One of my favourite aspects of functional programming is the emphasis on immutability - rather than mutating things and making direct changes to them, you work with copies and the differences are reflected in the construction. I won’t harp on about the benefits of doing this, but instead I’ll note that it isn’t all ponies and unicorns. Working with purely functional data can be difficult, especially when you have nested data structures; you often have to clone something deep inside and then reassemble everything by hand - yuck!

`Edward Kmett`

’s `lens`

package aims to solve this problem. `lens`

provides “families of lenses, isomorphisms, folds, traversals, getters and setters”. This is probably still a little unclear, and it’s easiest to see what `lens`

gives you from an example:

```
data Point = Point
_y :: Double } deriving (Show)
{ _x,
data Monster = Monster
_monsterLocation :: Point
{deriving (Show)
}
'Point
makeLenses ''Monster
makeLenses '
= Monster (Point 0 0) ogre
```

I’ve got 2 data structures for my little game - a 2D `Point`

, and a `Monster`

. I’ve made an example `Monster`

- the `ogre`

. All `Monster`

s have a location, and we presumably want them to move around. To move the `ogre`

without `lens`

, it might look like:

```
> ogre { _monsterLocation = (_monsterLocation ogre) {
λ= _x (_monsterLocation ogre) + 1
_x
} }Monster {_monsterLocation = Point {_x = 1.0, _y = 0.0}}
```

URGH! All of that, just to move 1 to the right?! Lets see how this looks with `lens`

:

```
> monsterLocation.x +~ 1 $ ogre
λMonster {_monsterLocation = Point {_x = 1.0, _y = 0.0}}
```

That’s much better! We’ve composed the `monsterLocation`

and `x`

lens to move into the `x`

part of the `Point`

of a `Monster`

, and then used `+~ 1`

to add one to it. Almost magically, these changes gets applied and our new `Monster`

is rebuild and returned to us.

`lens`

considers itself to come with “batteries included”, but this seems like it’s selling itself short - it really gives you a whole power station! As of this time of writing, lens has 99 operators and covers a huge range of operations you might wish to do on data. A recent addition is “prisms”, which are 0-or-1 target traversals, meaning they could give you either 1 answer or no answer at all, depending on the data that is viewed through them.

Natural numbers are a good example of this:

```
nat :: SimplePrism Integer Natural
= prism toInteger $ \ i ->
nat if i < 0
then Left i
else Right (fromInteger i)
```

Now we can ask if an `Int`

is a `Natural`

, by trying to view an `Int`

through the `nat`

prism:

```
> 5 ^? nat
λJust 5
> (-5) ^? nat
λNothing
```

Prisms fit in perfectly with the lens API, which means that we can compose them like any other lens - just like we did with `Monster`

s and `Point`

s above. In this example, we’ve got a pair of `Int`

s, perhaps from user input. We want to multiple each side of this input by 2, but *only* if it’s already a natural number. It sounds tricky, and that we’d likely need conditionals to pull it off, but not so with `lens`

!

```
> both.nat *~ 2 $ (-3,4)
λ-3,8)
(
> both.nat *~ 2 $ (8,4)
λ16,8) (
```

When `lens`

views the `(-3)`

through the `nat`

prism, it doesn’t view anything, because `(-3)`

is of course, not a natural number. As such, we just return `(-3)`

, unchanged. We’ve composed the `nat`

prism with `both`

to view “both sides” of a tuple through the `nat`

prism. This example is a variant of the official prism documentation, so be sure to check that out if you like this!

As always, I’ve only covered a tiny portion of the full API. `lens`

can also do traversals, monadic actions, folds, along with including a bunch of lens for common data structures such as `Set`

, `Text`

, `Vector`

and much more.

You can contact me via email at ollie@ocharles.org.uk or tweet to me @acid2. I share almost all of my work at GitHub. This post is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.