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Lenses are basically an abstraction for simultaneously specifying operations to
update and query immutable data
structures. Lenses are highly composable and can be
efficient. This library provides a rich
collection of partial
isomorphisms, lenses, and traversals,
collectively known as optics, for manipulating
JSON and users can write
new optics for manipulating non-JSON objects, such as
Immutable.js collections. A partial lens can *view* optional
data, *insert* new data, *update* existing data and *remove* existing data and
can, for example, provide *defaults* and maintain *required* data structure
parts. Try Lenses!

- Tutorial
- The why of optics
- Reference
- Stable subset
- Additional libraries
- Optics
- On partiality
- On indexing
- On immutability
- On composability
- On lens laws
- Operations on optics
`L.assign(optic, object, maybeData) ~> maybeData`

^{v11.13.0}`L.disperse(optic, [...maybeValues], maybeData) ~> maybeData`

^{v14.6.0}`L.modify(optic, (maybeValue, index) => maybeValue, maybeData) ~> maybeData`

^{v2.2.0}`L.modifyAsync(optic, (maybeValue, index) => maybeValuePromise, maybeData) ~> maybeDataPromise`

^{v13.12.0}`L.remove(optic, maybeData) ~> maybeData`

^{v2.0.0}`L.set(optic, maybeValue, maybeData) ~> maybeData`

^{v1.0.0}`L.traverse(algebra, (maybeValue, index) => operation, optic, maybeData) ~> operation`

^{v10.0.0}

- Nesting
`L.compose(...optics) ~> optic`

or`[...optics]`

^{v1.0.0}`L.flat(...optics) ~> optic`

^{v13.6.0}

- Recursing
`L.lazy(optic => optic) ~> optic`

^{v5.1.0}

- Adapting
`L.choices(optic, ...optics) ~> optic`

^{v11.10.0}`L.choose((maybeValue, index) => optic) ~> optic`

^{v1.0.0}`L.cond(...[(maybeValue, index) => testable, consequentOptic][, [alternativeOptic]]) ~> optic`

^{v13.1.0}`L.condOf(traversal, ...[(maybeValue, index) => testable, consequentOptic][, [alternativeOptic]]) ~> optic`

^{v13.5.0}`L.ifElse((maybeValue, index) => testable, optic, optic) ~> optic`

^{v13.1.0}`L.orElse(backupOptic, primaryOptic) ~> optic`

^{v2.1.0}

- Indices
`L.joinIx(optic) ~> optic`

^{v13.15.0}`L.mapIx((index, maybeValue) => index) ~> optic`

^{v13.15.0}`L.setIx(index) ~> optic`

^{v13.15.0}`L.skipIx(optic) ~> optic`

^{v13.15.0}`L.tieIx((innerIndex, outerIndex) => index, optic) ~> optic`

^{v13.15.0}

- Debugging
`L.getLog(lens, maybeData) ~> maybeValue`

^{v13.14.0}`L.log(...labels) ~> optic`

^{v3.2.0}

- Internals
`L.Identity ~> Monad`

^{v13.7.0}`L.IdentityAsync ~> Monadish`

^{v13.12.0}`L.Select ~> Applicative`

^{v14.0.0}`L.toFunction(optic) ~> optic`

^{v7.0.0}

- Transforms
- Operations on transforms
`L.transform(optic, maybeData) ~> maybeData`

^{v11.7.0}`L.transformAsync(optic, maybeData) ~> maybeDataPromise`

^{v13.12.0}

- Sequencing
`L.seq(...transforms) ~> transform`

^{v9.4.0}

- Transforming
`L.assignOp(object) ~> traversal`

^{v11.13.0}`L.modifyOp((maybeValue, index) => maybeValue) ~> traversal`

^{v11.7.0}`L.removeOp ~> traversal`

^{v11.7.0}`L.setOp(maybeValue) ~> traversal`

^{v11.7.0}

- Operations on transforms
- Traversals
- Creating new traversals
- Traversals and combinators
`L.children ~> traversal`

^{v13.3.0}`L.elems ~> traversal`

^{v7.3.0}`L.elemsTotal ~> traversal`

^{v13.11.0}`L.entries ~> traversal`

^{v11.21.0}`L.flatten ~> traversal`

^{v11.16.0}`L.keys ~> traversal`

^{v11.21.0}`L.leafs ~> traversal`

^{v13.3.0}`L.matches(/.../g) ~> traversal`

^{v10.4.0}`L.query(...traversals) ~> traversal`

^{v13.6.0}`L.satisfying((maybeValue, index) => testable) ~> traversal`

^{v13.3.0}`L.values ~> traversal`

^{v7.3.0}

- Querying
`L.chain((value, index) => optic, optic) ~> traversal`

^{v3.1.0}`L.choice(...optics) ~> traversal`

^{v2.1.0}`L.optional ~> traversal`

^{v3.7.0}`L.unless((maybeValue, index) => testable) ~> traversal`

^{v12.1.0}`L.when((maybeValue, index) => testable) ~> traversal`

^{v5.2.0}`L.zero ~> traversal`

^{v6.0.0}

- Folds over traversals
`L.all((maybeValue, index) => testable, traversal, maybeData) ~> boolean`

^{v9.6.0}`L.all1((maybeValue, index) => testable, traversal, maybeData) ~> boolean`

^{v14.4.0}`L.and(traversal, maybeData) ~> boolean`

^{v9.6.0}`L.and1(traversal, maybeData) ~> boolean`

^{v14.4.0}`L.any((maybeValue, index) => testable, traversal, maybeData) ~> boolean`

^{v9.6.0}`L.collect(traversal, maybeData) ~> [...values]`

^{v3.6.0}`L.collectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> [...values]`

^{v7.2.0}`L.collectTotal(traversal, maybeData) ~> [...maybeValues]`

^{v14.6.0}`L.collectTotalAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> [...maybeValues]`

^{v14.6.0}`L.concat(monoid, traversal, maybeData) ~> value`

^{v7.2.0}`L.concatAs((maybeValue, index) => value, monoid, traversal, maybeData) ~> value`

^{v7.2.0}`L.count(traversal, maybeData) ~> number`

^{v9.7.0}`L.countIf((maybeValue, index) => testable, traversal, maybeData) ~> number`

^{v11.2.0}`L.counts(traversal, maybeData) ~> map`

^{v11.21.0}`L.countsAs((maybeValue, index) => any, traversal, maybeData) ~> map`

^{v11.21.0}`L.foldl((value, maybeValue, index) => value, value, traversal, maybeData) ~> value`

^{v7.2.0}`L.foldr((value, maybeValue, index) => value, value, traversal, maybeData) ~> value`

^{v7.2.0}`L.forEach((maybeValue, index) => undefined, traversal, maybeData) ~> undefined`

^{v11.20.0}`L.forEachWith(() => context, (context, maybeValue, index) => undefined, traversal, maybeData) ~> context`

^{v13.4.0}`L.get(traversal, maybeData) ~> maybeValue`

^{v2.2.0}`L.getAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> maybeValue`

^{v14.0.0}`L.isDefined(traversal, maybeData) ~> boolean`

^{v11.8.0}`L.isEmpty(traversal, maybeData) ~> boolean`

^{v11.5.0}`L.join(string, traversal, maybeData) ~> string`

^{v11.2.0}`L.joinAs((maybeValue, index) => maybeString, string, traversal, maybeData) ~> string`

^{v11.2.0}`L.maximum(traversal, maybeData) ~> maybeValue`

^{v7.2.0}`L.maximumBy((maybeValue, index) => maybeKey, traversal, maybeData) ~> maybeValue`

^{v11.2.0}`L.mean(traversal, maybeData) ~> number`

^{v11.17.0}`L.meanAs((maybeValue, index) => maybeNumber, traversal, maybeData) ~> number`

^{v11.17.0}`L.minimum(traversal, maybeData) ~> maybeValue`

^{v7.2.0}`L.minimumBy((maybeValue, index) => maybeKey, traversal, maybeData) ~> maybeValue`

^{v11.2.0}`L.none((maybeValue, index) => testable, traversal, maybeData) ~> boolean`

^{v11.6.0}`L.or(traversal, maybeData) ~> boolean`

^{v9.6.0}`L.product(traversal, maybeData) ~> number`

^{v7.2.0}`L.productAs((maybeValue, index) => number, traversal, maybeData) ~> number`

^{v11.2.0}`L.select(traversal, maybeData) ~> maybeValue`

^{v9.8.0}`L.selectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> maybeValue`

^{v9.8.0}`L.sum(traversal, maybeData) ~> number`

^{v7.2.0}`L.sumAs((maybeValue, index) => number, traversal, maybeData) ~> number`

^{v11.2.0}

- Lenses
- Creating new lenses
`L.foldTraversalLens((traversal, maybeData) => maybeValue, traversal) ~> lens`

^{v11.5.0}`L.getter((maybeData, index) => maybeValue) ~> lens`

^{v13.16.0}`L.lens((maybeData, index) => maybeValue, (maybeValue, maybeData, index) => maybeData) ~> lens`

^{v1.0.0}`L.partsOf(traversal) ~> lens`

^{v14.6.0}`L.setter((maybeValue, maybeData, index) => maybeData) ~> lens`

^{v10.3.0}

- Enforcing invariants
`L.defaults(valueIn) ~> lens`

^{v2.0.0}`L.define(value) ~> lens`

^{v1.0.0}`L.normalize((value, index) => maybeValue) ~> lens`

^{v1.0.0}`L.required(valueOut) ~> lens`

^{v1.0.0}`L.reread((valueIn, index) => maybeValueIn) ~> lens`

^{v11.21.0}`L.rewrite((valueOut, index) => maybeValueOut) ~> lens`

^{v5.1.0}

- Lensing array-like objects
`L.append ~> lens`

^{v1.0.0}`L.cross([...lenses]) ~> lens`

^{v14.3.0}`L.filter((maybeValue, index) => testable) ~> lens`

^{v1.0.0}`L.find((maybeValue, index, {hint: index}) => testable[, {hint: index}]) ~> lens`

^{v1.0.0}`L.findWith(optic[, {hint: index}]) ~> optic`

^{v1.0.0}`L.first ~> lens`

^{v13.1.0}`L.index(elemIndex) ~> lens`

or`elemIndex`

^{v1.0.0}`L.last ~> lens`

^{v9.8.0}`L.prefix(maybeBegin) ~> lens`

^{v11.12.0}`L.slice(maybeBegin, maybeEnd) ~> lens`

^{v8.1.0}`L.suffix(maybeEnd) ~> lens`

^{v11.12.0}

- Lensing objects
`L.pickIn({prop: lens, ...props}) ~> lens`

^{v11.11.0}`L.prop(propName) ~> lens`

or`propName`

^{v1.0.0}`L.props(...propNames) ~> lens`

^{v1.4.0}`L.propsOf(object) ~> lens`

^{v11.13.0}`L.removable(...propNames) ~> lens`

^{v9.2.0}

- Lensing strings
`L.matches(/.../) ~> lens`

^{v10.4.0}

- Providing defaults
`L.valueOr(valueOut) ~> lens`

^{v3.5.0}

- Transforming data
`L.pick({prop: lens, ...props}) ~> lens`

^{v1.2.0}`L.replace(maybeValueIn, maybeValueOut) ~> lens`

^{v1.0.0}

- Creating new lenses
- Isomorphisms
- Operations on isomorphisms
- Creating new isomorphisms
`L.iso(maybeData => maybeValue, maybeValue => maybeData) ~> isomorphism`

^{v5.3.0}`L.mapping([patternFwd, patternBwd] | (...variables) => [patternFwd, patternBwd]) ~> isomorphism`

^{v14.8.0}`L._ ~> pattern`

^{v14.8.0}

`L.mappings([...[patternFwd, patternBwd]] | (...variables) => [...[patternFwd, patternBwd]]) ~> isomorphism`

^{v14.8.0}

- Isomorphism combinators
`L.alternatives(isomorphism, ...isomorphisms) ~> isomorphism`

^{v14.7.0}`L.applyAt(elementsOptic, isomorphism) ~> isomorphism`

^{v14.9.0}`L.array(isomorphism) ~> isomorphism`

^{v11.19.0}`L.conjugate(contextIsomorphism, isomorphism) ~> isomorphism`

^{v14.9.0}`L.inverse(isomorphism) ~> isomorphism`

^{v4.1.0}`L.iterate(isomorphism) ~> isomorphism`

^{v14.3.0}`L.orAlternatively(backupIsomorphism, primaryIsomorphism) ~> isomorphism`

^{v14.7.0}

- Basic isomorphisms
`L.complement ~> isomorphism`

^{v9.7.0}`L.identity ~> isomorphism`

^{v1.3.0}`L.is(value) ~> isomorphism`

^{v11.1.0}`L.subset(maybeValue => testable) ~> isomorphism`

^{v14.3.0}

- Array isomorphisms
`L.indexed ~> isomorphism`

^{v11.21.0}`L.reverse ~> isomorphism`

^{v11.22.0}`L.singleton ~> isomorphism`

^{v11.18.0}

- Object isomorphisms
`L.disjoint(propName => propName) ~> isomorphism`

^{v13.13.0}`L.keyed ~> isomorphism`

^{v11.21.0}`L.multikeyed ~> isomorphism`

^{v14.1.0}

- Standard isomorphisms
`L.json({reviver, replacer, space}) ~> isomorphism`

^{v11.3.0}`L.uri ~> isomorphism`

^{v11.3.0}`L.uriComponent ~> isomorphism`

^{v11.3.0}

- Standardish isomorphisms
`L.querystring ~> isomorphism`

^{v14.2.0}

- String isomorphisms
`L.dropPrefix(prefix) ~> isomorphism`

^{v13.8.0}`L.dropSuffix(suffix) ~> isomorphism`

^{v13.8.0}`L.replaces(substringIn, substringOut) ~> isomorphism`

^{v13.8.0}`L.split(separator[, separatorRegExp]) ~> isomorphism`

^{v13.8.0}`L.uncouple(separator[, separatorRegExp]) ~> isomorphism`

^{v13.8.0}

- Arithmetic isomorphisms
`L.add(number) ~> isomorphism`

^{v13.9.0}`L.divide(number) ~> isomorphism`

^{v13.9.0}`L.multiply(number) ~> isomorphism`

^{v13.9.0}`L.negate ~> isomorphism`

^{v13.9.0}`L.subtract(number) ~> isomorphism`

^{v13.9.0}

- Interop
- Fantasy Land
`L.FantasyFunctor ~> Functor`

^{v14.5.0}`L.fromFantasy(TypeRep) ~> Functor|Applicative|Monad`

^{v14.5.0}`L.fromFantasyApplicative(TypeRep) ~> Applicative`

^{v14.5.0}`L.fromFantasyMonad(TypeRep) ~> Monad`

^{v14.5.0}

- JSON Pointer
`L.pointer(jsonPointer) ~> lens`

^{v11.21.0}

- Fantasy Land
- Auxiliary
`L.seemsArrayLike(anything) ~> boolean`

^{v11.4.0}

- Examples
- Deepening topics
- Advanced topics
- Background
- Contributing

Let's look at an example that is based on an actual early use case that lead to
the development of this library. What we have is an external HTTP API that both
produces and consumes JSON objects that include, among many other properties, a
`titles`

property:

```
var sampleTitles = {
titles: [
{language: 'en', text: 'Title'},
{language: 'sv', text: 'Rubrik'}
]
}
```

We ultimately want to present the user with a rich enough editor, with features
such as undo-redo and
validation, for
manipulating the content represented by those JSON objects. The `titles`

property is really just one tiny part of the data model, but, in this tutorial,
we only look at it, because it is sufficient for introducing most of the basic
ideas.

So, what we'd like to have is a way to access the `text`

of titles in a given
language. Given a language, we want to be able to

- get the corresponding text,
- update the corresponding text,
- insert a new text and the immediately surrounding object in a new language, and
- remove an existing text and the immediately surrounding object.

Furthermore, when updating, inserting, and removing texts, we'd like the operations to treat the JSON as immutable and create new JSON objects with the changes rather than mutate existing JSON objects, because this makes it trivial to support features such as undo-redo and can also help to avoid bugs associated with mutable state.

Operations like these are what lenses are good at. Lenses can be seen as a
simple embedded DSL
for specifying data manipulation and querying functions. Lenses allow you to
focus on an element in a data structure by specifying a path from the root of
the data structure to the desired element. Given a lens, one can then perform
operations, like `get`

and `set`

, on the element that the
lens focuses on.

Let's first import the libraries

```
import * as L from 'partial.lenses'
import * as R from 'ramda'
```

and ▶ play just a bit with lenses.

Note that links with the ▶ play symbol, take you to an interactive version of this page where almost all of the code snippets are editable and evaluated in the browser. There is also a separate playground page that allows you to quickly try out lenses.

As mentioned earlier, with lenses we can specify a path to focus on an element.
To specify such a path we use primitive lenses like
`L.prop(propName)`

, to access a named property of an object, and
`L.index(elemIndex)`

, to access an element at a given index in an
array, and compose the path using `L.compose(...lenses)`

.

So, to just get at the `titles`

array of the `sampleTitles`

we can use
the lens `L.prop('titles')`

:

```
L.get(L.prop('titles'), sampleTitles)
```

To focus on the first element of the `titles`

array, we compose with
the `L.index(0)`

lens:

```
L.get(L.compose(L.prop('titles'), L.index(0)), sampleTitles)
```

Then, to focus on the `text`

, we compose with `L.prop('text')`

:

```
L.get(L.compose(L.prop('titles'), L.index(0), L.prop('text')), sampleTitles)
```

We can then use the same composed lens to also set the `text`

:

```
L.set(
L.compose(L.prop('titles'), L.index(0), L.prop('text')),
'New title',
sampleTitles
)
```

In practise, specifying ad hoc lenses like this is not very useful. We'd like to access a text in a given language, so we want a lens parameterized by a given language. To create a parameterized lens, we can write a function that returns a lens. Such a lens should then find the title in the desired language.

Furthermore, while a simple path lens like above allows one to get and set an existing text, it doesn't know enough about the data structure to be able to properly insert new and remove existing texts. So, we will also need to specify such details along with the path to focus on.

Let's then just compose a parameterized lens for accessing the
`text`

of titles:

```
var textIn = language => L.compose(
L.prop('titles'),
L.normalize(R.sortBy(L.get('language'))),
L.find(R.whereEq({language})),
L.valueOr({language, text: ''}),
L.removable('text'),
L.prop('text')
)
```

Take a moment to read through the above definition line by line. Each part
either specifies a step in the path to select the desired element or a way in
which the data structure must be treated at that point. The
`L.prop(...)`

parts are already familiar. The other parts we will
mention below.

Thanks to the parameterized search part,
`L.find(R.whereEq({language}))`

, of the lens composition, we can use
it to query titles:

```
L.get(textIn('sv'), sampleTitles)
```

The `L.find`

lens is given a predicate that it then uses to find an
element from an array to focus on. In this case the predicate is specified with
the help of Ramda's `R.whereEq`

function
that creates an equality predicate from a given template object.

Partial lenses can generally deal with missing data. In this case, when
`L.find`

doesn't find an element, it instead works like a lens to
append a new element into an array.

So, if we use the partial lens to query a title that does not exist, we get the default:

```
L.get(textIn('fi'), sampleTitles)
```

We get this value, rather than `undefined`

, thanks to the ```
L.valueOr({language,
text: ''})
```

part of our lens composition, which ensures that we get
the specified value rather than `null`

or `undefined`

. We get the default even
if we query from `undefined`

:

```
L.get(textIn('fi'), undefined)
```

With partial lenses, `undefined`

is the equivalent of
non-existent.

As with ordinary lenses, we can use the same lens to update titles:

```
L.set(textIn('en'), 'The title', sampleTitles)
```

The same partial lens also allows us to insert new titles:

```
L.set(textIn('fi'), 'Otsikko', sampleTitles)
```

There are a couple of things here that require attention.

The reason that the newly inserted object not only has the `text`

property, but
also the `language`

property is due to the ```
L.valueOr({language, text:
''})
```

part that we used to provide a default.

Also note the position into which the new title was inserted. The array of
titles is kept sorted thanks to the
`L.normalize(R.sortBy(L.get('language')))`

part of our lens.
The `L.normalize`

lens transforms the data when either read or
written with the given function. In this case we used Ramda's
`R.sortBy`

to specify that we want the titles
to be kept sorted by language.

Finally, we can use the same partial lens to remove titles:

```
L.set(textIn('sv'), undefined, sampleTitles)
```

Note that a single title `text`

is actually a part of an object. The key to
having the whole object vanish, rather than just the `text`

property, is the
`L.removable('text')`

part of our lens composition. It makes it
so that when the `text`

property is set to `undefined`

, the result will be
`undefined`

rather than merely an object without the `text`

property.

If we remove all of the titles, we get an empty array:

```
L.set(L.seq(textIn('sv'), textIn('en')), undefined, sampleTitles)
```

Above we use `L.seq`

to run the `L.set`

operation over both
of the focused titles.

Take out one (or more) `L.normalize(...)`

,
`L.valueOr(...)`

or `L.removable(...)`

part(s)
from the lens composition and try to predict what happens when you rerun the
examples with the modified lens composition. Verify your reasoning by actually
rerunning the examples.

For clarity, the previous code snippets avoided some of the shorthands that this library supports. In particular,

`L.compose(...)`

can be abbreviated as an array`[...]`

,`L.prop(propName)`

can be abbreviated as`propName`

, and`L.set(l, undefined, s)`

can be abbreviated as`L.remove(l, s)`

.

It is also typical to compose lenses out of short paths following the schema of the JSON data being manipulated. Recall the lens from the start of the example:

```
L.compose(
L.prop('titles'),
L.normalize(R.sortBy(L.get('language'))),
L.find(R.whereEq({language})),
L.valueOr({language, text: ''}),
L.removable('text'),
L.prop('text')
)
```

Following the structure or schema of the JSON, we could break this into three separate lenses:

- a lens for accessing the titles of a model object,
- a parameterized lens for querying a title object from titles, and
- a lens for accessing the text of a title object.

Furthermore, we could organize the lenses to reflect the structure of the JSON model:

```
var Title = {
text: [L.removable('text'), 'text']
}
var Titles = {
titleIn: language => [
L.find(R.whereEq({language})),
L.valueOr({language, text: ''})
]
}
var Model = {
titles: ['titles', L.normalize(R.sortBy(L.get('language')))],
textIn: language => [Model.titles, Titles.titleIn(language), Title.text]
}
```

We can now say:

```
L.get(Model.textIn('sv'), sampleTitles)
```

This style of organizing lenses is overkill for our toy example. In a more
realistic case the `sampleTitles`

object would contain many more properties.
Also, rather than composing a lens, like `Model.textIn`

above, to access a leaf
property from the root of our object, we might actually compose lenses
incrementally as we inspect the model structure.

So far we have used a lens to manipulate individual items. This library also supports traversals that compose with lenses and can target multiple items. Continuing on the tutorial example, let's define a traversal that targets all the texts:

`var texts = [Model.titles, L.elems, Title.text]`

What makes the above a traversal is the `L.elems`

part. The result
of composing a traversal with a lens is a traversal. The other parts of the
above composition should already be familiar from previous examples. Note how
we were able to use the previously defined `Model.titles`

and `Title.text`

lenses.

Now, we can use the above traversal to `collect`

all the texts:

```
L.collect(texts, sampleTitles)
```

More generally, we can map and fold over texts. For example, we
could use `L.maximumBy`

to find a title with the maximum length:

```
L.maximumBy(R.length, texts, sampleTitles)
```

Of course, we can also modify texts. For example, we could uppercase all the titles:

```
L.modify(texts, R.toUpper, sampleTitles)
```

We can also manipulate texts selectively. For example, we could remove all the texts that are longer than 5 characters:

```
L.remove([texts, L.when(t => t.length > 5)], sampleTitles)
```

This concludes the tutorial. The reference documentation contains lots of tiny examples and a few more involved examples. The examples section describes a couple of lens compositions we've found practical as well as examples that may help to see possibilities beyond the immediately obvious. The wiki contains further examples and playground links. There is also a document that describes a simplified implementation of optics in a similar style as the implementation of this library. Last, but perhaps not least, there is also a page of Partial Lenses Exercises to solve.

Optics provide a way to decouple the operation to perform on an element or elements of a data structure from the details of selecting the element or elements and the details of maintaining the integrity of the data structure. In other words, a selection algorithm and data structure invariant maintenance can be expressed as a composition of optics and used with many different operations.

Consider how one might approach the tutorial problem without
optics. One could, for example, write a collection of operations like
`getText`

, `setText`

, `addText`

, and `remText`

:

```
var getEntry = R.curry(
(language, data) => data.titles.find(R.whereEq({language}))
)
var hasText = R.pipe(getEntry, Boolean)
var getText = R.pipe(getEntry, R.defaultTo({}), R.prop('text'))
var mapProp = R.curry(
(fn, prop, obj) => R.assoc(prop, fn(R.prop(prop, obj)), obj)
)
var mapText = R.curry(
(language, fn, data) => mapProp(
R.map(R.ifElse(R.whereEq({language}), mapProp(fn, 'text'), R.identity)),
'titles',
data
)
)
var remText = R.curry(
(language, data) => mapProp(
R.filter(R.complement(R.whereEq({language}))),
'titles'
)
)
var addText = R.curry(
(language, text, data) => mapProp(R.append({language, text}), 'titles', data)
)
var setText = R.curry(
(language, text, data) => mapText(language, R.always(text), data)
)
```

You can definitely make the above operations both cleaner and more robust. For
example, consider maintaining the ordering of texts and the handling of cases
such as using `addText`

when there already is a text in the specified language
and `setText`

when there isn't. With partial optics, however, you separate the
selection and data structure invariant maintenance from the operations as
illustrated in the tutorial and due to the separation of concerns
that tends to give you a lot of robust functionality in a small amount of
code.

The combinators provided by this library are available as named imports. Typically one just imports the library as:

`import * as L from 'partial.lenses'`

This library has historically been developed in a fairly aggressive manner so
that features have been marked as obsolete and removed in subsequent major
versions. This can be particularly burdensome for developers of libraries that
depend on partial lenses. To help the development of such libraries, this
section specifies a tiny subset of this library as *stable*. While it is
possible that the stable subset is later extended, nothing in the stable subset
will ever be changed in a backwards incompatible manner.

The following operations, with the below mentioned limitations, constitute the stable subset:

`L.compose(...optics) ~> optic`

is stable with the exception that one must not depend on being able to compose optics with ordinary functions. Also, the use of arrays to denote composition is not part of the stable subset. Note that`L.compose()`

is guaranteed to be equivalent to the`L.identity`

optic.`L.get(lens, maybeData) ~> maybeValue`

is stable without limitations.`L.lens(maybeData => maybeValue, (maybeValue, maybeData) => maybeData) ~> lens`

is stable with the exception that one must not depend on the user specified getter and setter functions being passed more than 1 and 2 arguments, respectively, and one must make no assumptions about any extra parameters being passed.`L.modify(optic, maybeValue => maybeValue, maybeData) ~> maybeData`

is stable with the exception that one must not depend on the user specified function being passed more than 1 argument and one must make no assumptions about any extra parameters being passed.`L.remove(optic, maybeData) ~> maybeData`

is stable without limitations.`L.set(optic, maybeValue, maybeData) ~> maybeData`

is stable without limitations.

The main intention behind the stable subset is to enable a dependent library to make basic use of lenses created by client code using the dependent library.

In retrospect, the stable subset has existed since version 2.2.0.

The main Partial Lenses library aims to provide robust general purpose combinators for dealing with plain JavaScript data. Combinators that are more experimental or specialized in purpose or would require additional dependencies aside from the Infestines library, which is mainly used for the currying helpers it provides, are not provided.

Currently the following additional Partial Lenses libraries exist:

The abstractions, traversals, lenses, and
isomorphisms, provided by this library are collectively known
as *optics*. Traversals can target any number of elements. Lenses are a
restriction of traversals that target a single element. Isomorphisms are a
restriction of lenses with an inverse.

In addition to basic bidirectional optics, this library also supports more arbitrary transforms using optics with sequencing and transform ops. Transforms allow operations, such as modifying a part of data structure multiple times or even in a loop, that are not possible with basic optics.

Some optics libraries provide many more abstractions, such as "optionals",
"prisms" and "folds", to name a few, forming a DAG. Aside from being
conceptually important, many of those abstractions are not only useful but
required in a statically typed setting where data structures have precise
constraints on their shapes, so to speak, and operations on data structures must
respect those constraints at *all* times.

On the other hand, in a dynamically typed language like JavaScript, the shapes
of run-time objects are naturally *malleable*. Nothing immediately breaks if a
new object is created as a copy of another object by adding or removing a
property, for example. We can exploit this to our advantage by considering all
optics as *partial* and manage with a smaller amount of distinct classes of
optics.

By definition, a *total
function*, or just a *function*, is defined for all possible inputs. A *partial
function*, on the other hand, may not be defined for all inputs.

As an example, consider an operation to return the first element of an array. Such an operation cannot be total unless the input is restricted to arrays that have at least one element. One might think that the operation could be made total by returning a special value in case the input array is empty, but that is no longer the same operation—the special value is not the first element of the array.

Now, in partial lenses, the idea is that in case the input does not match the
expectation of an optic, then the input is treated as being `undefined`

, which
is the equivalent of non-existent: reading through the optic
gives `undefined`

and writing through the optic replaces the focus with the
written value. This makes the optics in this library partial and allows
specific partial optics, such as the simple `L.prop`

lens, to be used
in a wider range of situations than corresponding total optics.

Making all optics partial has a number of consequences. For one thing, it can
potentially hide bugs: an incorrectly specified optic treats the input as
`undefined`

and may seem to work without raising an error. We have not found
this to be a major source of bugs in practice. However, partiality also has a
number of benefits. In particular, it allows optics to seamlessly support both
insertion and removal. It also allows to reduce the number of necessary
abstractions and it tends to make compositions of optics more concise with fewer
required parts, which both help to avoid bugs.

Optics in this library support a simple unnested form of indexing. When focusing on an array element or an object property, the index of the array element or the key of the object property is passed as the index to user defined functions operating on that focus.

For example:

```
L.get(
[L.find(R.equals('bar')), (value, index) => ({value, index})],
['foo', 'bar', 'baz']
)
```

```
L.modify(L.values, (value, key) => ({key, value}), {x: 1, y: 2})
```

Only optics directly operating on array elements and object properties produce
indices. Most optics do not have an index of their own and they pass the index
given by the preceding optic as their index. For example, `L.when`

doesn't have an index by itself, but it passes through the index provided by the
preceding optic:

```
L.collectAs(
(value, index) => ({value, index}),
[L.elems, L.when(x => x > 2)],
[3, 1, 4, 1]
)
```

```
L.collectAs(
(value, key) => ({value, key}),
[L.values, L.when(x => x > 2)],
{x: 3, y: 1, z: 4, w: 1}
)
```

When accessing a focus deep inside a data structure, the indices along the path to the focus are not collected into a path. However, it is possible to use index manipulating combinators to construct paths of indices and more. For example:

```
L.collectAs(
(value, path) => [L.collect(L.flatten, path), value],
L.lazy(rec => L.ifElse(R.is(Object), [L.joinIx(L.children), rec], [])),
{a: {b: {c: 'abc'}}, x: [{y: [{z: 'xyz'}]}]}
)
```

The reason for not collecting paths by default is that doing so would be
relatively expensive due to the additional allocations. The
`L.choose`

combinator can also be useful in cases where there is a
need to access some index or context along the path to a focus.

Starting with version 10.0.0, to strongly guide away from
mutating data structures, optics call
`Object.freeze`

on any new objects they create when `NODE_ENV`

is not `production`

.

Why only non-`production`

builds? Because `Object.freeze`

can be quite
expensive and the main benefit is in catching potential bugs early during
development.

Also note that optics do not implicitly "deep freeze" data structures given to them or freeze data returned by user defined functions. Only objects newly created by optic functions themselves are frozen.

Starting with version 13.10.0, the possibility that
optics do not unnecessarily clone input data structures is explicitly
acknowledged. In case all elements of an array or object produced by an optic
operation would be the same, as determined by
`Object.is`

,
then it is allowed, but not guaranteed, for the optic operation to return the
input as is.

A lot of libraries these days claim to be composable. Is any collection of functions composable? In the opinion of the author of this library, in order for something to be called "composable", a couple of conditions must be fulfilled:

- There must be an operation or operations that perform composition.
- There must be simple laws on how compositions behave.

Conversely, if there is no operation to perform composition or there are no useful simplifying laws on how compositions behave, then one should not call such a thing composable.

Now, optics are composable in several ways and in each of those ways there is an operation to perform the composition and laws on how such composed optics behave. Here is a table of the means of composition supported by this library:

Form | Operation(s) | Semantics |
---|---|---|

Nesting | `L.compose(...optics)` or `[...optics]` |
Monoid over unityped optics |

Recursing | `L.lazy(optic => optic)` |
Fixed point |

Adapting | `L.choices(optic, ...optics)` |
Semigroup over optics |

Querying | `L.choice(...optics)` and `L.chain(value => optic, optic)` |
MonadPlus over traversals |

Picking | `L.pick({...prop:lens})` |
Product of lenses |

Branching | `L.branch({...prop:traversal})` |
Coproduct of traversals |

Sequencing | `L.seq(...transforms)` |
Monad over transforms |

The above table and, in particular, the semantics column is by no means complete. In particular, the documentation of this library does not generally spell out proofs of the semantics.

Aside from understanding laws on how forms of composition behave, it is useful to understand laws that are specific to operations on lenses and optics, in general. As described in the paper A clear picture of lens laws, many laws have been formulated for lenses and it can be useful to have lenses that do not necessarily obey some laws.

Here is a snippet that demonstrates that partial lenses can obey the laws of, so
called, *very well-behaved lenses*:

```
function test(actual, expected) {
return R.equals(actual, expected) || {actual, expected}
}
var VeryWellBehavedLens = ({lens, data, elemA, elemB}) => ({
GetSet: test(L.set(lens, L.get(lens, data), data), data),
SetGet: test(L.get(lens, L.set(lens, elemA, data)), elemA),
SetSet: test(
L.set(lens, elemB, L.set(lens, elemA, data)),
L.set(lens, elemB, data)
)
})
VeryWellBehavedLens({elemA: 2, elemB: 3, data: {x: 1}, lens: 'x' })
```

You might want to ▶ play with the laws in your browser.

*Note*, however, that *partial* lenses are not (total) lenses. `undefined`

is
given special meaning and should not appear in the manipulated data.

For some reason there seems to be a persistent myth that partial lenses cannot obey lens laws. The issue a little more interesting than a simple yes or no. The short answer is that partial lenses can obey lens laws. However, for practical reasons there are many combinators in this library that, alone, do not obey lens laws. Nevertheless even such combinators can be used in lens compositions that obey lens laws.

Consider the `L.find`

combinator. The truth is that it doesn't by
itself obey lens laws. Here is an example:

```
L.get(L.find(R.equals(1)), L.set(L.find(R.equals(1)), 2, []))
```

As you can see, `L.find(R.equals(1))`

does not obey the `SetGet`

aka
`Put-Get`

law. Does this make the `L.find`

combinator useless? Far
from it.

Consider the following lens:

`var valOf = key => [L.find(R.whereEq({key})), L.defaults({key}), 'val']`

The `valOf`

lens constructor is for accessing association arrays that contain
`{key, val}`

pairs. For example:

```
var sampleAssoc = [{key: 'x', val: 42}, {key: 'y', val: 24}]
L.set(valOf('x'), 101, [])
```

```
L.get(valOf('x'), sampleAssoc)
```

```
L.get(valOf('z'), sampleAssoc)
```

```
L.set(valOf('x'), undefined, sampleAssoc)
```

```
L.set(valOf('x'), 13, sampleAssoc)
```

It obeys lens laws:

```
VeryWellBehavedLens({
elemA: 2,
elemB: 3,
data: [{key: 'x', val: 13}],
lens: valOf('x')
})
```

Before you try to break it, note that a lens returned by `valOf(key)`

is only
supposed to work on valid association arrays. A valid association array must
not contain duplicate keys, `undefined`

is not valid `val`

, and the order of
elements is not significant. (Note that you could also add
`L.rewrite(R.sortBy(L.get('key')))`

to the composition to ensure
that elements stay in the same order.)

The gist of this example is important. Even if it is the case that not all
parts of a lens composition obey lens laws, it can be that a composition taken
as a whole obeys lens laws. The reason why this use of `L.find`

results in a lawful partial lens is that the lenses composed after it restricts
the scope of the lens so that one cannot modify the `key`

.

`L.assign(optic, object, maybeData) ~> maybeData`

`L.assign`

allows one to merge the given object into the object or objects
focused on by the given optic.

For example:

```
L.assign(L.elems, {y: 1}, [{x: 3, y: 2}, {x: 4}])
```

`L.disperse(optic, [...maybeValues], maybeData) ~> maybeData`

`L.disperse`

replaces values in focuses targeted by the given optic with
optional values taken from the given array-like object.
See also `L.partsOf`

.

For example:

```
L.disperse(
L.leafs,
['a', undefined, 'b', 'c', 'd'],
[[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]]
)
```

To understand `L.disperse`

, it is perhaps helpful to consider under what
conditions the following equations hold:

```
ColDis: L.disperse(o, L.collectTotal(o, d), d) = d
DisCol: L.collectTotal(o, L.disperse(o, vs, d)) = vs
DisDis: L.disperse(o, vs, L.disperse(o, vs0, d)) = L.disperse(o, vs, d)
```

The point is that `L.disperse`

is roughly to `L.collectTotal`

as `L.set`

is to `L.get`

. However, just like with
`L.set`

and `L.get`

, the equations do not
hold for all (combinations of) optics (and arrays of values).

`L.modify(optic, (maybeValue, index) => maybeValue, maybeData) ~> maybeData`

`L.modify`

allows one to map over the elements focused on by the given optic.

For example:

```
L.modify(['elems', 0, 'x'], R.inc, {elems: [{x: 1, y: 2}, {x: 3, y: 4}]})
```

```
L.modify(
['elems', L.elems, 'x'],
R.dec,
{elems: [{x: 1, y: 2}, {x: 3, y: 4}]}
)
```

`L.modifyAsync(optic, (maybeValue, index) => maybeValuePromise, maybeData) ~> maybeDataPromise`

`L.modifyAsync`

allows one to map an asynchronous function over the elements
focused on by the given optic. The result of `L.modifyAsync`

is always a
promise.

For example:

```
log(
L.modifyAsync(
['elems', L.elems, 'x'],
async x => x - 1,
{elems: [{x: 1, y: 2}, {x: 3, y: 4}]}
)
)
```

`L.remove(optic, maybeData) ~> maybeData`

`L.remove`

allows one to remove the elements focused on by the given optic.

For example:

```
L.remove([0, L.defaults({}), 'x'], [{x: 1}, {x: 2}, {x: 3}])
```

```
L.remove([L.elems, 'x', L.when(x => x > 1)], [{x: 1}, {x: 2, y: 1}, {x: 3}])
```

Note that `L.remove(optic, maybeData)`

is equivalent to ```
L.set(lens, undefined,
maybeData)
```

. With partial lenses, setting to `undefined`

typically has
the effect of removing the focused element.

`L.set(optic, maybeValue, maybeData) ~> maybeData`

`L.set`

allows one to replace the elements focused on by the given optic with
the specified value.

For example:

```
L.set(['a', 0, 'x'], 11, {id: 'z'})
```

```
L.set([L.elems, 'x', L.when(x => x > 1)], -1, [{x: 1}, {x: 2, y: 1}, {x: 3}])
```

Note that `L.set(lens, maybeValue, maybeData)`

is equivalent to ```
L.modify(lens,
R.always(maybeValue), maybeData)
```

.

`L.traverse(algebra, (maybeValue, index) => operation, optic, maybeData) ~> operation`

`L.traverse`

maps each focus to an operation and returns an operation that runs
those operations in-order and collects the results. The
`algebra`

argument must be either a
`Functor`

,
`Applicative`

,
or
`Monad`

depending on the optic as specified in `L.toFunction`

.

Here is a bit involved example that uses the State applicative and `L.traverse`

to replace elements in a data structure by the number of times those elements
have appeared at that point in the data structure:

```
var State = {
of: result => state => ({state, result}),
ap: (x2yS, xS) => state0 => {
const {state: state1, result: x2y} = x2yS(state0)
const {state, result: x} = xS(state1)
return {state, result: x2y(x)}
},
map: (x2y, xS) => State.ap(State.of(x2y), xS),
run: (s, xS) => xS(s).result
}
var count = x => x2n => {
const k = `${x}`
const n = (x2n[k] || 0) + 1
return {result: n, state: L.set(k, n, x2n)}
}
State.run({}, L.traverse(State, count, L.elems, [1, 2, 1, 1, 2, 3, 4, 3, 4, 5]))
```

The `L.compose`

combinator allows one to build optics that deal
with nested data structures.

`L.compose(...optics) ~> optic`

or `[...optics]`

`L.compose`

creates a nested composition of the given optics and ordinary
functions such that in `L.compose(bigger, smaller)`

the `smaller`

optic can only
see and manipulate the part of the whole as seen through the `bigger`

optic.
See also `L.toFunction`

.

The following equations characterize composition:

```
L.compose() = L.identity
L.compose(l) = l
L.modify(L.compose(o, ...os)) = R.compose(L.modify(o), ...os.map(L.modify))
L.get(L.compose(o, ...os)) = R.pipe(L.get(o), ...os.map(L.get))
```

Furthermore, in this library, an array of optics `[...optics]`

is treated as a
composition `L.compose(...optics)`

. Using the array notation, the above
equations can be written as:

```
[] = L.identity
[l] = l
L.modify([o, ...os]) = R.compose(L.modify(o), ...os.map(L.modify))
L.get([o, ...os]) = R.pipe(L.get(o), ...os.map(L.get))
```

For example:

```
L.set(['a', 1], 'a', {a: ['b', 'c']})
```

```
L.get(['a', 1], {a: ['b', 'c']})
```

You can also directly compose optics with ordinary functions. The result of such a composition is a read-only optic.

For example:

```
L.get(['x', x => x + 1], {x: 1})
```

```
L.set(['x', x => x + 1], 3, {x: 1})
```

Note that eligible ordinary functions must have a maximum arity of two: the
first argument will be the data and second will be the index. Both can, of
course, be `undefined`

. Also starting from version
11.0.0 it is not guaranteed that such ordinary functions
would not be passed other arguments and therefore such functions should not
depend on the number of arguments being passed nor on any arguments beyond the
first two.

Note that `R.compose`

is not the same as
`L.compose`

.

`L.flat(...optics) ~> optic`

`L.flat`

is like `L.compose`

except that `L.flatten`

is composed around and between the given optics. In other words, ```
L.flat(o1,
..., oN)
```

is equivalent to ```
L.compose(L.flatten, o1, L.flatten, ..., L.flatten,
oN, L.flatten)
```

.

The `L.lazy`

combinator allows one to build optics that deal with
nested or recursive data structures of arbitrary depth. It also allows one to
build transforms with loops.

`L.lazy(optic => optic) ~> optic`

`L.lazy`

can be used to construct optics lazily. The function given to `L.lazy`

is passed a forwarding proxy to its return value and can also make forward
references to other optics and possibly construct a recursive optic.

Note that when using `L.lazy`

to construct a recursive optic, it will only work
in a meaningful way when the recursive uses are either precomposed
or presequenced with some other optic in a way that neither causes
immediate nor unconditional recursion.

For example, here is a traversal that targets all the primitive elements in a data structure of nested arrays and objects:

```
var primitives = L.lazy(
rec => L.ifElse(R.is(Object), [L.children, rec], L.optional)
)
```

Note that the above creates a cyclic representation of the traversal and a
similar traversal named `L.leafs`

is provided out-of-the-box.

Now, for example:

```
L.collect(primitives, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
```

```
L.modify(primitives, x => x+1, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
```

```
L.remove(
[primitives, L.when(x => 3 <= x && x <= 4)],
[[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]]
)
```

Adapting combinators allow one to build optics that adapt to their input.

`L.choices(optic, ...optics) ~> optic`

`L.choices`

returns a partial optic that acts like the first of the given optics
whose view is not `undefined`

on the given data structure. When the views of
all of the given optics are `undefined`

, the returned optic acts like the last
of the given optics. See also `L.orElse`

, `L.choice`

,
and `L.alternatives`

.

For example:

```
L.set([L.elems, L.choices('a', 'd')], 3, [{R: 1}, {a: 1}, {d: 2}])
```

`L.choose((maybeValue, index) => optic) ~> optic`

`L.choose`

creates an optic whose operation is determined by the given function
that maps the underlying view, which can be `undefined`

, to an optic. In other
words, the `L.choose`

combinator allows an optic to be constructed *after*
examining the data structure being manipulated. See also `L.cond`

.

For example:

```
var majorAxis = L.choose(
({x, y} = {}) => Math.abs(x) < Math.abs(y) ? 'y' : 'x'
)
L.get(majorAxis, {x: -3, y: 1})
```

```
L.modify(majorAxis, R.negate, {x: -3, y: 1})
```

`L.cond(...[(maybeValue, index) => testable, consequentOptic][, [alternativeOptic]]) ~> optic`

`L.cond`

creates an optic whose operation is selected from the given optics and
predicates on the underlying view. See also `L.condOf`

,
`L.choose`

and `L.ifElse`

.

```
L.cond( [ predicate, consequent ]
, ...
[ , [ alternative ] ] )
```

`L.cond`

is not curried unlike most functions in this library. `L.cond`

can be
given any number of `[predicate, consequent]`

pairs. The *predicates* are
functions on the underlying view and are tested sequentially. The *consequents*
are optics and `L.cond`

acts like the consequent corresponding to the first
predicate that returns true. The last argument to `L.cond`

can be an
`[alternative]`

singleton, where the *alternative* is an optic to be used in
case none of the predicates return true. If all predicates return false and
there is no alternative, `L.cond`

acts like `L.zero`

.

For example:

```
var minorAxis = L.cond(
[({x, y} = {}) => Math.abs(y) < Math.abs(x), 'y'],
['x']
)
L.get(minorAxis, {x: -3, y: 1})
```

```
L.modify(minorAxis, R.negate, {x: -3, y: 1})
```

Note that it is better to omit the predicate from the alternative

`L.cond(..., [alternative])`

than to use a catch all predicate like `R.T`

`L.cond(..., [R.T, alternative])`

because in the latter case `L.cond`

cannot determine that a user defined
predicate will always be true and has to construct a more expensive optic.

Note that when no `[alternative]`

is specified, `L.cond`

returns a
traversal, because the default `L.zero`

is a
traversal.

Note that `L.cond`

can be implemented using `L.choose`

, but not
vice versa. `L.choose`

not only allows the optic to be chosen
dynamically, but also allows the optic to be constructed dynamically and using
the data at the focus.

`L.condOf(traversal, ...[(maybeValue, index) => testable, consequentOptic][, [alternativeOptic]]) ~> optic`

`L.condOf`

is like `L.cond`

except the first argument to `L.condOf`

is a traversal whose focuses are tested with the predicates.

```
L.condOf(traversal,
[ predicate, consequent ]
, ...
[ , [ alternative ] ] )
```

`L.condOf`

acts like the *consequent* optic of first `[predicate, consequent]`

pair whose *predicate* accepts any focus produced by the traversal.
The last argument to `L.condOf`

can be an `[alternative]`

singleton, where the
*alternative* is an optic to be used in case none of the predicates accepts
any focus produced by the traversal. If there is no `[alternative]`

`L.zero`

is used.

For example:

```
L.get(
L.condOf(
'type',
[R.equals('title'), 'text'],
[R.equals('text'), 'body']
),
{type: 'text', body: 'Try writing this with `L.cond`.'}
)
```

Note that `L.condOf(t, [p1, o1], ..., [pN, oN], [o])`

is roughly equivalent to a
combination of `L.any`

and `L.cond`

: ```
L.cond([L.any(p1, t),
o1], ..., [L.any(pN, t), oN], [o])
```

.

Note that when no `[alternative]`

is specified, `L.condOf`

returns a
traversal, because the default `L.zero`

is a
traversal.

`L.ifElse((maybeValue, index) => testable, optic, optic) ~> optic`

`L.ifElse`

creates an optic whose operation is selected based on the given
predicate from the two given optics. If the predicate is truthy on the value at
focus, the first of the given optics is used. Otherwise the second of the given
optics is used. See also `L.cond`

.

For example:

```
L.modify(L.ifElse(Array.isArray, L.elems, L.values), R.inc, [1, 2, 3])
```

```
L.modify(L.ifElse(Array.isArray, L.elems, L.values), R.inc, {x: 1, y: 2, z: 3})
```

`L.orElse(backupOptic, primaryOptic) ~> optic`

`L.orElse(backupOptic, primaryOptic)`

acts like `primaryOptic`

when its view is
not `undefined`

and otherwise like `backupOptic`

. See also
`L.orAlternatively`

.

Note that `L.choice(...optics)`

is equivalent to
`optics.reduceRight(L.orElse, L.zero)`

and `L.choices(...optics)`

is equivalent to `optics.reduceRight(L.orElse)`

.

The indexing combinators allow one to manipulate the indices passed down by optics. Although optics do not construct paths by default one can use the indexing combinators to construct paths. Because optics do not generally depend on the index values, it is also possible to use the index to pass down arbitrary information. For example, one could collect contexts or a list of values from the path to the focus and pass that down as the index.

`L.joinIx(optic) ~> optic`

`L.joinIx`

pairs the index produced by the inner optic with the incoming outer
index to form a (nested) path. In case either index is `undefined`

, no pair is
constructed and the other index is produced as is. See also
`L.skipIx`

and `L.mapIx`

.

For example:

```
L.get(
[
L.joinIx('a'),
L.joinIx('b'),
L.joinIx('c'),
R.pair
],
{a: {b: {c: 'abc'}}}
)
```

`L.mapIx((index, maybeValue) => index) ~> optic`

`L.mapIx`

passes the value returned by the given function as the index.

For example:

```
L.get(
[
L.joinIx('a'),
L.joinIx('b'),
L.joinIx('c'),
L.mapIx(L.collect(L.flatten)),
R.pair
],
{a: {b: {c: 'abc'}}}
)
```

`L.setIx(index) ~> optic`

`L.setIx`

passes the given value as the index. Note that `L.setIx(v)`

is
equivalent to `L.mapIx(R.always(v))`

. See also
`L.tieIx`

and `List`

indexing.

`L.skipIx(optic) ~> optic`

`L.skipIx`

passes the incoming outer index as the index from the optic. See
also `L.joinIx`

.

For example:

```
L.get(
[
L.joinIx('a'),
L.skipIx('b'),
L.joinIx('c'),
R.pair
],
{a: {b: {c: 'abc'}}}
)
```

`L.tieIx((innerIndex, outerIndex) => index, optic) ~> optic`

`L.tieIx`

sets the index to the result of the given function on the index
produced by the wrapped optic and the index passed from the outer context.

For example:

```
L.get(
[
L.setIx([]),
L.tieIx(R.append, 'a'),
L.tieIx(R.append, 'b'),
L.tieIx(R.append, 'c'),
R.pair
],
{a: {b: {c: 'abc'}}}
)
```

Note that both `L.skipIx`

and `L.joinIx`

can be
implemented via `L.tieIx`

.

`L.getLog(lens, maybeData) ~> maybeValue`

`L.getLog`

returns the element focused on by a lens from a data
structure like `L.get`

, but `L.getLog`

also
`console.log`

s
the sequence of values that the corresponding `L.set`

operation would
create. This can be useful for understanding why a particular value was
returned. `L.getLog`

, like `L.log`

, is intended for debugging.

For example:

```
L.getLog(['data', L.elems, 'y'], {data: [{x: 1}, {y: 2}]})
```

(If you are looking at the above snippet in the interactive version of this
page, then note that the
`console.log`

function is replaced by Klipse and the
replacement function unfortunately does not handle substitution strings
correctly.)

`L.log(...labels) ~> optic`

`L.log(...labels)`

is an identity optic that outputs
`console.log`

messages with the given labels (or format in
Node.js) when
data flows in either direction, `get`

or `set`

, through the lens. See also
`L.getLog`

.

For example:

```
L.set(['x', L.log('x')], '11', {x: 10})
```

```
L.set(['x', L.log('%s x: %j')], '11', {x: 10})
```

`L.Identity ~> Monad`

`L.Identity`

is the Static
Land
compatible identity
`Monad`

definition used by Partial Lenses.

`L.IdentityAsync ~> Monadish`

`L.IdentityAsync`

is like `L.Identity`

, but allows values to be
thenable.
JavaScript promises do not form a
monad,
which explains the "monadish". Fortunately one usually does not want nested
promises in which case the approximation can be close enough.

`L.Select ~> Applicative`

`L.Select`

is the Static
Land
compatible
`Applicative`

definition that extends the constant functor to select the first non-`undefined`

element.

The basis for `Select`

is the following
monoid
over JavaScript values:

```
var Defined = {
empty: _ => undefined,
concat: (l, r) => l !== undefined ? l : r
}
```

It is a monoid, because it satisfies the Monoid laws:

```
var MonoidLaws = (M, x, y, z) => ({
associativity: test(M.concat(M.concat(x, y), z), M.concat(x, M.concat(y, z))),
leftIdentity: test(M.concat(M.empty(), x), x) ,
rightIdentity: test(M.concat(x, M.empty()), x)
})
MonoidLaws(Defined, {Try: 'any'}, 'JavaScript', ['values'])
```

In Partial Lenses `undefined`

is used to represent
nothingness.

`L.toFunction(optic) ~> optic`

`L.toFunction`

converts a given optic, which can be a string, an
integer, an array, or a function to an optic function.

```
optic = string
| number
| [ ...optic ]
| (x, i) => /* ordinary function = read-only optic */
| (x, i, F, xi2yF) => /* optic function */
```

This can be useful for implementing new combinators that cannot otherwise be
implemented using the combinators provided by this library. See also
`L.traverse`

.

For isomorphisms and lenses, the returned optic function will have the signature

`(Maybe s, Index, Functor c, (Maybe a, Index) -> c b) -> c t`

for traversals the signature will be

`(Maybe s, Index, Applicative c, (Maybe a, Index) -> c b) -> c t`

and for transforms the signature will be

`(Maybe s, Index, Monad c, (Maybe a, Index) -> c b) -> c t`

Note that the above signatures are written using the "tupled" parameter notation
`(...) -> ...`

to denote that the functions are not curried.

The
`Functor`

,
`Applicative`

,
and
`Monad`

arguments are expected to conform to their Static
Land
specifications.

Note that, in conjunction with partial optics, it may be advantageous to have
the algebras to allow for partiality. With traversals it is also possible, for
example, to simply post compose optics with `L.optional`

to skip
`undefined`

elements.

Note that if you simply wish to perform an operation that needs roughly the full
expressive power of the underlying lens encoding, you should use
`L.traverse`

, because it is independent of the underlying
encoding, while `L.toFunction`

essentially exposes the underlying encoding and
it is better to avoid depending on that.

Ordinary optics are passive and bidirectional in such a way that the
same optic can be both read and written through. The underlying
implementation of this library also allows one to implement
active operations that don't quite provide the same kind of passive
bidirectionality, but can be used to flexibly modify data
structures. Such operations are called *transforms* in this library.

Unlike ordinary optics, transforms allow for monadic sequencing, which makes it possible to operate on a part of data structure multiple times. This allows operations that are impossible to implement using ordinary optics, but also potentially makes it more difficult to reason about the results. This ability also makes it impossible to read through transforms in the same sense as with ordinary optics.

Recall that lenses have a single focus and traversals
have multiple focuses that can then be operated upon using various operations
such as `L.modify`

. Although it is not strictly enforced by this
library, it is perhaps clearest to think that transforms have no focuses. A
transform using transform ops, that act as traversals of no
elements, can, and perhaps preferably should, be empty and should
be executed using `L.transform`

, which, unlike
`L.modify`

, takes no user defined operation to apply to focuses.

The line between transforms and optics is not entirely clear cut in the sense that it is technically possible to use various transform ops within an ordinary optic definition. Furthermore, it is also possible to use sequencing to create transforms that have focuses that can then be operated upon. The results of such uses don't quite follow the laws of ordinary optics, but may sometimes be useful.

`L.transform(optic, maybeData) ~> maybeData`

`L.transform(o, s)`

is shorthand for `L.modify(o, x => x, s)`

and
is intended for running transforms defined using transform
ops.

For example:

```
L.transform(
[L.elems, L.modifyOp(x => -x)],
[1, 2, 3]
)
```

Note that

`L.assign(o, x, s)`

is equivalent to`L.transform([o, L.assignOp(x)], s)`

,`L.modify(o, f, s)`

is equivalent to`L.transform([o, L.modifyOp(f)], s)`

,`L.set(o, x, s)`

is equivalent to`L.transform([o, L.setOp(x)], s)`

, and`L.remove(o, s)`

is equivalent to`L.transform([o, L.removeOp], s)`

.

`L.transformAsync(optic, maybeData) ~> maybeDataPromise`

`L.transformAsync`

is like `L.transform`

, but allows
`L.modifyOp`

operations to be asynchronous. The result of
`L.transformAsync`

is always a
promise.

For example:

```
log(
L.transformAsync(L.leafs, {
combine: Promise.resolve('a nested template'),
of: [Promise.resolve('promises')],
or: 'constants'
})
)
```

```
log(
L.transformAsync(
[L.elems, L.modifyOp(async x => -x)],
[1, 2, 3]
)
)
```

The `L.seq`

combinator allows one to build transforms
that modify their focus more than once.

`L.seq(...transforms) ~> transform`

`L.seq`

creates a transform that modifies the focus with each of the given
transforms in sequence.

Here is an example of a bottom-up transform over a data structure of nested objects and arrays:

```
var everywhere = L.lazy(
rec => L.ifElse(R.is(Object), L.seq([L.children, rec], []), [])
)
```

The above `everywhere`

transform is similar to the
`F.everywhere`

transform
of the `fastener`

zipper-library. Note
that the above `everywhere`

and the `primitives`

example differ in
that `primitives`

only targets the non-object and non-array elements of the data
structure while `everywhere`

also targets those.

```
L.modify(everywhere, x => [x], {xs: [{x: 1}, {x: 2}]})
```

Note that `L.seq`

, `L.choose`

, and `L.setOp`

can be
combined together as a
`Monad`

```
chain(x2t, t) = L.seq(t, L.choose(x2t))
of(x) = L.setOp(x)
```

which is not the same as the querying monad.

`L.assignOp(object) ~> traversal`

`L.assignOp`

creates a transform that merges the given object into the object in
focus. When used as a traversal, `L.assignOp`

acts as a traversal of no
elements. Usually, however, `L.assignOp`

is used within
transforms.

For example:

```
L.transform([L.elems, L.assignOp({y: 1})], [{x: 3}, {x: 4, y: 5}])
```

`L.modifyOp((maybeValue, index) => maybeValue) ~> traversal`

`L.modifyOp`

creates a transform that maps the focus with the given function.
When used as a traversal, `L.modifyOp`

acts as a traversal of no elements.
Usually, however, `L.modifyOp`

is used within transforms.

For example:

```
L.transform(
L.branch({
xs: [L.elems, L.modifyOp(R.inc)],
z: [L.optional, L.modifyOp(R.negate)],
ys: [L.elems, L.modifyOp(R.dec)]
}),
{xs: [1, 2, 3], ys: [1, 2, 3]}
)
```

`L.removeOp ~> traversal`

`L.removeOp`

is shorthand for `L.setOp(undefined)`

.

Here is an example based on a question from a user:

```
var sampleToFilter = {
elements: [
{time: 1, subelements: [1, 2, 3, 4]},
{time: 2, subelements: [1, 2, 3, 4]},
{time: 3, subelements: [1, 2, 3, 4]}
]
}
L.transform(
[
'elements',
L.elems,
L.ifElse(
elem => elem.time < 2,
L.removeOp,
['subelements', L.elems, L.when(i => i < 3), L.removeOp]
)
],
sampleToFilter
)
```

The idea is to filter the data both by `time`

and by `subelements`

.

`L.setOp(maybeValue) ~> traversal`

`L.setOp(x)`

is shorthand for `L.modifyOp(R.always(x))`

.

A traversal operates over a collection of non-overlapping focuses that are visited only once and can, for example, be collected, folded, modified, set and removed. Put in another way, a traversal specifies a set of paths to elements in a data structure.

`L.branch({prop: traversal, ...props}) ~> traversal`

`L.branch`

creates a new traversal from a given possibly nested template object
that specifies how the new traversal should visit the properties of an object.
If one thinks of traversals as specifying sets of paths, then the template can
be seen as mapping each property to a set of paths to traverse.

For example:

```
L.collect(
L.branch({first: L.elems, second: {value: []}}),
{first: ['x'], second: {value: 'y'}}
)
```

The use of `[]`

above might be puzzling at first.
`[]`

essentially specifies an empty path. So, when a property is
mapped to `[]`

in the template given to `L.branch`

, it means that
the element is to be visited by the resulting traversal.

Note that `L.branch`

is equivalent to `L.branchOr(L.zero)`

.

Note that you can also compose `L.branch`

with other optics. For example, you
can compose with `L.pick`

to create a traversal over specific
elements of an array:

```
L.modify(
[L.pick({z: 2, x: 0}), L.branch({x: [], z: []})],
R.negate,
[1, 2, 3]
)
```

See the BST traversal section for a more meaningful example.

`L.branchOr(traversal, {prop: traversal, ...props}) ~> traversal`

`L.branchOr`

creates a new traversal from a given traversal and a given possibly
nested template object. The template specifies how the new traversal should
visit the corresponding properties of an object. The separate traversal is used
for properties not defined in the template.

For example:

```
L.transform(L.branchOr(L.modifyOp(R.inc), {x: L.modifyOp(R.dec)}), {x: 0, y: 0})
```

Note that `L.branch`

is equivalent to
`L.branchOr(L.zero)`

and `L.values`

is equivalent to
`L.branchOr([], {})`

.

`L.branches(...propNames) ~> traversal`

`L.branches`

creates a new traversal that visits the specified properties of an
object. `L.branches(p1, ..., pN)`

is equivalent to ```
L.branch({[p1]: [],
..., [pN]: []})
```

.

`L.children ~> traversal`

`L.children`

is a traversal over the immediate children of the ordinary array or
plain object in focus. Children of objects whose constructor is neither `Array`

nor `Object`

are not traversed. See also `L.leafs`

.

For example:

```
L.modify(L.children, R.negate, {x: 3, y: 1})
```

```
L.modify(L.children, R.negate, [1, 2, 3])
```

`L.elems ~> traversal`

`L.elems`

is a traversal over the elements of an array-like
object. When written through, `L.elems`

always produces an `Array`

. See also
`L.values`

and `L.elemsTotal`

.

For example:

```
L.modify(['xs', L.elems, 'x'], R.inc, {xs: [{x: 1}, {x: 2}]})
```

Just like with other optics operating on array-like objects, when
manipulating non-`Array`

objects, `L.rewrite`

can be used to
convert the result to the desired type, if necessary:

```
L.modify(
[L.rewrite(xs => Int8Array.from(xs)), L.elems],
R.inc,
Int8Array.from([-1, 4, 0, 2, 4])
)
```

`L.elemsTotal ~> traversal`

`L.elemsTotal`

is a traversal over the elements of an array-like
object. When written through, `L.elemsTotal`

always produces an `Array`

.
Unlike `L.elems`

, `L.elemsTotal`

does not remove `undefined`

elements from the resulting array when written through.

For example:

```
L.modify([L.elemsTotal, L.when(R.is(Number))], R.negate, [1, undefined, 2])
```

`L.entries ~> traversal`

`L.entries`

is a traversal over the entries, or `[key, value]`

pairs, of an
object.

For example:

```
L.modify(L.entries, ([k, v]) => [v, k], {x: 'a', y: 'b'})
```

`L.flatten ~> traversal`

`L.flatten`

is a traversal over the elements of arbitrarily nested arrays.
Other array-like objects are treated as elements by `L.flatten`

.
In case the immediate target of `L.flatten`

is neither `undefined`

nor an array,
it is traversed.

For example:

```
L.join(' ', L.flatten, [[[1]], ['2'], 3])
```

`L.keys ~> traversal`

`L.keys`

is a traversal over the keys of an object.

For example:

```
L.modify(L.keys, R.toUpper, {x: 1, y: 2})
```

`L.leafs ~> traversal`

`L.leafs`

is a traversal that descends into ordinary arrays and plain objects
and focuses on non-`undefined`

elements whose constructor is neither `Array`

nor
`Object`

. See also `L.children`

.

For example:

```
L.modify(L.leafs, R.negate, [{x: 1, y: [2]}, 3])
```

`L.matches(/.../g) ~> traversal`

`L.matches`

, when given a regular expression with the
`global`

flag, `/.../g`

, is a partial traversal over the matches that the regular
expression gives over the focused string. See also `L.matches`

.

For example:

```
L.collect(
[
L.matches(/[^&=?]+=[^&=]+/g),
L.pick({name: L.matches(/^[^=]+/), value: L.matches(/[^=]+$/)})
],
'?first=foo&second=bar'
)
```

Note that an empty match terminates the traversal. It is possible to make use of that feature, but it is also possible that an empty match is due to an incorrect regular expression that can match the empty string.

`L.query(...traversals) ~> traversal`

`L.query`

is a traversal that searches for
defined elements within a nested data structure of ordinary
arrays and plain objects that are focused on by the given sequence of
traversals. `L.query`

gives similar power as the descendant
combinator
of CSS selectors.

Recall the tutorial example. Perhaps the easiest way to focus on all the texts is to just query for them:

```
L.collect(L.query('text'), sampleTitles)
```

So, to convert all the texts to upper case, one could write:

```
L.modify(L.query('text'), R.toUpper, sampleTitles)
```

To only modify the text of a specific language, one could write:

```
L.modify(
L.query(L.when(R.propEq('language', 'en')), 'text'),
R.toUpper,
sampleTitles
)
```

And one can also view the text of a specific language:

```
L.get(L.query(L.when(R.propEq('language', 'sv')), 'text'), sampleTitles)
```

Like CSS selectors, `L.query`

can be quite convenient, but should be used with
care. The search for matching elements can be expensive and specifying a query
that matches precisely the desired elements can be difficult.

Note that `L.query(...ts)`

is roughly equivalent to ```
ts.map(t =>
[L.satisfying(L.isDefined(t)), t])
```

and
`L.query(L.when(predicate))`

is roughly equivalent to
`L.satisfying(predicate)`

.

`L.satisfying((maybeValue, index) => testable) ~> traversal`

`L.satisfying`

is a traversal that focuses on elements that satisfy the given
predicate within a nested data structure of ordinary arrays and plain objects.
Children of objects whose constructor is neither `Array`

nor `Object`

are not
traversed. See also `L.query`

.

`L.values ~> traversal`

`L.values`

is a traversal over the values of an `instanceof Object`

. When
written through, `L.values`

always produces an `Object`

. See also
`L.elems`

.

For example:

```
L.modify(L.values, R.negate, {a: 1, b: 2, c: 3})
```

When manipulating objects with a non-`Object`

constructor

```
function XYZ(x, y, z) {
this.x = x
this.y = y
this.z = z
}
XYZ.prototype.norm = function () {
return this.x * this.x + this.y * this.y + this.z * this.z
}
```

`L.rewrite`

can be used to convert the result to the desired type,
if necessary:

```
var objectTo = C => o => Object.assign(Object.create(C.prototype), o)
L.modify([L.rewrite(objectTo(XYZ)), L.values], R.negate, new XYZ(1, 2, 3))
```

Note that `L.values`

is equivalent to `L.branchOr([], {})`

.

Querying combinators allow one to use optics to query data structures. Querying is distinguished from adapting in that querying defaults to an empty or read-only zero.

`L.chain((value, index) => optic, optic) ~> traversal`

`L.chain`

provides a monadic
chain
combinator for querying with optics. `L.chain(toOptic, optic)`

is equivalent to

```
L.compose(
optic,
L.choose(
(value, index) => value === undefined ? L.zero : toOptic(value, index)
)
)
```

Note that with the `R.always`

, `L.chain`

,
`L.choice`

and `L.zero`

combinators, one can consider
optics as subsuming the maybe monad.

`L.choice(...optics) ~> traversal`

`L.choice`

returns a partial optic that acts like the first of the given optics
whose view is not `undefined`

on the given data structure. When the views of
all of the given optics are `undefined`

, the returned optic acts like
`L.zero`

, which is the identity element of `L.choice`

. See also
`L.choices`

.

For example:

```
L.modify([L.elems, L.choice('a', 'd')], R.inc, [{R: 1}, {a: 1}, {d: 2}])
```

`L.optional ~> traversal`

`L.optional`

is an optic over an optional element. When used as a traversal,
and the focus is `undefined`

, the traversal is empty. When used as a lens, and
the focus is `undefined`

, the lens will be read-only.

As an example, consider the difference between:

```
L.set([L.elems, 'x'], 3, [{x: 1}, {y: 2}])
```

and:

```
L.set([L.elems, 'x', L.optional], 3, [{x: 1}, {y: 2}])
```

Note that `L.optional`

is equivalent to ```
L.when(x => x !==
undefined)
```

.

`L.unless((maybeValue, index) => testable) ~> traversal`

`L.unless`

allows one to selectively skip elements within a traversal. See also
`L.when`

.

For example:

```
L.modify([L.elems, L.unless(x => x < 0)], R.negate, [0, -1, 2, -3, 4])
```

`L.when((maybeValue, index) => testable) ~> traversal`

`L.when`

allows one to selectively skip elements within a traversal. See also
`L.unless`

.

For example:

```
L.modify([L.elems, L.when(x => x > 0)], R.negate, [0, -1, 2, -3, 4])
```

Note that `L.when(p)`

is equivalent to ```
L.choose((x, i) => p(x, i) ?
L.identity : L.zero)
```

.

`L.zero ~> traversal`

`L.zero`

is a traversal of no elements and is the identity element of
`L.choice`

and `L.chain`

.

For example:

```
L.collect(
[L.elems, L.cond([R.is(Array), L.elems], [R.is(Object), 'x'], [L.zero])],
[1, {x: 2}, [3, 4]]
)
```

`L.all((maybeValue, index) => testable, traversal, maybeData) ~> boolean`

`L.all`

determines whether all of the elements focused on by the given traversal
satisfy the given predicate.

For example:

```
L.all(
x => 1 <= x && x <= 6,
primitives,
[[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]]
)
```

See also: `L.any`

, `L.none`

, and
`L.getAs`

.

`L.all1((maybeValue, index) => testable, traversal, maybeData) ~> boolean`

`L.all1`

determines whether all and at least one of the elements focused on by
the given traversal satisfy the given predicate.

`L.and(traversal, maybeData) ~> boolean`

`L.and`

determines whether all of the elements focused on by the given traversal
are truthy.

For example:

```
L.and(L.elems, [])
```

Note that `L.and`

is equivalent to `L.all(x => x)`

. See also:
`L.or`

.

`L.and1(traversal, maybeData) ~> boolean`

`L.and1`

determines whether all and at least one of the elements focused on by
the given traversal are truthy.

`L.any((maybeValue, index) => testable, traversal, maybeData) ~> boolean`

`L.any`

determines whether any of the elements focused on by the given traversal
satisfy the given predicate.

For example:

```
L.any(x => x > 5, primitives, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
```

See also: `L.all`

, `L.none`

, and
`L.getAs`

.

`L.collect(traversal, maybeData) ~> [...values]`

`L.collect`

returns an array of the non-`undefined`

elements focused on by the
given traversal or lens from a data structure. See also
`L.collectTotal`

.

For example:

```
L.collect(['xs', L.elems, 'x'], {xs: [{x: 1}, {x: 2}]})
```

Note that `L.collect`

is equivalent to `L.collectAs(x => x)`

.

`L.collectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> [...values]`

`L.collectAs`

returns an array of the non-`undefined`

values returned by the
given function from the elements focused on by the given traversal. See also
`L.collectTotalAs`

.

For example:

```
L.collectAs(R.negate, ['xs', L.elems, 'x'], {xs: [{x: 1}, {x: 2}]})
```

`L.collectAs(toMaybe, traversal, maybeData)`

is equivalent to
`L.concatAs(toCollect, Collect, [traversal, toMaybe], maybeData)`

where `Collect`

and `toCollect`

are defined as follows:

```
var Collect = {empty: R.always([]), concat: R.concat}
var toCollect = x => x !== undefined ? [x] : []
```

So:

```
L.concatAs(
toCollect,
Collect,
['xs', L.elems, 'x', R.negate],
{xs: [{x: 1}, {x: 2}]}
)
```

The internal implementation of `L.collectAs`

is optimized and faster than the
above naïve implementation.

`L.collectTotal(traversal, maybeData) ~> [...maybeValues]`

`L.collectTotal`

returns an array of the elements focused on by the given
traversal or lens from a data structure. See also `L.collect`

.

```
L.collectTotal([L.elems, 'x'], [{x: 'a'}, {y: 'b'}])
```

`L.collectTotalAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> [...maybeValues]`

`L.collectTotalAs`

returns an array of the values returned by the given function
from the elements focused on by the given traversal. See also
`L.collectAs`

.

`L.concat(monoid, traversal, maybeData) ~> value`

`L.concat({empty, concat}, t, s)`

performs a fold, using the given `concat`

and
`empty`

operations, over the elements focused on by the given traversal or lens
`t`

from the given data structure `s`

. The `concat`

operation and the constant
returned by `empty()`

should form a
monoid
over the values focused on by `t`

.

For example:

```
var Sum = {empty: () => 0, concat: (x, y) => x + y}
L.concat(Sum, L.elems, [1, 2, 3])
```

Note that `L.concat`

is staged so that after given the first argument,
`L.concat(m)`

, a computation step is performed.

`L.concatAs((maybeValue, index) => value, monoid, traversal, maybeData) ~> value`

`L.concatAs(xMi2r, {empty, concat}, t, s)`

performs a map, using given function
`xMi2r`

, and fold, using the given `concat`

and `empty`

operations, over the
elements focused on by the given traversal or lens `t`

from the given data
structure `s`

. The `concat`

operation and the constant returned by `empty()`

should form a
monoid
over the values returned by `xMi2r`

.

For example:

```
L.concatAs(x => x, Sum, L.elems, [1, 2, 3])
```

Note that `L.concatAs`

is staged so that after given the first two arguments,
`L.concatAs(f, m)`

, a computation step is performed.

`L.count(traversal, maybeData) ~> number`

`L.count`

goes through all the elements focused on by the traversal and counts
the number of non-`undefined`

elements.

For example:

```
L.count([L.elems, 'x'], [{x: 11}, {y: 12}])
```

`L.countIf((maybeValue, index) => testable, traversal, maybeData) ~> number`

`L.countIf`

goes through all the elements focused on by the traversal and counts
the number of elements for which the given predicate returns a truthy value.

For example:

```
L.countIf(L.isDefined('x'), L.elems, [{x: 11}, {y: 12}])
```

`L.counts(traversal, maybeData) ~> map`

`L.counts`

returns a
map
of the counts of distinct values, including `undefined`

, focused on by the given
traversal.

For example:

```
Array.from(L.counts(L.elems, [3, 1, 4, 1]).entries())
```

`L.countsAs((maybeValue, index) => any, traversal, maybeData) ~> map`

`L.countsAs`

returns a
map
of the counts of distinct values, including `undefined`

, returned by the given
function from the values focused on by the given traversal.

For example:

```
Array.from(L.countsAs(Math.abs, L.elems, [3, -1, 4, 1]).entries())
```

`L.foldl((value, maybeValue, index) => value, value, traversal, maybeData) ~> value`

`L.foldl`

performs a fold from left over the elements focused on by the given
traversal. This is much like the
`reduce`

method of JavaScript arrays.

For example:

```
L.foldl((x, y) => x + y, 0, L.elems, [1, 2, 3])
```

Note that `L.forEachWith`

is much like an imperative version
of `L.foldl`

. Consider using it instead of using `L.foldl`

with an imperative
accumulator procedure.

`L.foldr((value, maybeValue, index) => value, value, traversal, maybeData) ~> value`

`L.foldr`

performs a fold from right over the elements focused on by the given
traversal. This is much like the
`reduceRight`

method of JavaScript arrays.

For example:

```
L.foldr((x, y) => x * y, 1, L.elems, [1, 2, 3])
```

`L.forEach((maybeValue, index) => undefined, traversal, maybeData) ~> undefined`

`L.forEach`

calls the given function for each focus of the traversal.

For example:

```
L.forEach(console.log, [L.elems, 'x', L.elems], [{x: [3]}, {x: [1, 4]}, {x: [1]}])
```

`L.forEachWith(() => context, (context, maybeValue, index) => undefined, traversal, maybeData) ~> context`

`L.forEachWith`

first calls the given thunk to get or create a context. Then it
calls the given function, with context as the first argument, for each focus of
the traversal. Finally the context is returned. This is much like an
imperative version of `L.foldl`

.

For example:

```
L.forEachWith(() => new Map(), (m, v, k) => m.set(k, v), L.values, {x: 2, y: 1})
```

Note that a new `Map`

is returned each time the above expression is evaluated.

`L.get(traversal, maybeData) ~> maybeValue`

`L.get`

returns the element focused on by a lens from a data
structure or goes lazily over the elements focused on by the given
traversal and returns the first non-`undefined`

element. See
also `L.getLog`

.

For example:

```
L.get('y', {x: 112, y: 101})
```

```
L.get([L.elems, 'y'], [{x:1}, {y:2}, {z:3}])
```

Note that `L.get`

is equivalent to `L.getAs(x => x)`

.

`L.getAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> maybeValue`

`L.getAs`

goes lazily over the elements focused on by the given traversal,
applying the given function to each element, and returns the first
non-`undefined`

value returned by the function.

```
L.getAs(x => x > 3 ? -x : undefined, L.elems, [3, 1, 4, 1, 5])
```

`L.getAs`

operates lazily. The user specified function is only applied to
elements until the first non-`undefined`

value is returned and after that
`L.getAs`

returns without examining more elements.

Note that `L.getAs`

can be used to implement many other operations over
traversals such as finding an element matching a predicate and checking whether
all/any elements match a predicate. For example, here is how you could
implement a for all predicate over traversals:

`var all = (p, t, s) => !L.getAs(x => p(x) ? undefined : true, t, s)`

Now:

```
all(x => x < 9, primitives, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
```

`L.isDefined(traversal, maybeData) ~> boolean`

`L.isDefined`

determines whether or not the given traversal focuses on any
non-`undefined`

element on the given data structure. When used with a lens,
`L.isDefined`

basically allows you to check whether the target of the lens
exists or, in other words, whether the data structure has the targeted element.
See also `L.isEmpty`

.

For example:

```
L.isDefined('x', {y: 1})
```

`L.isEmpty(traversal, maybeData) ~> boolean`

`L.isEmpty`

determines whether or not the given traversal focuses on any
elements, `undefined`

or otherwise, on the given data structure. Note that when
used with a lens, `L.isEmpty`

always returns `false`

, because lenses always have
a single focus. See also `L.isDefined`

.

For example:

```
L.isEmpty(L.flatten, [[], [[[], []], []]])
```

`L.join(string, traversal, maybeData) ~> string`

`L.join`

creates a string by joining the optional elements targeted by the given
traversal with the given delimiter.

For example:

```
L.join(', ', [L.elems, 'x'], [{x: 1}, {y: 2}, {x: 3}])
```

`L.joinAs((maybeValue, index) => maybeString, string, traversal, maybeData) ~> string`

`L.joinAs`

creates a string by converting the elements targeted by the given
traversal to optional strings with the given function and then joining those
strings with the given delimiter.

For example:

```
L.joinAs(JSON.stringify, ', ', L.elems, [{x: 1}, {y: 2}])
```

`L.maximum(traversal, maybeData) ~> maybeValue`

`L.maximum`

computes a maximum of the optional elements targeted by the
traversal.

For example:

```
L.maximum(L.elems, [1, 2, 3])
```

Note that elements are ordered according to the `>`

operator.

`L.maximumBy((maybeValue, index) => maybeKey, traversal, maybeData) ~> maybeValue`

`L.maximumBy`

computes a maximum of the elements targeted by the traversal based
on the optional keys returned by the given function. Elements for which the
returned key is `undefined`

are skipped.

For example:

```
L.maximumBy(R.length, L.elems, ['first', 'second', '--||--', 'third'])
```

Note that keys are ordered according to the `>`

operator.

`L.mean(traversal, maybeData) ~> number`

`L.mean`

computes the arithmetic mean of the optional numbers targeted by the
traversal.

For example:

```
L.mean([L.elems, 'x'], [{x: 1}, {ignored: 3}, {x: 2}])
```

`L.meanAs((maybeValue, index) => maybeNumber, traversal, maybeData) ~> number`

`L.meanAs`

computes the arithmetic mean of the optional numbers returned by the
given function for the elements targeted by the traversal.

For example:

```
L.meanAs((x, i) => x <= i ? undefined : x, L.elems, [3, 1, 4, 1])
```

`L.minimum(traversal, maybeData) ~> maybeValue`

`L.minimum`

computes a minimum of the optional elements targeted by the
traversal.

For example:

```
L.minimum(L.elems, [1, 2, 3])
```

Note that elements are ordered according to the `<`

operator.

`L.minimumBy((maybeValue, index) => maybeKey, traversal, maybeData) ~> maybeValue`

`L.minimumBy`

computes a minimum of the elements targeted by the traversal based
on the optional keys returned by the given function. Elements for which the
returned key is `undefined`

are skipped.

For example:

```
L.minimumBy(L.get('x'), L.elems, [{x: 1}, {x: -3}, {x: 2}])
```

Note that keys are ordered according to the `<`

operator.

`L.none((maybeValue, index) => testable, traversal, maybeData) ~> boolean`

`L.none`

determines whether none of the elements focused on by the given
traversal satisfy the given predicate.

For example:

```
L.none(x => x > 5, primitives, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
```

See also: `L.all`

, `L.any`

, and `L.getAs`

.

`L.or(traversal, maybeData) ~> boolean`

`L.or`

determines whether any of the elements focused on by the given traversal
is truthy.

For example:

```
L.or(L.elems, [])
```

Note that `L.or`

is equivalent to `L.any(x => x)`

. See also:
`L.and`

.

`L.product(traversal, maybeData) ~> number`

`L.product`

computes the product of the optional numbers targeted by the
traversal.

For example:

```
L.product(L.elems, [1, 2, 3])
```

`L.productAs((maybeValue, index) => number, traversal, maybeData) ~> number`

`L.productAs`

computes the product of the numbers returned by the given function
for the elements targeted by the traversal.

For example:

```
L.productAs((x, i) => x + i, L.elems, [3, 2, 1])
```

Note that unlike many other folds, `L.productAs`

expects the function to only
return numbers and `undefined`

is not treated in a special way. If you need to
skip elements, you can return the number `1`

.

`L.select(traversal, maybeData) ~> maybeValue`

**WARNING: L.select has been obsoleted. Just use L.get. See
CHANGELOG for details.**

`L.select`

goes lazily over the elements focused on by the given traversal and
returns the first non-`undefined`

element.

```
L.select([L.elems, 'y'], [{x:1}, {y:2}, {z:3}])
```

Note that `L.select`

is equivalent to `L.selectAs(x => x)`

.

`L.selectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> maybeValue`

**WARNING: L.selectAs has been obsoleted. Just use L.getAs.
See CHANGELOG for details.**

`L.selectAs`

goes lazily over the elements focused on by the given traversal,
applying the given function to each element, and returns the first
non-`undefined`

value returned by the function.

```
L.selectAs(x => x > 3 ? -x : undefined, L.elems, [3, 1, 4, 1, 5])
```

`L.selectAs`

operates lazily. The user specified function is only applied to
elements until the first non-`undefined`

value is returned and after that
`L.selectAs`

returns without examining more elements.

Note that `L.selectAs`

can be used to implement many other operations over
traversals such as finding an element matching a predicate and checking whether
all/any elements match a predicate. For example, here is how you could
implement a for all predicate over traversals:

`var all = (p, t, s) => !L.selectAs(x => p(x) ? undefined : true, t, s)`

Now:

```
all(x => x < 9, primitives, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
```

`L.sum(traversal, maybeData) ~> number`

`L.sum`

computes the sum of the optional numbers targeted by the traversal.

For example:

```
L.sum(L.elems, [1, 2, 3])
```

`L.sumAs((maybeValue, index) => number, traversal, maybeData) ~> number`

`L.sumAs`

computes the sum of the numbers returned by the given function for the
elements targeted by the traversal.

For example:

```
L.sumAs((x, i) => x + i, L.elems, [3, 2, 1])
```

Note that unlike many other folds, `L.sumAs`

expects the function to only return
numbers and `undefined`

is not treated in a special way. If you need to skip
elements, you can return the number `0`

.

Lenses always have a single focus which can be viewed directly. Put in another way, a lens specifies a path to a single element in a data structure.

`L.foldTraversalLens((traversal, maybeData) => maybeValue, traversal) ~> lens`

`L.foldTraversalLens`

creates a lens from a fold and a traversal. To make
sense, the fold should compute or pick a representative from the elements
focused on by the traversal such that when all the elements are equal then so is
the representative. See also `L.partsOf`

.

For example:

```
L.get(L.foldTraversalLens(L.minimum, L.elems), [3, 1, 4])
```

```
L.set(L.foldTraversalLens(L.minimum, L.elems), 2, [3, 1, 4])
```

See the Collection toggle section for a more interesting example.

`L.getter((maybeData, index) => maybeValue) ~> lens`

`L.getter(get)`

is shorthand for `L.lens(get, x => x)`

. See also
`L.reread`

.

`L.lens((maybeData, index) => maybeValue, (maybeValue, maybeData, index) => maybeData) ~> lens`

`L.lens`

creates a new primitive lens. The first parameter is the *getter* and
the second parameter is the *setter*. The setter takes two parameters: the
first is the value written and the second is the data structure to write into.

One should think twice before introducing a new primitive lens—most of the
combinators in this library have been introduced to reduce the need to write new
primitive lenses. With that said, there are still valid reasons to create new
primitive lenses. For example, here is a lens that we've used in production,
written with the help of Moment.js, to bidirectionally
convert a pair of `start`

and `end`

times to a duration:

```
var timesAsDuration = L.lens(
({start, end} = {}) => {
if (undefined === start)
return undefined
if (undefined === end)
return 'Infinity'
return moment.duration(moment(end).diff(moment(start))).toJSON()
},
(duration, {start = moment().toJSON()} = {}) => {
if (undefined === duration || 'Infinity' === duration) {
return {start}
} else {
return {
start,
end: moment(start).add(moment.duration(duration)).toJSON()
}
}
}
)
```

Now, for example:

```
L.get(
timesAsDuration,
{
start: '2016-12-07T09:39:02.451Z',
end: moment('2016-12-07T09:39:02.451Z').add(10, 'hours').toISOString()
}
)
```

```
L.set(
timesAsDuration,
'PT10H',
{start: '2016-12-07T09:39:02.451Z', end: '2016-12-07T09:39:02.451Z'}
)
```

When composed with `L.pick`

, to flexibly pick the `start`

and `end`

times, the above can be adapted to work in a wide variety of cases. However,
the above lens will never be added to this library, because it would require
adding dependency to Moment.js.

See the Interfacing with Immutable.js section for another
example of using `L.lens`

.

`L.partsOf(traversal) ~> lens`

`L.partsOf`

creates a lens from a given traversal. When read through, the
result is always an array of elements targeted by the traversal as if produced
by `L.collectTotal`

. When written through, the elements of
the written array-like object are used to replace the
focuses of the traversal as if done by `L.disperse`

. See also
`L.foldTraversalLens`

.

For example:

```
L.set(
L.partsOf([L.elems, 'x']),
[3, 4],
[{x: 1}, {y: 2}]
)
```

`L.setter((maybeValue, maybeData, index) => maybeData) ~> lens`

`L.setter(set)`

is shorthand for `L.lens(x => x, set)`

. See also
`L.rewrite`

.

`L.defaults(valueIn) ~> lens`

`L.defaults`

is used to specify a default context or value for an element in
case it is missing. When set with the default value, the effect is to remove
the element. This can be useful for both making partial lenses with propagating
removal and for avoiding having to check for and provide default values
elsewhere. See also `L.valueOr`

.

For example:

```
L.get(['items', L.defaults([])], {})
```

```
L.get(['items', L.defaults([])], {items: [1, 2, 3]})
```

```
L.set(['items', L.defaults([])], [], {items: [1, 2, 3]})
```

Note that `L.defaults(valueIn)`

is equivalent to ```
L.replace(undefined,
valueIn)
```

.

`L.define(value) ~> lens`

`L.define`

is used to specify a value to act as both the default value and the
required value for an element.

```
L.get(['x', L.define(null)], {y: 10})
```

```
L.set(['x', L.define(null)], undefined, {y: 10})
```

Note that `L.define(value)`

is equivalent to ```
[L.required(value),
L.defaults(value)]
```

.

`L.normalize((value, index) => maybeValue) ~> lens`

`L.normalize`

maps the value with same given transform when read and written and
implicitly maps `undefined`

to `undefined`

. `L.normalize(fn)`

is equivalent to
composing `L.reread(fn)`

and `L.rewrite(fn)`

.

One use case for `normalize`

is to make it easy to determine whether, after a
change, the data has actually changed. By keeping the data normalized, a simple
`R.equals`

comparison will do.

`L.required(valueOut) ~> lens`

`L.required`

is used to specify that an element is not to be removed; in case it
is removed, the given value will be substituted instead.

For example:

```
L.remove(['item'], {item: 1})
```

```
L.remove(['item', L.required(null)], {item: 1})
```

Note that `L.required(valueOut)`

is equivalent to ```
L.replace(valueOut,
undefined)
```

.

`L.reread((valueIn, index) => maybeValueIn) ~> lens`

`L.reread`

maps the value with the given transform on read and implicitly maps
`undefined`

to `undefined`

. See also `L.normalize`

and
`L.getter`

.

`L.rewrite((valueOut, index) => maybeValueOut) ~> lens`

`L.rewrite`

maps the value with the given transform when written and implicitly
maps `undefined`

to `undefined`

. See also `L.normalize`

and
`L.setter`

.

One use case for `rewrite`

is to re-establish data structure invariants after
changes.

See the BST as a lens section for a meaningful example.

Objects that have a non-negative integer `length`

and strings, which are not
considered `Object`

instances in JavaScript, are considered *array-like* objects
by partial optics. See also `L.seemsArrayLike`

.

When writing through a lens or traversal that operates on array-like objects,
the result is always a plain `Array`

. For example:

```
L.set(1, 'a', 'LoLa')
```

It may seem like the result should be of the same type as the object being manipulated, but that is problematic, because

- the focus of a
*partial*optic is always optional, so there might not be an original array-like object whose type to use, and - manipulation of the elements can change their types, so they may no longer be compatible with the type of the original array-like object.

Therefore, instead, when manipulating strings or array-like non-`Array`

objects,
`L.rewrite`

can be used to explicitly convert the result to the
desired type, if necessary. For example:

```
L.set([L.rewrite(R.join('')), 1], 'a', 'LoLa')
```

Also, when manipulating array-like objects, partial lenses generally ignore
everything but the `length`

property and the integer properties from `0`

to
`length-1`

.

`L.append ~> lens`

`L.append`

is a write-only lens that can be used to append values to an
array-like object. The view of `L.append`

is always `undefined`

.

For example:

```
L.get(L.append, ['x'])
```

```
L.set(L.append, 'x', undefined)
```

```
L.set(L.append, 'x', ['z', 'y'])
```

Note that `L.append`

is equivalent to `L.index(i)`

with the index
`i`

set to the length of the focused array or 0 in case the focus is not a
defined array.

`L.cross([...lenses]) ~> lens`

`L.cross`

constructs a lens or isomorphism between fixed length arrays or tuples
from the given array of lenses or isomorphisms. The optic returned by `L.cross`

is strict such that in case any elements of the resulting array in either
direction would be `undefined`

then the whole result will be `undefined`

.

For example

```
L.get(L.cross(['x', [], 'y']), [{x: 1, y: 2}, 2, {x: 3, y: 4}])
```

```
L.set(L.cross(['x', [], 'y']), [-1, -2, -4], [{x: 1, y: 2}, 2, {x: 3, y: 4}])
```

`L.filter((maybeValue, index) => testable) ~> lens`

`L.filter`

operates on array-like objects. When not viewing an
array-like object, the result is `undefined`

. When viewing an array-like
object, only elements matching the given predicate will be returned. When set,
the resulting array will be formed by concatenating the elements of the set
array-like object and the elements of the complement of the filtered focus.

For example:

```
L.set(L.filter(x => x <= '2'), 'abcd', '3141592')
```

**NOTE**: If you are merely modifying a data structure, and don't need to limit
yourself to lenses, consider using the `L.elems`

traversal composed
with `L.when`

.

An alternative design for filter could implement a smarter algorithm to combine
arrays when set. For example, an algorithm based on edit
distance could be used to maintain
relative order of elements. While this would not be difficult to implement, it
doesn't seem to make sense, because in most cases use of
`L.normalize`

or `L.rewrite`

would be preferable.
Also, the `L.elems`

traversal composed with `L.when`

will
retain order of elements.

`L.find((maybeValue, index, {hint: index}) => testable[, {hint: index}]) ~> lens`

`L.find`

operates on array-like objects like
`L.index`

, but the index to be viewed is determined by finding the
first element from the focus that matches the given predicate. When no matching
element is found the effect is same as with `L.append`

.

```
L.remove(L.find(x => x <= 2), [3, 1, 4, 1, 5, 9, 2])
```

`L.find`

is designed to operate efficiently when used repeatedly. To this end,
`L.find`

can be given an object with a `hint`

property and when no hint object
is passed, a new object will be allocated internally. Repeated searches are
started from the closest existing index to the `hint`

and then by increasing
distance from that index. The `hint`

is updated after each search and the
`hint`

can also be mutated from the outside. The `hint`

object is also passed
to the predicate as the third argument. This makes it possible to both
practically eliminate the linear search and to implement the predicate without
allocating extra memory for it.

For example:

```
L.modify(
[L.find(R.whereEq({id: 2}), {hint: 2}), 'value'],
R.toUpper,
[
{id: 3, value: 'a'},
{id: 2, value: 'b'},
{id: 1, value: 'c'},
{id: 4, value: 'd'},
{id: 5, value: 'e'}
]
)
```

Note that `L.find`

by itself does not satisfy all lens laws. To fix this, you
can e.g. post compose `L.find`

with lenses that ensure that the property being
tested by the predicate given to `L.find`

cannot be written to. See
here for discussion and an example.

`L.findWith(optic[, {hint: index}]) ~> optic`

`L.findWith`

chooses an index from an array-like object through
which the given optic has a non-`undefined`

view and then returns an optic that
focuses on that.

For example:

```
L.get(L.findWith('x'), [{z: 6}, {x: 9}, {y: 6}])
```

```
L.set(L.findWith('x'), 3, [{z: 6}, {x: 9}, {y: 6}])
```

`L.first ~> lens`

`L.first`

is a synonym for `L.index(0)`

or `0`

and
focuses on the first element of an array-like object or works
like `L.append`

in case no such element exists. See also
`L.last`

.

For example:

```
L.get(L.first, ['a', 'b'])
```

`L.index(elemIndex) ~> lens`

or `elemIndex`

`L.index(elemIndex)`

or just `elemIndex`

focuses on the element at specified
index of an array-like object.

- When not viewing an index with a defined element, the result is
`undefined`

. - When setting to
`undefined`

, the element is removed from the resulting array, shifting all higher indices down by one. - When setting a defined value to an index that is higher than the length of the
array-like object, the missing elements will be filled with
`undefined`

.

For example:

```
L.set(2, 'z', ['x', 'y', 'c'])
```

```
L.remove(0, ['x'])
```

`L.last ~> lens`

`L.last`

focuses on the last element of an array-like object or
works like `L.append`

in case no such element exists. See also
`L.first`

.

Focusing on an empty array or `undefined`

results in returning `undefined`

. For
example:

```
L.get(L.last, [1, 2, 3])
```

```
L.get(L.last, [])
```

Setting value with `L.last`

sets the last element of the object or appends the
value if the focused object is empty or `undefined`

. For example:

```
L.set(L.last, 5, [1, 2, 3])
```

```
L.set(L.last, 1, [])
```

`L.prefix(maybeBegin) ~> lens`

`L.prefix`

focuses on a range of elements of an array-like object
starting from the beginning of the object. `L.prefix`

is a special case of
`L.slice`

.

The end of the range is determined as follows:

- non-negative values are relative to the beginning of the array-like object,
`Infinity`

is the end of the array-like object,- negative values are relative to the end of the array-like object,
`-Infinity`

is the beginning of the array-like object, and`undefined`

is the end of the array-like object.

For example:

```
L.set(L.prefix(0), [1], [2, 3])
```

`L.slice(maybeBegin, maybeEnd) ~> lens`

`L.slice`

focuses on a specified range of elements of an
array-like object. See also `L.prefix`

and
`L.suffix`

.

The range is determined like with the standard
`slice`

method of arrays:

- non-negative values are relative to the beginning of the array-like object,
`Infinity`

is the end of the array-like object,- negative values are relative to the end of the array-like object,
`-Infinity`

is the beginning of the array-like object, and`undefined`

gives the defaults: 0 for the begin and length for the end.

For example:

```
L.get(L.slice(1, -1), [1, 2, 3, 4])
```

```
L.set(L.slice(-2, undefined), [0], [1, 2, 3, 4])
```

`L.suffix(maybeEnd) ~> lens`

`L.suffix`

focuses on a range of elements of an array-like object
starting from the end of the object. `L.suffix`

is a special case of
`L.slice`

.

The beginning of the range is determined as follows:

- non-negative values are relative to the end of the array-like object,
`Infinity`

is the beginning of the array-like object,- negative values are relative to the beginning of the array-like object,
`-Infinity`

is the end of the array-like object, and`undefined`

is the beginning of the array-like object.

Note that the rules above are different from the rules for determining the
beginning of `L.slice`

.

For example:

```
L.set(L.suffix(1), [4, 1], [3, 1, 3])
```

Anything that is an `instanceof Object`

is considered an object by partial
lenses.

When writing through an optic that operates on objects, the result is always a
plain `Object`

. For example:

```
function Custom(gold, silver, bronze) {
this.gold = gold
this.silver = silver
this.bronze = bronze
}
L.set('silver', -2, new Custom(1, 2, 3))
```

When manipulating objects whose constructor is not `Object`

,
`L.rewrite`

can be used to convert the result to the desired type,
if necessary:

```
L.set([L.rewrite(objectTo(Custom)), 'silver'], -2, new Custom(1, 2, 3))
```

Partial lenses also generally guarantees that the creation order of keys is preserved (even though the library used to print out evaluation results from code snippets might not preserve the creation order). For example:

```
for (var k in L.set('silver', -2, new Custom(1, 2, 3)))
console.log(k)
```

When creating new objects, partial lenses generally ignore everything but own string keys. In particular, properties from the prototype chain are not copied and neither are properties with symbol keys.

`L.pickIn({prop: lens, ...props}) ~> lens`

`L.pickIn`

creates a lens from the given possibly nested object template of
lenses similar to `L.pick`

except that the lenses in the template are
relative to their path in the template. This means that using `L.pickIn`

you
can effectively create a kind of filter for a nested object structure. See also
`L.props`

.

For example:

```
L.get(
L.pickIn({meta: {file: [], ext: []}}),
{meta: {file: './foo.txt', base: 'foo', ext: 'txt'}}
)
```

`L.prop(propName) ~> lens`

or `propName`

`L.prop(propName)`

or just `propName`

focuses on the specified object property.

- When not viewing a defined object property, the result is
`undefined`

. - When writing to a property, the result is always an
`Object`

. - When setting property to
`undefined`

, the property is removed from the result.

When setting or removing properties, the order of keys is preserved.

For example:

```
L.get('y', {x: 1, y: 2, z: 3})
```

```
L.set('y', -2, {x: 1, y: 2, z: 3})
```

When manipulating objects whose constructor is not `Object`

,
`L.rewrite`

can be used to convert the result to the desired type,
if necessary:

```
L.set([L.rewrite(objectTo(XYZ)), 'z'], 3, new XYZ(3, 1, 4))
```

`L.props(...propNames) ~> lens`

`L.props`

focuses on a subset of properties of an object, allowing one to treat
the subset of properties as a unit. The view of `L.props`

is `undefined`

when
none of the properties is defined. This allows `L.props`

to be used with
e.g. `L.choices`

. Otherwise the view is an object containing a
subset of the properties. Setting through `L.props`

updates the whole subset of
properties, which means that any missing properties are removed if they did
exists previously. When set, any extra properties are ignored.

```
L.set(L.props('x', 'y'), {x: 4}, {x: 1, y: 2, z: 3})
```

Note that `L.props(k1, ..., kN)`

is equivalent to ```
L.pick({[k1]: k1, ..., [kN]:
kN})
```

and `L.pickIn({[k1]: [], ..., [kN]: []})`

.

`L.propsOf(object) ~> lens`

`L.propsOf(o)`

is shorthand for `L.props(...Object.keys(o))`

allowing one to focus on the properties specified via the given sample object.

`L.removable(...propNames) ~> lens`

`L.removable`

creates a lens that, when written through, replaces the whole
result with `undefined`

if none of the given properties is defined in the
written object. `L.removable`

is designed for making removal propagate through
objects.

Contrast the following examples:

```
L.remove('x', {x: 1, y: 2})
```

```
L.remove([L.removable('x'), 'x'], {x: 1, y: 2})
```

Also note that, in a composition, `L.removable`

is likely preceded by
`L.valueOr`

(or `L.defaults`

) like in the
tutorial example. In such a pair, the preceding lens gives a
default value when reading through the lens, allowing one to use such a lens to
insert new objects. The following lens then specifies that removing the then
focused property (or properties) should remove the whole object. In cases where
the shape of the incoming object is know, `L.defaults`

can
replace such a pair.

`L.matches(/.../) ~> lens`

`L.matches`

, when given a regular expression without the
`global`

flags, `/.../`

, is a partial lens over the match. When there is no match, or
the target is not a string, then `L.matches`

will be read-only. See also
`L.matches`

.

For example:

```
L.set(L.matches(/\.[^./]+$/), '.txt', '/dir/file.ext')
```

`L.valueOr(valueOut) ~> lens`

`L.valueOr`

is an asymmetric lens used to specify a default value in case the
focus is `undefined`

or `null`

. When set, `L.valueOr`

behaves like the identity
lens. See also `L.defaults`

.

For example:

```
L.get(L.valueOr(0), null)
```

```
L.set(L.valueOr(0), 0, 1)
```

```
L.remove(L.valueOr(0), 1)
```

Note that `L.valueOr(otherwise)`

is equivalent to ```
L.getter(x => x != null ?
x : otherwise)
```

.

`L.pick({prop: lens, ...props}) ~> lens`

`L.pick`

creates a lens out of the given possibly nested object template of
lenses and allows one to pick apart a data structure and then put it back
together. When viewed, `undefined`

properties are not added to the result and
if the result would be an empty object, the result will be `undefined`

. This
allows `L.pick`

to be used with e.g. `L.choices`

. Otherwise an
object is created, whose properties are obtained by viewing through the lenses
of the template. When set with an object, the properties of the object are set
to the context via the lenses of the template.

For example, let's say we need to deal with data and schema in need of some semantic restructuring:

`var sampleFlat = {px: 1, py: 2, vx: 1, vy: 0}`

We can use `L.pick`

to create a lens to pick apart the data and put it back
together into a more meaningful structure:

`var sanitize = L.pick({pos: {x: 'px', y: 'py'}, vel: {x: 'vx', y: 'vy'}})`

Note that in the template object the lenses are relative to the root focus of
`L.pick`

.

We now have a better structured view of the data:

```
L.get(sanitize, sampleFlat)
```

That works in both directions:

```
L.modify([sanitize, 'pos', 'x'], R.add(5), sampleFlat)
```

**NOTE:** In order for a lens created with `L.pick`

to work in a predictable
manner, the given lenses must operate on independent parts of the data
structure. As a trivial example, in `L.pick({x: 'same', y: 'same'})`

both of
the resulting object properties, `x`

and `y`

, address the same property of the
underlying object, so writing through the lens will give unpredictable results.

Note that, when set, `L.pick`

simply ignores any properties that the given
template doesn't mention. Also note that the underlying data structure need not
be an object.

Note that the `sanitize`

lens defined above can also been seen as an
isomorphism between the "flat" and "nested" forms of the data.
It can even be inverted using `L.inverse`

:

```
L.get(L.inverse(sanitize), {pos: {x: 1, y: 2}, vel: {x: 1, y: 0}})
```

`L.replace(maybeValueIn, maybeValueOut) ~> lens`

`L.replace(maybeValueIn, maybeValueOut)`

, when viewed, replaces the value
`maybeValueIn`

with `maybeValueOut`

and vice versa when set.

For example:

```
L.get(L.replace(1, 2), 1)
```

```
L.set(L.replace(1, 2), 2, 0)
```

The main use case for `replace`

is to handle optional and required properties
and elements. In most cases, rather than using `replace`

, you will make
selective use of `defaults`

, `required`

and
`define`

.

Isomorphisms are lenses with a kind of inverse. The focus of an isomorphism is the whole data structure rather than a part of it.

More specifically, a lens, `iso`

, is an isomorphism if the following equations
hold for all `x`

and `y`

in the domain and range, respectively, of the lens:

```
L.set(iso, L.get(iso, x), undefined) = x
L.get(iso, L.set(iso, y, undefined)) = y
```

The above equations mean that `x => L.get(iso, x)`

and ```
y => L.set(iso, y,
undefined)
```

are inverses of each other.

That is the general idea. Strictly speaking it is not required that the two functions are precisely inverses of each other. It can be useful to have "isomorphisms" that, when written through, actually change the data structure. For that reason the name "adapter", rather than "isomorphism", is sometimes used for the concept.

In this library there is no type distinction between partial lenses and partial
isomorphisms. Among other things this means that some lens combinators, such as
`L.pick`

, can also be used to create isomorphisms. On the other
hand, some forms of optic composition, particularly adapting and
querying, do not work properly on (inverted) isomorphisms.

`L.getInverse(isomorphism, maybeData) ~> maybeData`

`L.getInverse`

views through an isomorphism in the inverse direction.

For example:

```
var expect = (p, f) => x => p(x) ? f(x) : undefined
var offBy1 = L.iso(expect(R.is(Number), R.inc), expect(R.is(Number), R.dec))
L.getInverse(offBy1, 1)
```

Note that `L.getInverse(iso, data)`

is equivalent to ```
L.set(iso, data,
undefined)
```

.

Also note that, while `L.getInverse`

makes most sense when used with an
isomorphism, it is valid to use `L.getInverse`

with *partial* lenses in general.
Doing so essentially constructs a minimal data structure that contains the given
value. For example:

```
L.getInverse('meaning', 42)
```

`L.iso(maybeData => maybeValue, maybeValue => maybeData) ~> isomorphism`

`L.iso`

creates a new primitive isomorphism from the given pair of functions.
Usually the given functions should be inverses of each other, but that isn't
strictly necessary. The functions should also be partial so that when the input
doesn't match their expectation, the output is mapped to `undefined`

.

For example:

```
var reverseString = L.iso(
expect(R.is(String), R.reverse),
expect(R.is(String), R.reverse)
)
L.modify(
[
L.uriComponent,
L.json(),
'bottle',
0,
reverseString,
L.rewrite(R.join('')),
0
],
R.toUpper,
'%7B%22bottle%22%3A%5B%22egassem%22%5D%7D'
)
```

`L.mapping([patternFwd, patternBwd] | (...variables) => [patternFwd, patternBwd]) ~> isomorphism`

`L.mapping`

creates an isomorphism based on the given pair of patterns. A
pattern can be an arbitrarily nested structure of plain arrays and plain objects
containing variables or constant values. Variables other than `L._`

are
obtained using a function that returns the pair of patterns when given variables
by `L.mapping`

. When reading, all properties and elements of the input data
structure must be explicitly matched by the pattern and each variable must match
a non-`undefined`

value. When a variable appears multiple times in a pattern,
the matches must be structurally equal. Variables can further be used with the
`...variable`

rest-spread notation within objects and arrays and will match or
substitute to zero or more object properties or array elements. Only a single
rest-spread match can be used within a single object or array pattern. See also
`L.mappings`

.

For example:

```
L.get(
L.mapping((x, y) => [[x, L._, ...y], {x, y}]),
['a', 'b', 'c', 'd']
)
```

```
L.getInverse(
L.array(
L.alternatives(
L.mapping(['foo', 'bar']),
L.mapping(['you', 'me'])
)
),
['me', 'bar']
)
```

As an aside, the way variables are introduced into the patterns in `L.mapping`

by using a function could be described as a simple use of
HOAS.

`L._ ~> pattern`

`L._`

is a don't care or ignore pattern for use with `L.mapping`

and `L.mappings`

. When reading, a `L._`

pattern matches any
non-`undefined`

value and each use of `L._`

is considered as a new variable so
the values matched by them do not need to be equal. When writing, uses of `L._`

translate to `undefined`

and `undefined`

values are not written to objects nor
arrays by `L.mapping`

.

`L.mappings([...[patternFwd, patternBwd]] | (...variables) => [...[patternFwd, patternBwd]]) ~> isomorphism`

`L.mappings`

is a shorthand for multiple `L.mapping`

`L.alternatives`

.

Basically

`L.mappings((...variables) => [patternPair1, ..., patternPairN])`

is equivalent to

```
L.alternatives(
L.mappings((...variables) => patternPair1),
...,
L.mappings((...variables) => patternPairN)
)
```

For example:

```
L.getInverse(
L.array(L.mappings((x, y) => [[[x, y], {x, y}], [{x, y}, [x, y]]])),
[['a', 'b'], {x: 1, y: 2}]
)
```

`L.alternatives(isomorphism, ...isomorphisms) ~> isomorphism`

`L.alternatives`

returns a partial isomorphism that, in both read and write
directions, acts like the first of the given partial isomorphisms whose view is
not `undefined`

on the given data structure. See also
`L.orAlternatively`

and `L.choices`

.

For example:

```
L.modify(
L.alternatives(
L.negate,
L.dropPrefix('-')
),
R.toString,
-1
)
```

`L.applyAt(elementsOptic, isomorphism) ~> isomorphism`

`L.applyAt`

creates an isomorphism by applying the given isomorphism at each
focus of the given optic. See also `L.conjugate`

.

For example:

```
L.get(L.applyAt(L.entries, L.reverse), {bar: 'foo', value: 'key'})
```

`L.array(isomorphism) ~> isomorphism`

`L.array`

lifts an isomorphism between elements, `a ≅ b`

, to an isomorphism
between an array-like object and an array of elements, ```
[a] ≅
[b]
```

.

For example:

```
L.getInverse(L.array(L.pick({x: 'y', z: 'x'})), [{x:2, z:1}, {x:4, z:3}])
```

Elements mapped to `undefined`

by the isomorphism on elements are removed from
the resulting array in both directions.

`L.conjugate(contextIsomorphism, isomorphism) ~> isomorphism`

`L.conjugate(context, iso)`

is shorthand for ```
[context, iso,
L.inverse(context)]
```

and allows one to apply an isomorphism, or transform data
with an isomorphism, within the codomain of another isomorphism. `L.conjugate`

can be seen as an optimized version of `L.applyAt`

for cases where
the elements optic is an isomorphism.

For example:

```
L.get(L.conjugate(L.uncouple('='), L.reverse), 'key=value')
```

`L.inverse(isomorphism) ~> isomorphism`

`L.inverse`

returns the inverse of the given isomorphism. Note that this
operation only makes sense on isomorphisms.

For example:

```
L.get(L.inverse(offBy1), 1)
```

`L.iterate(isomorphism) ~> isomorphism`

`L.iterate`

returns a partial isomorphism that applies the given partial
isomorphism repeatedly until it produces `undefined`

at which point the previous
result is produced.

For example:

```
var reverseStep = L.mapping((xs, y, ys) => [
[ys, [y, ...xs]],
[[y, ...ys], xs]
])
L.get(L.iterate(reverseStep), [[], [3, 1, 4, 1]])
```

```
L.getInverse(L.iterate(reverseStep), [[1, 4, 1, 3], []])
```

`L.orAlternatively(backupIsomorphism, primaryIsomorphism) ~> isomorphism`

`L.orAlternatively(backupIsomorphism, primaryIsomorphism)`

, in both read and
write direction, acts like `primaryIsomorphism`

when its view is not `undefined`

and otherwise like `backupIsomorphism`

. See also `L.orElse`

.

Note that `L.alternatives(...isomorphisms)`

is equivalent to
`isomorphisms.reduceRight(L.orAlternatively)`

.

`L.complement ~> isomorphism`

`L.complement`

is an isomorphism that performs logical negation of any
non-`undefined`

value when either read or written through.

For example:

```
L.set(
[L.complement, L.log()],
'Could be anything truthy',
'Also converted to bool'
)
```

`L.identity ~> isomorphism`

`L.identity`

is the identity element of lens composition and also the identity
isomorphism. `L.identity`

can also been seen as specifying an empty path.
Indeed, in this library, when used as an optic, `L.identity`

is equivalent to
`[]`

. The following equations characterize `L.identity`

:

```
L.get(L.identity, x) = x
L.modify(L.identity, f, x) = f(x)
L.compose(L.identity, l) = l
L.compose(l, L.identity) = l
```

`L.is(value) ~> isomorphism`

`L.is`

reads the given value as `true`

and everything else as `false`

and writes
`true`

as the given value and everything else as `undefined`

. See
here for an example.

`L.subset(maybeValue => testable) ~> isomorphism`

`L.subset`

returns an isomorphism that acts like the identity when the data
passes the given predicate and otherwise maps the data to `undefined`

.

`L.indexed ~> isomorphism`

`L.indexed`

is an isomorphism between an array-like object and an
array of `[index, value]`

pairs.

For example:

```
L.modify(
[
L.rewrite(R.join('')),
L.indexed,
L.normalize(R.sortBy(L.get(1))),
0,
1
],
R.toUpper,
'optics'
)
```

`L.reverse ~> isomorphism`

`L.reverse`

is an isomorphism between an array-like object
and its reverse.

For example:

```
L.join(', ', [L.reverse, L.elems], 'abc')
```

`L.singleton ~> isomorphism`

`L.singleton`

is a partial isomorphism between an array-like
object, `[x]`

, that contains a single element and that element `x`

. When
written through with a non-`undefined`

value, the result is an array containing
the value.

For example:

`L.modify(L.singleton, R.negate, [1]) // [-1]`

Note that in case the target of `L.singleton`

is an array-like object that does
not contain exactly one element, then the view will be `undefined`

. The reason
for this behaviour is that it allows `L.singleton`

to not only be used to access
the first element of an array-like object, but to also check that the object is
of the expected form.

`L.disjoint(propName => propName) ~> isomorphism`

`L.disjoint`

divides an object into disjoint subsets based on the given function
that maps keys to group keys.

For example:

```
L.collect(
L.lazy(rec => L.cond(
[R.is(Array), [L.elems, rec]],
[R.is(Object), [
L.disjoint(key => key === 'children' ? 'nest' : 'rest'),
L.branch({rest: [], nest: ['children', rec]})
]]
)),
{
id: 1,
value: 'root',
children: [
{id: 2, value: 'a', children: []},
{id: 3, value: 'b', extra: 1}
]
}
)
```

`L.keyed ~> isomorphism`

`L.keyed`

is an isomorphism between an object and an array of `[key, value]`

pairs.

For example:

```
L.get(L.keyed, {a: 1, b: 2})
```

`L.multikeyed ~> isomorphism`

`L.multikeyed`

is an isomorphism between an object and an array of ```
[key,
value]
```

pairs where a `key`

may appear multiple times and in which case the
corresponding object property value is an array. See also
`L.querystring`

.

An application of `L.multikeyed`

is manipulating URL query strings. For
example:

```
var querystring = [
L.dropPrefix('?'),
L.replaces('+', '%20'),
L.split('&'),
L.array([
L.uncouple('='),
L.array(L.uriComponent)
]),
L.inverse(L.multikeyed)
]
```

```
L.get(querystring, '?foo=bar&abc=xyz&abc=123')
```

```
L.set(
[querystring, 'foo'],
'baz',
'?foo=bar&abc=xyz&abc=123'
)
```

Several pairs of standard functions, such as the
`decodeURIComponent`

and
`encodeURIComponent`

functions, form partial isomorphisms. Some of those pairs of functions are
wrapped for direct use as isomorphisms in this library, such as the
`L.uriComponent`

isomorphism.

Invalid inputs are sometimes reported by standard functions by throwing
`Error`

objects. As a general principle, performing an otherwise valid read or write
through an optic in this library should not throw on invalid inputs to support
optimistic queries and updates. On the other hand, discarding the information
provided by a thrown
`Error`

object is undesirable. Therefore standard isomorphisms based on throwing
standard functions catch and pass the error as the result. For example:

```
L.get(L.uriComponent, '%') instanceof Error // Does not throw!
```

Such errors can be, for example, filtered out via composition to obtain the
ordinary partial behavior of producing `undefined`

for unexpected inputs:

```
L.get(
[
L.uriComponent,
L.unless(R.is(Error))
],
'%'
)
```

`L.json({reviver, replacer, space}) ~> isomorphism`

`L.json({reviver, replacer, space})`

returns an isomorphism based on the
standard
`JSON.parse`

and
`JSON.stringify`

functions. Parsing errors are caught and passed as
results. The optional `reviver`

is passed to
`JSON.parse`

and the optional `replacer`

and `space`

are passed to
`JSON.stringify`

.

For example:

```
L.transform(
[L.json(), 'foo', L.elems, L.modifyOp(R.negate)],
'{"foo":[3,1,4]}'
)
```

`L.uri ~> isomorphism`

`L.uri`

is an isomorphism based on the standard
`decodeURI`

and
`encodeURI`

functions. Decoding errors are caught and passed as
results.

`L.uriComponent ~> isomorphism`

`L.uriComponent`

is an isomorphism based on the standard
`decodeURIComponent`

and
`encodeURIComponent`

functions. Decoding errors are caught and passed as
results.

`L.querystring ~> isomorphism`

`L.querystring`

is an isomorphism between URL query strings and parameter
objects. `L.querystring`

approximates Node's Query
String functionality, but does not
produce identical results. See also `L.dropPrefix`

.

For example:

```
L.getInverse(L.querystring, { foo: 'bar', abc: ['xyz', 123], corge: '' })
```

`L.dropPrefix(prefix) ~> isomorphism`

`L.dropPrefix`

drops the given prefix from the beginning of the string when read
through and adds it when written through. In case the input does not contain
the prefix, the result is `undefined`

, which allows `L.dropPrefix`

to be used as
a predicate. See also `L.dropSuffix`

.

For example:

```
L.get(L.dropPrefix('?'), '?foo=bar')
```

```
L.getInverse(L.dropPrefix('?'), 'foo=bar')
```

`L.dropSuffix(suffix) ~> isomorphism`

`L.dropSuffix`

drops the given suffix from the end of the string when read
through and adds it when written through. In case the input does not contain
the suffix, the result is `undefined`

, which allows `L.dropSuffix`

to be used as
a predicate. See also `L.dropPrefix`

.

For example:

```
L.get(L.dropSuffix('.bar'), 'foo.bar')
```

```
L.getInverse(L.dropSuffix('.bar'), 'foo')
```

`L.replaces(substringIn, substringOut) ~> isomorphism`

`L.replaces`

replaces substrings in the string passing through both when read
and written.

For example:

```
L.get(L.replaces('+', ' '), 'Is+this too+much?')
```

```
L.getInverse(L.replaces('+', ' '), 'Is URL+encoding fun?')
```

`L.split(separator[, separatorRegExp]) ~> isomorphism`

`L.split`

splits a string with given separator into an array when read through
and joins an array of strings into a string with the separator when written
through. The second argument to `L.split`

is optional and specifies the pattern
to be used for splitting instead of the default separator string. See also
`L.uncouple`

.

For example:

```
L.get(L.split(',', /\s*,\s*/), 'comma, separated, items')
```

```
L.getInverse(L.split('&'), ['roses=red', 'violets=blue', 'sugar=sweet'])
```

`L.uncouple(separator[, separatorRegExp]) ~> isomorphism`

`L.uncouple`

splits a string with the given separator into a pair when read
through and joins a pair of strings into a string with the separator when
written through. In case the input string does not contain the separator, the
second element of the pair will be an empty string. Likewise, if the second
element of the pair is an empty string, no separator is written to the resulting
string. The second argument to `L.uncouple`

is optional and specifies the
pattern to be used for splitting instead of the default separator string. See
also `L.split`

.

For example:

```
L.get(L.uncouple('=', /\s*=\s*/), 'foo = bar')
```

```
L.getInverse(L.uncouple('='), ['key', ''])
```

`L.add(number) ~> isomorphism`

`L.add`

adds the given constant to the number in focus when read through and
subtracts when written through.

For example:

```
L.get(L.add(1), 2)
```

`L.divide(number) ~> isomorphism`

`L.divide`

divides the number in focus by the given constant when read through
and multiplies when written through.

For example:

```
L.get(L.divide(2), 6)
```

`L.multiply(number) ~> isomorphism`

`L.multiply`

multiplies the number in focus by the given constant when read
through and divides when written through.

For example:

```
L.get(L.multiply(2), 3)
```

`L.negate ~> isomorphism`

`L.negate`

negates the number in focus when either read or written through.

For example:

```
L.get(L.negate, 2)
```

`L.subtract(number) ~> isomorphism`

`L.subtract`

subtracts the given constant from the number in focus when read
through and adds when written through.

For example:

```
L.get(L.subtract(1), 3)
```

Partial Lenses directly supports only the Static Land specification, but it is possible to also use Fantasy Land compatible types with Partial Lenses. Note that many Fantasy Land compatible libraries are also directly Static Land compatible and can be used directly with Partial Lenses without using the below conversion functions.

`L.FantasyFunctor ~> Functor`

`L.FantasyFunctor`

is a Static Land compatible functor that dispatches to the
`fantasy-land/map`

method.

`L.fromFantasy(TypeRep) ~> Functor|Applicative|Monad`

`L.fromFantasy`

attempts to convert a given Fantasy Land compatible type
representative to a Static Land compatible functor, applicative, or monad based
on which dynamic and static methods the type representative provides. See also
`L.fromFantasyApplicative`

and
`L.fromFantasyMonad`

.

`L.fromFantasyApplicative(TypeRep) ~> Applicative`

`L.fromFantasyApplicative`

converts a given Fantasy Land compatible type
representative of an applicative to a Static Land compatible applicative. The
type must provide a static `fantasy-land/of`

method and dynamic
`fantasy-land/map`

and `fantasy-land/ap`

methods. See also
`L.fromFantasy`

.

`L.fromFantasyMonad(TypeRep) ~> Monad`

`L.fromFantasyMonad`

converts a given Fantasy Land compatible type
representative of a monad to a Static Land compatible monad. The type must
provide a static `fantasy-land/of`

method and dynamic `fantasy-land/map`

,
`fantasy-land/ap`

, and `fantasy-land/chain`

methods. See also
`L.fromFantasy`

.

`L.pointer(jsonPointer) ~> lens`

`L.pointer`

converts a valid JSON Pointer
(string) into a bidirectional lens. Works with JSON
String and URI Fragment
Identifier representations.

For Example:

```
L.get(L.pointer('/foo/0'), {foo: [1, 2]})
```

```
L.modify(L.pointer('#/foo/1'), x => x + 1, {foo: [1, 2]})
```

`L.seemsArrayLike(anything) ~> boolean`

`L.seemsArrayLike`

determines whether the given value is an `instanceof Object`

that has a non-negative integer `length`

property or a string, which are not
Objects in JavaScript. In this library, such values are considered
array-like objects that can be manipulated with various optics.

Note that this function is intentionally loose, which is also intentionally apparent from the name of this function. JavaScript includes many array-like values, including normal arrays, typed arrays, and strings. Unfortunately there seems to be no simple way to directly and precisely test for all of those. Testing explicitly for every standard variation would be costly and might not cover user defined types. Fortunately, optics are targeting specific paths inside data-structures, rather than completely arbitrary values, which means that even a loose test can be accurate enough.

Note that if you are new to lenses, then you probably want to start with the tutorial.

A case that we have run into multiple times is where we have an array of constant strings that we wish to manipulate as if it was a collection of boolean flags:

`var sampleFlags = ['id-19', 'id-76']`

Here is a parameterized lens that does just that:

```
var flag = id => [
L.normalize(R.sortBy(R.identity)),
L.find(R.equals(id)),
L.is(id)
]
```

Now we can treat individual constants as boolean flags:

```
L.get(flag('id-69'), sampleFlags)
```

```
L.get(flag('id-76'), sampleFlags)
```

In both directions:

```
L.set(flag('id-69'), true, sampleFlags)
```

```
L.set(flag('id-76'), false, sampleFlags)
```

It is not atypical to have UIs where one selection has an effect on other
selections. For example, you could have an UI where you can specify `maximum`

and `initial`

values for some measure and the idea is that the `initial`

value
cannot be greater than the `maximum`

value. One way to deal with this
requirement is to implement it in the lenses that are used to access the
`maximum`

and `initial`

values. This way the UI components that allows the user
to edit those values can be dumb and do not need to know about the restrictions.

One way to build such a lens is to use a combination of `L.props`

(or, in more complex cases, `L.pick`

) to limit the set of properties
to deal with, and `L.rewrite`

to insert the desired restriction
logic. Here is how it could look like for the `maximum`

:

```
var maximum = [
L.props('maximum', 'initial'),
L.rewrite(props => {
const {maximum, initial} = props
if (maximum < initial)
return {maximum, initial: maximum}
else
return props
}),
'maximum'
]
```

Now:

```
L.set(maximum, 5, {maximum: 10, initial: 8, something: 'else'})
```

A typical element of UIs that display a list of selectable items is a checkbox to select or unselect all items. For example, the TodoMVC spec includes such a checkbox. The state of a checkbox is a single boolean. How do we create a lens that transforms a collection of booleans into a single boolean?

The state of a todo list contains a boolean `completed`

flag per item:

`var sampleTodos = [{completed: true}, {completed: false}, {completed: true}]`

We can address those flags with a traversal:

`var completedFlags = [L.elems, 'completed']`

To compute a single boolean out of a traversal over booleans we can use the
`L.and`

fold and use that to define a lens parameterized over flag
traversals using `L.foldTraversalLens`

:

`var selectAll = L.foldTraversalLens(L.and)`

Now we can say, for example:

```
L.get(selectAll(completedFlags), sampleTodos)
```

```
L.set(selectAll(completedFlags), true, sampleTodos)
```

As an exercise define `unselectAll`

using the `L.or`

fold. How does it
differ from `selectAll`

?

Binary search trees might initially seem to be outside the scope of definable lenses. However, given basic BST operations, one could easily wrap them as a primitive partial lens. But could we leverage lens combinators to build a BST lens more compositionally?

We can. The `L.cond`

combinator allows for dynamic selection of
lenses based on examining the data structure being manipulated. Using
`L.cond`

we can write the ordinary BST logic to pick the correct
branch based on the key in the currently examined node and the key that we are
looking for. So, here is our first attempt at a BST lens:

```
var searchAttempt = key => L.lazy(rec => [
L.cond(
[n => !n || key === n.key, L.defaults({key})],
[n => key < n.key, ['smaller', rec]],
[['greater', rec]]
)
])
var valueOfAttempt = key => [searchAttempt(key), 'value']
```

Note that we also make use of the `L.lazy`

combinator to create a
recursive lens with a cyclic representation.

This actually works to a degree. We can use the `valueOfAttempt`

lens
constructor to build a binary tree. Here is a little helper to build a tree
from pairs:

```
var fromPairs = R.reduce(
(t, [k, v]) => L.set(valueOfAttempt(k), v, t),
undefined
)
```

Now:

```
var sampleBST = fromPairs([[3, 'g'], [2, 'a'], [1, 'm'], [4, 'i'], [5, 'c']])
sampleBST
```

However, the above `searchAttempt`

lens constructor does not maintain the BST
structure when values are being removed:

```
L.remove(valueOfAttempt(3), sampleBST)
```

How do we fix this? We could check and transform the data structure to a BST
after changes. The `L.rewrite`

combinator can be used for that
purpose. Here is a naïve rewrite to fix a tree after value removal:

```
var naiveBST = L.rewrite(n => {
if (undefined !== n.value) return n
const s = n.smaller, g = n.greater
if (!s) return g
if (!g) return s
return L.set(search(s.key), s, g)
})
```

Here is a working `search`

lens and a `valueOf`

lens constructor:

```
var search = key => L.lazy(rec => [
naiveBST,
L.cond(
[n => !n || key === n.key, L.defaults({key})],
[n => key < n.key, ['smaller', rec]],
[['greater', rec]]
)
])
var valueOf = key => [search(key), 'value']
```

Now we can also remove values from a binary tree:

```
L.remove(valueOf(3), sampleBST)
```

As an exercise, you could improve the rewrite to better maintain balance.
Perhaps you might even enhance it to maintain a balance condition such as
AVL or
Red-Black. Another
worthy exercise would be to make it so that the empty binary tree is `null`

rather than `undefined`

.

What about traversals over BSTs? We can use the
`L.branch`

combinator to define an in-order traversal over the
values of a BST:

```
var values = L.lazy(rec => [
L.optional,
naiveBST,
L.branch({smaller: rec, value: [], greater: rec})
])
```

Given a binary tree `sampleBST`

we can now manipulate it as a whole. For
example:

```
L.join('-', values, sampleBST)
```

```
L.modify(values, R.toUpper, sampleBST)
```

```
L.remove([values, L.when(x => x > 'e')], sampleBST)
```

Immutable.js is a popular library providing immutable data structures. As argued in Lenses with Immutable.js it can be useful to be able to manipulate Immutable.js data structures using optics.

When interfacing external libraries with partial lenses one does need to consider whether and how to support partiality. Partial lenses allow one to insert new and remove existing elements rather than just view and update existing elements.

`List`

indexingHere is a primitive partial lens for indexing
`List`

written using
`L.lens`

:

```
var getList = i => xs => Immutable.List.isList(xs) ? xs.get(i) : undefined
var setList = i => (x, xs) => {
if (!Immutable.List.isList(xs))
xs = Immutable.List()
if (x !== undefined)
return xs.set(i, x)
return xs.delete(i)
}
var idxList = i => [L.lens(getList(i), setList(i)), L.setIx(i)]
```

Note how the above uses `isList`

to check the input. When viewing, in case the
input is not a `List`

, the proper result is `undefined`

. When updating the
proper way to handle a non-`List`

is to treat it as empty. Also, when updating,
we treat `undefined`

as a request to `delete`

rather than `set`

. `idxList`

also
uses `L.setIx`

to set the index to the given index `i`

.

We can now view existing elements:

```
var sampleList = Immutable.List(['a', 'l', 'i', 's', 't'])
L.get(idxList(2), sampleList)
```

Update existing elements:

```
L.modify(idxList(1), R.toUpper, sampleList)
```

And remove existing elements:

```
L.remove(idxList(0), sampleList)
```

We can also create lists from non-lists:

```
L.set(idxList(0), 'x', undefined)
```

And we can also append new elements:

```
L.set(idxList(5), '!', sampleList)
```

Consider what happens when the index given to `idxList`

points further beyond
the last element. Both the `L.index`

lens and the above lens add
`undefined`

values, which is not ideal with partial lenses, because of the
special treatment of `undefined`

. In practise, however, it is not typical to
`set`

elements except to append just after the last element.

Fortunately we do not need Immutable.js data structures to provide a compatible
*partial*
`traverse`

function to support traversals, because it is also possible to
implement traversals simply by providing suitable isomorphisms between
Immutable.js data structures and JSON. Here is a partial
isomorphism between `List`

and arrays:

```
var fromList = xs => Immutable.List.isList(xs) ? xs.toArray() : undefined
var toList = xs => R.is(Array, xs) && xs.length ? Immutable.List(xs) : undefined
var isoList = L.iso(fromList, toList)
```

So, now we can compose a traversal over `List`

as:

`var seqList = [isoList, L.elems]`

And all the usual operations work as one would expect, for example:

```
L.remove([seqList, L.when(c => c < 'i')], sampleList)
```

And:

```
L.joinAs(
R.toUpper,
'',
[seqList, L.when(c => c <= 'i')],
sampleList
)
```

`L.filter`

, `L.find`

, `L.get`

, and `L.when`

`L.filter`

, `L.find`

, `L.get`

, and
`L.when`

serve related, but different, purposes and it is important
to understand their differences in order to make best use of them.

Here is a table of their call patterns and type signatures:

Call pattern | Type signature |
---|---|

`L.filter((value, index) => bool) ~> lens` |
`L.filter: ((Maybe a, Index) -> Boolean) -> PLens [a] [a]` |

`L.find((value, index) => bool) ~> lens` |
`L.find: ((Maybe a, Index) -> Boolean) -> PLens [a] a` |

`L.get(traversal, data) ~> value` |
`L.get: PTraversal s a -> Maybe s -> Maybe a` |

`L.when((value, index) => bool) ~> optic` |
`L.when: ((Maybe a, Index) -> Boolean) -> POptic a a` |

As can be read from above, both `L.filter`

and `L.find`

introduce lenses, `L.get`

eliminates a traversal, and
`L.when`

introduces an optic, which will always be a traversal in
this section. We can also read that `L.filter`

and
`L.find`

operate on arrays, while `L.get`

and
`L.when`

operate on arbitrary traversals. Yet another thing to make
note of is that both `L.find`

and `L.get`

are many-to-one
while both `L.filter`

and `L.when`

retain cardinality.

The following equations relate the operations in the read direction:

```
L.get([L.filter(p), 0]) = L.get(L.find(p))
L.get([L.elems, L.when(p)]) = L.get(L.find(p))
L.collect([L.elems, L.when(p)]) = L.get(L.filter(p))
```

In the write direction there are no such simple equations.

`L.find`

can be used to create a bidirectional view of an element in
an array identified by a given predicate. Despite the name, `L.find`

is probably not what one should use to generally search for something in a data
structure.

`L.get`

(and `L.getAs`

) can be used to search
for an element in a data structure following an arbitrary traversal. That
traversal can, of course, also make use of `L.when`

to filter elements
or to limit the traversal.

`L.filter`

can be used to create a bidirectional view of a subset
of elements of an array matching a given predicate. `L.filter`

should probably be the least most commonly used of the bunch. If the end goal
is simply to manipulate multiple elements, it is preferable to use a combination
of `L.elems`

and `L.when`

, because then no intermediate
array of the elements is
computed.

Traversals do not materialize intermediate aggregates and it is useful to understand this performance characteristic.

Consider the following naïve use of Ramda:

```
var sumPositiveXs = R.pipe(
R.flatten,
R.map(R.prop('x')),
R.filter(R.lt(0)),
R.sum
)
var sampleXs = [[{x: 1}], [{x: -2}, {x: 2}]]
sumPositiveXs(sampleXs)
```

A performance problem in the above naïve `sumPositiveXs`

function is that aside
from the last step, `R.sum`

, every step of the computation, `R.flatten`

,
`R.map(R.prop('x'))`

, and `R.filter(R.lt(0))`

, creates an intermediate array
that is only used by the next step of the computation and is then thrown away.
When dealing with large amounts of data this kind of composition can cause
performance issues.

Please note that the above example is *intentionally naïve*. In Ramda one can
use transducers to avoid building such intermediate
results although in
this particular case the use of `R.flatten`

makes things a bit more interesting, because it doesn't (at the time of writing)
act as a transducer in Ramda (version 0.24.1).

Using traversals one could perform the same summations as

```
L.sum([L.flatten, 'x', L.when(R.lt(0))], sampleXs)
```

and, thankfully, it doesn't create intermediate arrays. This is the case with traversals in general.

`L.choose`

The function given to `L.choose`

is called each time the optic is
used and any allocations done by the function are consequently repeated.

Consider the following example:

`L.choose(x => Array.isArray(x) ? [L.elems, 'data'] : 'data')`

A performance issue with the above is that each time it is used on an array, a
new composition, `[L.elems, 'data']`

, is allocated. Performance may be improved
by moving the allocation outside of `L.choose`

:

```
var onArray = [L.elems, 'data']
L.choose(x => Array.isArray(x) ? onArray : 'data')
```

In cases like above you can also use the more restricted `L.cond`

combinator:

`L.cond([Array.isArray, [L.elems, 'data']], ['data'])`

This has the advantage that the optics are constructed only once.

The distribution of this library includes a prebuilt and minified browser
bundle. However,
this library is not designed to be primarily used via that bundle. Rather, this
library is bundled with Rollup, uses `/*#__PURE__*/`

annotations to help UglifyJS do better
dead code elimination, and uses `process.env.NODE_ENV`

to detect `'production'`

mode to discard some warnings and error checks. This means that when using
Rollup with replace and
uglify plugins to build
browser bundles, the generated bundles will basically only include what you use
from this library.

For best results, increasing the number of compression passes may allow UglifyJS to eliminate more dead code. Here is a sample snippet from a Rollup config:

```
import replace from 'rollup-plugin-replace'
import {uglify} from 'rollup-plugin-uglify'
// ...
export default {
plugins: [
replace({
'process.env.NODE_ENV': JSON.stringify('production')
}),
// ...
uglify({
compress: {
passes: 3
}
})
]
}
```

In late 2015, while implementing UIs for manipulating fairly complex JSON objects, we wrote a module of additional lens combinators on top of Ramda's lenses. Lenses allowed us to operate on nested objects in a compositional manner and, thanks to treating data as immutable, also made it easy to provide undo-redo. Pretty quickly, however, it became evident that Ramda's support for lenses left room for improvement.

First of all, upto and including Ramda version 0.24.1, Ramda's lenses didn't deal with non-existent focuses consistently:

```
R.view(R.lensPath(['x', 'y']), {})
// undefined
R.view(R.compose(R.lensProp('x'), R.lensProp('y')), {})
// TypeError: Cannot read property 'y' of undefined
```

(In Ramda version 0.25.0, roughly two years later, both of the above now
return `undefined`

.)

In addition to using lenses to view and set, we also wanted to have the ability to insert and remove. In other words, we wanted full CRUD semantics, because that is what our UIs also had to provide.

We also wanted lenses to have the ability to search for things, because we often had to deal with e.g. arrays containing objects with unique IDs aka association lists.

All of these considerations give rise to a notion of partiality, which is what the Partial Lenses library set out to explore in early 2016. Since then the library has grown to a comprehensive, high-performance, optics library, supporting not only partial lenses, but also isomorphisms, traversals, and also a notion of transforms.

There are several lens and optics libraries for JavaScript. In this section I'd like to very briefly elaborate on a number design choices made during the course of developing this library.

Making all optics partial allows optics to not only view and update existing elements, but also to insert, replace (as in replace with data of different type) and remove elements and to do so in a seamless and efficient way. In a library based on total lenses, one needs to e.g. explicitly compose lenses with prisms to deal with partiality. This not only makes the optic compositions more complex, but can also have a significant negative effect on performance.

The downside of implicit partiality is the potential to create incorrect optics that signal errors later than when using total optics.

JSON is the data-interchange format of choice today. By being able to effectively and efficiently manipulate JSON data structures directly, one can avoid using special internal representations of data and make things simpler (e.g. no need to convert from JSON to efficient immutable collections and back).

`undefined`

`undefined`

is arguably a natural choice in JavaScript to represent nothingness:

`undefined`

is the result of an attempt to access non-existent properties of objects.`undefined`

is the result of functions that do not explicitly return another value.`undefined`

is not a valid JSON value and does not get mixed up with valid JSON values.- We can form a monoid over JavaScript values by treating
`undefined`

as zero.

Some libraries use `null`

, but that is arguably a poor choice, because `null`

is
a valid JSON value, which means that when accessing JSON data a result of `null`

is ambiguous.

One downside of using `undefined`

is that it can sometimes be a valid value.
Fortunately this is fairly rarely the case so inventing a new value to represent
nothingness doesn't seem to add much.

Some libraries implement special `Maybe`

types, but the benefits do not seem
worth the trouble nor the disadvantages in this context. The main disadvantage
is that wrapping values with `Just`

objects introduces a significant performance
overhead due to extra allocations, because operations with optics do not
otherwise necessarily require large numbers of allocations and can be made
highly efficient. Also, a `Maybe`

monad
is not necessary for optics. A
monoid
is sufficient for optics based on
applicatives,
because applicatives do not have a join operation and are not nested like
monads.

Not having an explicit `Just`

object means that dealing with values such as
`Just Nothing`

requires special consideration.

Aside from the brevity, allowing strings and non-negative integers to be directly used as optics allows one to avoid allocating closures for such optics. This can provide significant time and, more importantly, space savings in applications that create large numbers of lenses to address elements in data structures.

The downside of allowing such special values as optics is that the internal implementation needs to be careful to deal with them at any point a user given value needs to be interpreted as an optic.

Aside from the brevity, treating an array of optics as a
composition allows the library to be optimized to deal with simple
paths highly efficiently and eliminate the need for separate primitives like
`assocPath`

and
`dissocPath`

for performance reasons.
Client code can also manipulate such simple paths as data.

One interesting consequence of partiality is that it becomes possible to invert isomorphisms without explicitly making it possible to extract the forward and backward functions from an isomorphism. A simple internal implementation based on functors and applicatives seems to be expressive enough for a wide variety of operations.

By providing combinators for creating new traversals,
lenses and isomorphisms, client code need not depend on the
internal implementation of optics. The current version of this library exposes
the internal implementation via `L.toFunction`

, but it would
not be unreasonable to not provide such an operation. Only very few
applications need to know the internal representation of optics.

Indexing in partial lenses is unnested, very simple and based on the indices and keys of the underlying data structures. When indexing was added, it essentially introduced no performance degradation, but since then a few operations have been added that do require extra allocations to support indexing. It is also possible to compose optics so as to create nested indices or paths, but currently no combinator is directly provided for that.

The algebraic structures used in partial lenses follow the Static Land specification rather than the Fantasy Land specification. Static Land does not require wrapping values in objects, which translates to a significant performance advantage throughout the library, because fewer allocations are required.

However, the original
reason
for switching to use Static Land was that correct
implementation of `traverse`

requires the
ability to construct a value of a given applicative type without having any
instance of said applicative type. This means that one has to explicitly pass
something, e.g. a function `of`

, through optics to make that possible. This
eliminates a major notational advantage of Fantasy Land. In Static Land, which
can basically be seen as using the dictionary translation of type classes, one
already passes the algebra module to combinators.

Concern for performance has been a part of the work on partial lenses for some time. The basic principles can be summarized in order of importance:

- Minimize overheads
- Micro-optimize for common cases
- Avoid stack overflows
- Avoid quadratic algorithms
- Avoid optimizations that require large amounts of code
- Run benchmarks continuously to detect performance regressions

Here are a few benchmark results on partial lenses (as `L`

version 13.1.1) with
Node.js v8.9.3 and some roughly equivalent operations using
Ramda (as `R`

version 0.25.0), Ramda
Lens (as `P`

version 0.1.2), Flunc
Optics (as `O`

version 0.0.2),
Optika (as `K`

version 0.0.2),
lodash.get (as `_get`

version
4.4.2), and unchanged (as `U`

version 1.0.4). As always with benchmarks, you should take these numbers with a
pinch of salt and preferably try and measure your actual use cases!

```
29,261,559/s 1.00 L.get(L_find_id_5000, ids)
6,263,306/s 1.00 R.reduceRight(add, 0, xs100)
702,855/s 8.91 L.foldr(add, 0, L.elems, xs100)
223,260/s 28.05 xs100.reduceRight(add, 0)
3,516/s 1781.23 O.Fold.foldrOf(O.Traversal.traversed, addC, 0, xs100)
11,221/s 1.00 R.reduceRight(add, 0, xs100000)
242/s 46.28 L.foldr(add, 0, L.elems, xs100000)
61/s 183.44 xs100000.reduceRight(add, 0)
0/s Infinity O.Fold.foldrOf(O.Traversal.traversed, addC, 0, xs100000) -- STACK OVERFLOW
5,768,818/s 1.00 {let s=0; for (let i=0; i<xs100.length; ++i) s+=xs100[i]; return s}
3,966,543/s 1.45 L.sum(L.elems, xs100)
1,761,821/s 3.27 K.traversed().sumOf(xs100)
1,088,094/s 5.30 L.foldl(add, 0, L.elems, xs100)
1,028,546/s 5.61 xs100.reduce(add, 0)
559,221/s 10.32 L.concat(Sum, L.elems, xs100)
43,679/s 132.07 R.reduce(add, 0, xs100)
39,374/s 146.51 R.sum(xs100)
19,643/s 293.68 P.sumOf(P.traversed, xs100)
3,972/s 1452.40 O.Fold.sumOf(O.Traversal.traversed, xs100)
2,502/s 2305.79 O.Fold.foldlOf(O.Traversal.traversed, addC, 0, xs100)
1,191,166/s 1.00 L.maximum(L.elems, xs100)
2,880/s 413.63 O.Fold.maximumOf(O.Traversal.traversed, xs100)
637,283/s 1.00 {let s=0; for (let i=0; i<xsss100.length; ++i) for (let j=0, xss=xsss100[i]; j<xss.length; ++j) for (let k=0, xs=xss[j]; k<xs.length; ++k) s+=xs[i]; return s}
322,280/s 1.98 K_t_t_t.sumOf(xsss100)
266,188/s 2.39 L.foldl(add, 0, L_e_e_e, xsss100)
251,599/s 2.53 L.foldl(add, 0, [L.elems, L.elems, L.elems], xsss100)
182,952/s 3.48 K.traversed().traversed().traversed().sumOf(xsss100)
164,781/s 3.87 L.sum(L_e_e_e, xsss100)
159,784/s 3.99 L.sum([L.elems, L.elems, L.elems], xsss100)
157,992/s 4.03 L.concat(Sum, [L.elems, L.elems, L.elems], xsss100)
4,281/s 148.86 P.sumOf(R.compose(P.traversed, P.traversed, P.traversed), xsss100)
804/s 792.17 O.Fold.sumOf(R.compose(O.Traversal.traversed, O.Traversal.traversed, O.Traversal.traversed), xsss100)
2,493,770/s 1.00 K.traversed().arrayOf(xs100)
973,139/s 2.56 L.collect(L.elems, xs100)
784,513/s 3.18 xs100.map(I.id)
3,034/s 821.88 O.Fold.toListOf(O.Traversal.traversed, xs100)
250,527/s 1.00 L.collect(L_e_e_e, xsss100)
237,554/s 1.05 L.collect([L.elems, L.elems, L.elems], xsss100)
44,751/s 5.60 {let acc=[]; xsss100.forEach(x0 => {x0.forEach(x1 => {acc = acc.concat(x1)})}); return acc}
38,308/s 6.54 K_t_t_t.arrayOf(xsss100)
35,206/s 7.12 K.traversed().traversed().traversed().arrayOf(xsss100)
9,223/s 27.16 R.chain(R.chain(R.identity), xsss100)
735/s 341.03 O.Fold.toListOf(R.compose(O.Traversal.traversed, O.Traversal.traversed, O.Traversal.traversed), xsss100)
61,367/s 1.00 L.collect(L.flatten, xsss100)
21,566/s 2.85 R.flatten(xsss100)
15,709,764/s 1.00 xs.map(inc)
14,296,101/s 1.10 L.modify(L.elems, inc, xs)
2,992,297/s 5.25 R.map(inc, xs)
1,470,281/s 10.68 K.traversed().over(xs, inc)
508,177/s 30.91 O.Setter.over(O.Traversal.traversed, inc, xs)
323,509/s 48.56 P.over(P.traversed, inc, xs)
531,273/s 1.00 L.modify(L.elems, inc, xs1000)
91,098/s 5.83 xs1000.map(inc)
85,445/s 6.22 R.map(inc, xs1000)
84,705/s 6.27 K.traversed().over(xs1000, inc)
379/s 1400.14 O.Setter.over(O.Traversal.traversed, inc, xs1000) -- QUADRATIC
350/s 1518.84 P.over(P.traversed, inc, xs1000) -- QUADRATIC
193,914/s 1.00 L.modify(L_e_e_e, inc, xsss100)
178,651/s 1.09 L.modify([L.elems, L.elems, L.elems], inc, xsss100)
100,368/s 1.93 K_t_t_t.over(xsss100, inc)
88,725/s 2.19 K.traversed().traversed().traversed().over(xsss100, inc)
86,297/s 2.25 xsss100.map(x0 => x0.map(x1 => x1.map(inc)))
11,834/s 16.39 R.map(R.map(R.map(inc)), xsss100)
3,583/s 54.12 O.Setter.over(R.compose(O.Traversal.traversed, O.Traversal.traversed, O.Traversal.traversed), inc, xsss100)
2,859/s 67.82 P.over(R.compose(P.traversed, P.traversed, P.traversed), inc, xsss100)
51,874,299/s 1.00 L.get(1, xs)
35,680,586/s 1.45 _get(xs, 1)
19,954,170/s 2.60 U.get(1, xs)
13,182,372/s 3.94 R.nth(1, xs)
1,956,697/s 26.51 R.view(l_1, xs)
1,419,735/s 36.54 K.idx(1).get(xs)
154,267,077/s 1.00 L_get_1(xs)
18,509,602/s 8.33 L.get(1)(xs)
5,174,261/s 29.81 R_nth_1(xs)
3,140,154/s 49.13 R.nth(1)(xs)
2,969,585/s 51.95 U_get_1(xs)
2,415,058/s 63.88 U.get(1)(xs)
31,500,628/s 1.00 L.set(1, 0, xs)
9,391,877/s 3.35 xs.map((x, i) => i === 1 ? 0 : x)
7,110,172/s 4.43 {let ys = xs.slice(); ys[1] = 0; return ys}
5,074,836/s 6.21 U.set(1, 0, xs)
3,072,405/s 10.25 R.update(1, 0, xs)
947,676/s 33.24 K.idx(1).set(xs, 0)
815,287/s 38.64 R.set(l_1, 0, xs)
38,524,625/s 1.00 L.get('y', xyz)
17,349,278/s 2.22 _get(xyz, 'y')
16,429,516/s 2.34 U.get('y', xyz)
9,193,603/s 4.19 R.prop('y', xyz)
1,770,509/s 21.76 R.view(l_y, xyz)
1,434,326/s 26.86 K.key('y').get(xyz)
68,577,224/s 1.00 L_get_y(xyz)
15,435,254/s 4.44 L.get('y')(xyz)
4,702,316/s 14.58 R_prop_y(xyz)
2,821,439/s 24.31 U_get_y(xyz)
2,774,587/s 24.72 R.prop('y')(xyz)
2,304,145/s 29.76 U.get('y')(xyz)
7,450,898/s 1.00 R.assoc('y', 0, xyz)
7,322,941/s 1.02 L.set('y', 0, xyz)
1,895,793/s 3.93 U.set('y', 0, xyz)
995,035/s 7.49 K.key('y').set(xyz, 0)
875,025/s 8.52 R.set(l_y, 0, xyz)
12,154,904/s 1.00 _get(axay, [0, 'x', 0, 'y'])
11,297,478/s 1.08 L.get([0, 'x', 0, 'y'], axay)
10,140,829/s 1.20 R.path([0, 'x', 0, 'y'], axay)
4,275,282/s 2.84 U.get([0, 'x', 0, 'y'], axay)
1,706,187/s 7.12 R.view(l_0x0y, axay)
767,316/s 15.84 K_0_x_0_y.get(axay)
492,426/s 24.68 R.view(l_0_x_0_y, axay)
3,635,072/s 1.00 L.set([0, 'x', 0, 'y'], 0, axay)
931,074/s 3.90 U.set([0, 'x', 0, 'y'], 0, axay)
741,621/s 4.90 R.assocPath([0, 'x', 0, 'y'], 0, axay)
573,987/s 6.33 K_0_x_0_y.set(axay, 0)
398,742/s 9.12 R.set(l_0x0y, 0, axay)
266,083/s 13.66 R.set(l_0_x_0_y, 0, axay)
3,571,529/s 1.00 L.modify([0, 'x', 0, 'y'], inc, axay)
578,551/s 6.17 K_0_x_0_y.over(axay, inc)
453,113/s 7.88 R.over(l_0x0y, inc, axay)
285,952/s 12.49 R.over(l_0_x_0_y, inc, axay)
31,022,872/s 1.00 L.remove(1, xs)
3,430,687/s 9.04 R.remove(1, 1, xs)
3,029,069/s 10.24 U.remove(1, xs)
7,992,802/s 1.00 L.remove('y', xyz)
2,435,349/s 3.28 R.dissoc('y', xyz)
1,196,219/s 6.68 U.remove('y', xyz)
19,206,167/s 1.00 _get(xyzn, ['x', 'y', 'z'])
12,018,401/s 1.60 L.get(['x', 'y', 'z'], xyzn)
10,435,414/s 1.84 R.path(['x', 'y', 'z'], xyzn)
4,598,735/s 4.18 U.get(['x', 'y', 'z'], xyzn)
1,881,768/s 10.21 R.view(l_xyz, xyzn)
848,943/s 22.62 K_xyz.get(xyzn)
683,515/s 28.10 R.view(l_x_y_z, xyzn)
154,207/s 124.55 O.Getter.view(o_x_y_z, xyzn)
3,864,421/s 1.00 L.set(['x', 'y', 'z'], 0, xyzn)
1,068,844/s 3.62 U.set(['x', 'y', 'z'], 0, xyzn)
1,066,246/s 3.62 R.assocPath(['x', 'y', 'z'], 0, xyzn)
672,562/s 5.75 K_xyz.set(xyzn, 0)
499,486/s 7.74 R.set(l_xyz, 0, xyzn)
398,131/s 9.71 R.set(l_x_y_z, 0, xyzn)
200,548/s 19.27 O.Setter.set(o_x_y_z, 0, xyzn)
1,280,471/s 1.00 R.find(x => x > 3, xs100)
1,066,129/s 1.20 L.getAs(x => x > 3 ? x : undefined, L.elems, xs100)
2,529/s 506.25 O.Fold.findOf(O.Traversal.traversed, x => x > 3, xs100)
9,325,674/s 1.00 L.getAs(x => x < 3 ? x : undefined, L.elems, xs100)
4,411,876/s 2.11 R.find(x => x < 3, xs100)
2,473/s 3770.86 O.Fold.findOf(O.Traversal.traversed, x => x < 3, xs100) -- NO SHORTCUT EVALUATION
10,090/s 1.00 L.sum([L.elems, x => x+1, x => x*2, L.when(x => x%2 === 0)], xs1000)
3,838/s 2.63 R.transduce(R.compose(R.map(x => x+1), R.map(x => x*2), R.filter(x => x%2 === 0)), (x, y) => x+y, 0, xs1000)
3,166/s 3.19 R.pipe(R.map(x => x+1), R.map(x => x*2), R.filter(x => x%2 === 0), R.sum)(xs1000)
216,761/s 1.00 R.forEach(I.id, xs1000)
190,861/s 1.14 L.forEach(I.id, L.elems, xs1000)
115,582/s 1.88 xs1000.forEach(I.id)
252,911/s 1.00 L.forEach(I.id, L_e_e_e, xsss100)
237,600/s 1.06 L.forEach(I.id, [L.elems, L.elems, L.elems], xsss100)
99,597/s 2.54 xsss100.forEach(xss100 => xss100.forEach(xs100 => xs100.forEach(I.id)))
29,031/s 8.71 R.forEach(R.forEach(R.forEach(I.id)), xsss100)
5,717/s 1.00 L.minimum(L.elems, xs10000)
5,670/s 1.01 L.minimumBy(x => -x, L.elems, xs10000)
3,464/s 1.65 R.reduceRight(R.min, -Infinity, xs10000)
2,330/s 2.45 R.reduce(R.min, -Infinity, xs10000)
2,319/s 2.47 R.reduceRight(R.minBy(x => -x), Infinity, xs10000)
1,761/s 3.25 R.reduce(R.minBy(x => -x), Infinity, xs10000)
149,352/s 1.00 L.mean(L.elems, xs1000)
3,882/s 38.48 R.mean(xs1000)
5,768,842/s 1.00 L.remove(50, xs100)
1,766,663/s 3.27 R.remove(50, 1, xs100)
5,097,235/s 1.00 L.set(50, 2, xs100)
1,468,277/s 3.47 R.update(50, 2, xs100)
761,548/s 6.69 K.idx(50).set(xs100, 2)
583,231/s 8.74 R.set(l_50, 2, xs100)
75,197/s 1.00 L.remove(5000, xs10000)
38,157/s 1.97 R.remove(5000, 1, xs10000)
62,694/s 1.00 L.set(5000, 2, xs10000)
25,116/s 2.50 R.update(5000, 2, xs10000)
6,126,231/s 1.00 L.modify(L.values, inc, xyz)
382,949/s 1.00 L.modify(L.values, inc, xs10o)
46,114/s 8.30 L.modify(L.values, inc, xs100o)
4,858/s 78.83 L.modify(L.values, inc, xs1000o)
464/s 825.35 L.modify(L.values, inc, xs10000o)
645,308/s 1.00 L.modify(flatten, inc, nested)
373,998/s 1.73 L.modify(everywhere, incNum, nested)
937,120/s 1.00 L.modify(flatten, inc, xs10)
804,249/s 1.17 L.modify(everywhere, incNum, xs10)
156,861/s 1.00 L.modify(flatten, inc, xs100)
151,030/s 1.04 L.modify(everywhere, incNum, xs100)
17,261/s 1.00 L.modify(flatten, inc, xs1000)
16,558/s 1.04 L.modify(everywhere, incNum, xs1000)
1,618,143/s 1.00 L.set(xyzs, 1, undefined)
1,179,525/s 1.37 L.set(L.seq('x', 'y', 'z'), 1, undefined)
284,950/s 1.00 L.modify(values, x => x + x, bst)
443,036/s 1.00 L.collect(values, bst)
97,632/s 1.00 fromPairs(bstPairs)
56,276/s 1.00 L.get(L.slice(100, -100), xs10000)
40,472/s 1.39 R.slice(100, -100, xs10000)
5,911,415/s 1.00 L.get(L.slice(1, -1), xs)
5,544,989/s 1.07 R.slice(1, -1, xs)
3,188,865/s 1.00 L.get(L.slice(10, -10), xs100)
2,672,422/s 1.19 R.slice(10, -10, xs100)
9,386,623/s 1.00 L.get(L.defaults(1), 2)
8,851,162/s 1.06 L.get(L.defaults(1), undefined)
30,073,738/s 1.00 L.get(defaults1, undefined)
28,660,806/s 1.05 L.get(defaults1, 2)
10,012,353/s 1.00 L.get(L.define(1), 2)
9,817,035/s 1.02 L.get(L.define(1), undefined)
46,427,067/s 1.00 L.get(define1, undefined)
45,966,952/s 1.01 L.get(define1, 2)
15,312,111/s 1.00 L.get(L.valueOr(1), null)
15,106,079/s 1.01 L.get(L.valueOr(1), undefined)
14,284,098/s 1.07 L.get(L.valueOr(1), 2)
46,380,800/s 1.00 L.get(valueOr1, 2)
46,052,173/s 1.01 L.get(valueOr1, undefined)
45,749,521/s 1.01 L.get(valueOr1, null)
49,394/s 1.00 L.concatAs(toList, List, L.elems, xs100)
49,965/s 1.00 L.modify(L.flatten, inc, xsss100)
7,833,540/s 1.00 L.getAs(x => x > 3 ? x : undefined, L.elems, pi)
4,448,086/s 1.76 R.find(x => x > 3, pi)
32,770/s 239.05 O.Fold.findOf(O.Traversal.traversed, x => x > 3, pi)
6,140,005/s 1.00 L.get(L.find(x => x !== 1, {hint: 0}), xs)
5,933,954/s 1.03 L.get(L.find(x => x !== 1), xs)
4,608,258/s 1.33 R.find(x => x !== 1, xs)
1,320,062/s 1.00 R.find(x => x !== 1, xs100)
902,106/s 1.46 L.get(L.find(x => x !== 1), xs100)
900,911/s 1.47 L.get(L.find(x => x !== 1, {hint: 0}), xs100)
186,687/s 1.00 R.find(x => x !== 1, xs1000)
109,054/s 1.71 L.get(L.find(x => x !== 1, {hint: 0}), xs1000)
108,286/s 1.72 L.get(L.find(x => x !== 1), xs1000)
4,331,759/s 1.00 L.get(valueOr0x0y, axay)
4,233,734/s 1.02 L.get(define0x0y, axay)
3,894,676/s 1.11 L.get(defaults0x0y, axay)
865,866/s 1.00 L.set(valueOr0x0y, 1, undefined)
856,274/s 1.01 L.set(define0x0y, 1, undefined)
770,947/s 1.12 L.set(defaults0x0y, 1, undefined)
1,150,943/s 1.00 L.set(L.findWith('x'), 2, axay)
6,793,006/s 1.00 L.get(aEb, {x: 1})
6,290,285/s 1.08 L.get(abS, {x: 1})
4,201,828/s 1.62 L.get(abM, {x: 1})
3,072,564/s 2.21 L.get(L.orElse('a', 'b'), {x: 1})
2,295,497/s 2.96 L.get(L.choices('a', 'b'), {x: 1})
4,075,886/s 1.00 L.get(abcS, {x: 1})
4,019,108/s 1.01 L.get(aEbEc, {x: 1})
3,267,810/s 1.25 L.get(abcM, {x: 1})
1,401,479/s 2.91 L.get(L.choices('a', 'b', 'c'), {x: 1})
1,122,000/s 3.63 L.get(L.choice('a', 'b', 'c'), {x: 1})
1,309,555/s 1.00 L.set(L.props('x', 'y'), {x: 2, y: 3}, {x: 1, y: 2, z: 4})
```

Various operations on *partial lenses have been optimized for common cases*, but
there is definitely a lot of room for improvement. The goal is to make partial
lenses fast enough that performance isn't the reason why you might not want to
use them.

See bench.js for details.

As said in the first sentence of this document, lenses are convenient for performing updates on individual elements of immutable data structures. Having abilities such as nesting, adapting, recursing and restructuring using lenses makes the notion of an individual element quite flexible and, even further, traversals make it possible to selectively target zero or more elements of non-trivial data structures in a single operation. It can be tempting to try to do everything with lenses, but that will likely only lead to misery. It is important to understand that lenses are just one of many functional abstractions for working with data structures and sometimes other approaches can lead to simpler or easier solutions. Zippers, for example, are, in some ways, less principled and can implement queries and transforms that are outside the scope of lenses and traversals.

One type of use case which we've ran into multiple times and falls out of the sweet spot of lenses is performing uniform transforms over data structures. For example, we've run into the following use cases:

- Eliminate all references to an object with a particular id.
- Transform all instances of certain objects over many paths.
- Filter out extra fields from objects of varying shapes and paths.

One approach to making such whole data structure spanning updates is to use a simple bottom-up transform. Here is a simple implementation for JSON based on ideas from the Uniplate library:

```
var descend = (w2w, w) => R.is(Object, w) ? R.map(w2w, w) : w
var substUp = (h2h, w) => descend(h2h, descend(w => substUp(h2h, w), w))
var transform = (w2w, w) => w2w(substUp(w2w, w))
```

`transform(w2w, w)`

basically just performs a single-pass bottom-up transform
using the given function `w2w`

over the given data structure `w`

. Suppose we
are given the following data:

```
var sampleBloated = {
just: 'some',
extra: 'crap',
that: [
'we',
{
want: 'to',
filter: ['out'],
including: {the: 'following', extra: true, fields: 1}
}
]
}
```

We can now remove the `extra`

`fields`

like this:

```
transform(
R.ifElse(
R.allPass([R.is(Object), R.complement(R.is(Array))]),
L.remove(L.props('extra', 'fields')),
R.identity
),
sampleBloated
)
```

Lenses are an old concept and there are dozens of academic papers on lenses and dozens of lens libraries for various languages. Below are just a few links—feel free to suggest more!

- A Little Lens Starter Tutorial
- A clear picture of lens laws
- An Introduction Into Lenses In JavaScript
- Functional Lenses, How Do They Work
- Lenses with Immutable.js
- Polymorphic Update with van Laarhoven Lenses
- Profunctor Optics: Modular Data Accessors

- 5outh/nanoscope
- DrBoolean/lenses
- fantasyland/fantasy-lenses
- flunc/optics
- gcanti/monocle-ts
- hallettj/safety-lens
- ochafik/es6-lenses
- phadej/optika
- ramda/ramda-lens
- thisismN/lentil

Contributions in the form of pull requests are welcome!

Before starting work on a major PR, it is a good idea to open an issue or maybe ask on gitter whether the contribution sounds like something that should be added to this library.

If you allow us to make changes to your PR, it can make the process smoother: Allowing changes to a pull request branch created from a fork. We also welcome starting the PR sooner, before it is ready to be merged, rather than later so we know what is going on and can help.

Aside from the code changes, a PR should also include tests, and documentation.

When implementing partial optics it is important to consider the behavior of the optics when the focus doesn't match the expectation of the optic and also whether the optic should propagate removal. Such behavior should also be tested.

It is best not to commit changes to generated files in PRs. Some of the files
in `docs`

, and `dist`

directories are generated.

The `prepare`

script is the usual way to build after changes:

`npm run prepare`

It builds the `dist`

and `docs`

files and runs the lint rules and tests. You
can also run the scripts for those subtasks separately.

There is also a watch mode for development:

`npm run watch`

It starts watching the source files and runs dist and docs builds and tests after changes.

The tests in this library are written in a slightly atypical manner using thunks that are also used as the test descriptions. This way one doesn't need to invent names or write prose for tests.

There is also a special test that checks the arity of the exports. You'll notice it immediately if you add an export.

The `test/types.js`

file contains contract or type predicates
for the library primitives. Those are also used when running tests to check
that the implementation matches the contracts. When you implement a new
combinator, you will also need to add a contract for the combinator.

When testing a partial optics, you should generally test both read and, usually
more importantly, write behaviour including attempts to read `undefined`

or
unexpected data (both of these should be handled as `undefined`

) and writing
`undefined`

.

The `docs`

folder contains the generated documentation. You can open the file
locally:

`open docs/index.html`

To actually build the docs (translate the markdown to html), you can run

`npm run docs`

or you can use the watch

`npm run watch`

which builds the docs if you save a `.md`

file. The watch also runs
LiveReload so if you have the plugin, your browser
will refresh automatically after changes.

```
document.querySelector('.loading-message').className = "loading-hidden";
ga('send', 'event', 'completed', 'load', Math.round((Date.now() - startTime)/1000));
accelerate_klipse();
```