
<td><code>mappend</code> to the target monoidal value(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Fold.html#v:headOf"><code>headOf</code>,<a href="http://ekmett.github.com/lens/Control-Lens-Fold.html#v:-94--63-"><code>^?</code></a></td>
<td/><td/><td/>
<td>Return <code>Just</code> the first target or <code>Nothing</code></td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Fold.html#v:toListOf"><code>toListOf</code>,<a href="http://ekmett.github.com/lens/Control-Lens-Fold.html#v:-94-.."><code>^..</code></a></td>
<td/><td/><td/>
<td>Return a list of the target(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Action.html#v:perform"><code>perform</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-Action.html#v:performs"><code>performs</code></a><a href="http://ekmett.github.com/lens/Control-Lens-Action.html#v:-94-!"><code>^!</code></a></td>
<td/>
<td/>
<td/>
<td>Perform monadic action(s)</td>
</tr>
<tr><th colspan=5><a href="http://ekmett.github.com/lens/Control-Lens.html">Control.Lens</a> (Indexed)</th></tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-IndexedSetter.html#v:iover"><code>iover</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-IndexedSetter.html#v:imapOf"><code>imapOf</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-IndexedSetter.html#v:-37--64--126-"><code>%@~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-IndexedLens.html#v:-60--37--64--126-"><code><%@~</code></td>
<td><a href=http://ekmett.github.com/lens/Control-Lens-IndexedSetter.html#v:-37--64--126-"><code>%@=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Control-Lens-IndexedLens.html#v:-60--37--64--61-"><code><%@=</code></td>
<td>Update target(s) with access to the index.</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Control-Lens-Indexed.html#v:withIndex"><code>withIndex</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-IndexedTraversal.html#v:itraverseOf"><code>itraverseOf</code></a>,<a href="http://ekmett.github.com/lens/Control-Lens-IndexedLens.html#v:-37--37--64--126-"><code>%%@~</code></a></td>
<td/>
<td><a href="http://ekmett.github.com/lens/Control-Lens-IndexedLens.html#v:-37--37--64--61-"><code>%%@=</code></a></td>
<td/>
<td>Update target(s) with an <code>Applicative</code> or auxiliary result with access to the index.</td>
</tr>
<tr><th colspan=5><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html">Data.Bits.Lens</a></th></tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html#v:-124--126-"><code>.|.~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html#v:-60--124--126-"><code><.|.~</code></td>
<td><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html#v:-124--61-"><code>.|.=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html#v:-60--124--61-"><code><.|.=</code></td>
<td>Bitwise or target(s)</td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html#v:-38--126-"><code>.&.~</code></a></td>
<td><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html#v:-60--38--126-"><code><.&.~</code></td>
<td><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html#v:-38--61-"><code>.&.=</code></a></td>
<td><a href="http://ekmett.github.com/lens/Data-Bits-Lens.html#v:-60--38--61-"><code><.&.=</code></td>
<td>Bitwise and target(s)</td>
</tr>
<tr><th colspan=5><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html">System.FilePath.Lens</a></th></tr>
<tr>
<td><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html#v:-60--47--62--126-"><code></>~</code></a></td>
<td><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html#v:-60--60--47--62--126-"><code><</>~</code></td>
<td><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html#v:-60--47--62--61-"><code></>=</code></a></td>
<td><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html#v:-60--60--47--62--61-"><code><</>=</code></td>
<td>Append a relative path to a <code>FilePath</code></td>
</tr>
<tr>
<td><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html#v:-60-.-62--126-"><code><.>~</code></a></td>
<td><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html#v:-60--60-.-62--126-"><code><<.>~</code></td>
<td><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html#v:-60-.-62--61-"><code><.>=</code></a></td>
<td><a href="http://ekmett.github.com/lens/System-FilePath-Lens.html#v:-60--60-.-62--61-"><code><<.>=</code></td>
<td>Append a file extension to a <code>FilePath</code></td>
</tr>
</tbody>
</table>
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