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Partial Lenses · Gitter GitHub stars npm

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!

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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

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.

Getting started

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

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.

A partial lens to access title texts

Let's then just compose a parameterized lens for accessing the text of titles:

var textIn = language => L.compose(
  L.valueOr({language, 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.

Querying data

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.

Missing data can be expected

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.

Updating data

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

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

Inserting data

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.

Removing data

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,

Systematic decomposition

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.valueOr({language, text: ''}),

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

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.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.

Manipulating multiple items

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)

Next steps

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.

The why of optics

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({language}), mapProp(fn, 'text'), R.identity)),
var remText = R.curry(
  (language, data) => mapProp(
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'

Stable subset

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:

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.

Additional libraries

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.

On partiality

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.

On indexing

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.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:

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

  (value, path) => [L.collect(L.flatten, path), value],
  L.lazy(rec => L.ifElse(, [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.

On immutability

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

On composability

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:

  1. There must be an operation or operations that perform composition.
  2. 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.

On lens laws

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.

Myth: Partial Lenses are not lawful

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:

  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.

Operations on optics

L.assign(optic, object, maybeData) ~> maybeData v11.13.0

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 v14.6.0

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:

  ['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 v2.2.0

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

For example:

L.modify(['elems', 0, 'x'],, {elems: [{x: 1, y: 2}, {x: 3, y: 4}]})
  ['elems', L.elems, 'x'],
  {elems: [{x: 1, y: 2}, {x: 3, y: 4}]}
L.modifyAsync(optic, (maybeValue, index) => maybeValuePromise, maybeData) ~> maybeDataPromise v13.12.0

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:

    ['elems', L.elems, 'x'],
    async x => x - 1,
    {elems: [{x: 1, y: 2}, {x: 3, y: 4}]}
L.remove(optic, maybeData) ~> maybeData v2.0.0

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 v1.0.0

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 v10.0.0

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)}
}{}, 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] v1.0.0

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),
   L.get(L.compose(o, ...os)) = R.pipe(L.get(o),

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),
   L.get([o, ...os]) = R.pipe(L.get(o),

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 v13.6.0

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 v5.1.0

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(, [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}]])
  [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 v11.10.0

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 v1.0.0

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 v13.1.0

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

For example:

var minorAxis = L.cond(
  [({x, y} = {}) => Math.abs(y) < Math.abs(x), 'y'],

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 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 v13.5.0

L.condOf is like L.cond except the first argument to L.condOf is a traversal whose focuses are tested with the predicates.

         [ 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] is used.

For example:

    [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 is a traversal.

L.ifElse((maybeValue, index) => testable, optic, optic) ~> optic v13.1.0

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),, [1, 2, 3])
L.modify(L.ifElse(Array.isArray, L.elems, L.values),, {x: 1, y: 2, z: 3})
L.orElse(backupOptic, primaryOptic) ~> optic v2.1.0

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, 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 v13.15.0

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:

  {a: {b: {c: 'abc'}}}
L.mapIx((index, maybeValue) => index) ~> optic v13.15.0

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

For example:

  {a: {b: {c: 'abc'}}}
L.setIx(index) ~> optic v13.15.0

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 v13.15.0

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

For example:

  {a: {b: {c: 'abc'}}}
L.tieIx((innerIndex, outerIndex) => index, optic) ~> optic v13.15.0

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.tieIx(R.append, 'a'),
    L.tieIx(R.append, 'b'),
    L.tieIx(R.append, 'c'),
  {a: {b: {c: 'abc'}}}

Note that both L.skipIx and L.joinIx can be implemented via L.tieIx.


L.getLog(lens, maybeData) ~> maybeValue v13.14.0

L.getLog returns the element focused on by a lens from a data structure like L.get, but L.getLog also console.logs 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 v3.2.0

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 v13.7.0

L.Identity is the Static Land compatible identity Monad definition used by Partial Lenses.

L.IdentityAsync ~> Monadish v13.12.0

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 v14.0.0

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 v7.0.0

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.

Operations on transforms

L.transform(optic, maybeData) ~> maybeData v11.7.0

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

Note that

L.transformAsync(optic, maybeData) ~> maybeDataPromise v13.12.0

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:

  L.transformAsync(L.leafs, {
    combine: Promise.resolve('a nested template'),
    of: [Promise.resolve('promises')],
    or: 'constants'
    [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 v9.4.0

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(, 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 v11.13.0

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 v11.7.0

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:

    xs: [L.elems, L.modifyOp(],
    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 v11.7.0

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]}

      elem => elem.time < 2,
      ['subelements', L.elems, L.when(i => i < 3), L.removeOp]

The idea is to filter the data both by time and by subelements.

L.setOp(maybeValue) ~> traversal v11.7.0

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.

Creating new traversals

L.branch({prop: traversal, ...props}) ~> traversal v5.1.0

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.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(

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

See the BST traversal section for a more meaningful example.

L.branchOr(traversal, {prop: traversal, ...props}) ~> traversal v13.2.0

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(, {x: L.modifyOp(R.dec)}), {x: 0, y: 0})

Note that L.branch is equivalent to L.branchOr( and L.values is equivalent to L.branchOr([], {}).

L.branches(...propNames) ~> traversal v13.5.0

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]: []}).

Traversals and combinators

L.children ~> traversal v13.3.0

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 v7.3.0

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'],, {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.rewrite(xs => Int8Array.from(xs)), L.elems],,
  Int8Array.from([-1, 4, 0, 2, 4])
L.elemsTotal ~> traversal v13.11.0

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.negate, [1, undefined, 2])
L.entries ~> traversal v11.21.0

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 v11.16.0

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 v11.21.0

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 v13.3.0

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 v10.4.0

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.pick({name: L.matches(/^[^=]+/), value: L.matches(/[^=]+$/)})

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 v13.6.0

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.query(L.when(R.propEq('language', 'en')), 'text'),

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 => [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 v13.3.0

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 v7.3.0

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 v3.1.0

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

    (value, index) => value === undefined ? : toOptic(value, index)

Note that with the R.always, L.chain, L.choice and combinators, one can consider optics as subsuming the maybe monad.

L.choice(...optics) ~> traversal v2.1.0

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, which is the identity element of L.choice. See also L.choices.

For example:

L.modify([L.elems, L.choice('a', 'd')],, [{R: 1}, {a: 1}, {d: 2}])
L.optional ~> traversal v3.7.0

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}])


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 v12.1.0

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 v5.2.0

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 : ~> traversal v6.0.0 is a traversal of no elements and is the identity element of L.choice and L.chain.

For example:

  [L.elems, L.cond([,  L.elems], [, 'x'], [])],
  [1, {x: 2}, [3, 4]]

Folds over traversals

L.all((maybeValue, index) => testable, traversal, maybeData) ~> boolean v9.6.0

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

For example:

  x => 1 <= x && x <= 6,
  [[[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 v14.4.0

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 v9.6.0

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 v14.4.0

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 v9.6.0

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] v3.6.0

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] v7.2.0

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] : []


  ['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] v14.6.0

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] v14.6.0

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 v7.2.0

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 v7.2.0

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 v9.7.0

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 v11.2.0

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 v11.21.0

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 v11.21.0

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 v7.2.0

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 v7.2.0

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 v11.20.0

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 v13.4.0

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 v9.8.0

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 v14.0.0

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)


all(x => x < 9, primitives, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
L.isDefined(traversal, maybeData) ~> boolean v11.8.0

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 v11.5.0

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 v11.2.0

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 v11.2.0

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 v7.2.0

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 v11.2.0

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 v11.17.0

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 v11.17.0

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 v7.2.0

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 v11.2.0

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 v11.6.0

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 v9.6.0

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 v7.2.0

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 v11.2.0

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., maybeData) ~> maybeValue v9.8.0

WARNING: has been obsoleted. Just use L.get. See CHANGELOG for details. goes lazily over the elements focused on by the given traversal and returns the first non-undefined element.[L.elems, 'y'], [{x:1}, {y:2}, {z:3}])

Note that is equivalent to L.selectAs(x => x).

L.selectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> maybeValue v9.8.0

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)


all(x => x < 9, primitives, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
L.sum(traversal, maybeData) ~> number v7.2.0

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 v11.2.0

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.

Creating new lenses

L.foldTraversalLens((traversal, maybeData) => maybeValue, traversal) ~> lens v11.5.0

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 v13.16.0

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 v1.0.0

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 {
        end: moment(start).add(moment.duration(duration)).toJSON()

Now, for example:

    start: '2016-12-07T09:39:02.451Z',
    end: moment('2016-12-07T09:39:02.451Z').add(10, 'hours').toISOString()
  {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 v14.6.0

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.partsOf([L.elems, 'x']),
  [3, 4],
  [{x: 1}, {y: 2}]
L.setter((maybeValue, maybeData, index) => maybeData) ~> lens v10.3.0

L.setter(set) is shorthand for L.lens(x => x, set). See also L.rewrite.

Enforcing invariants

L.defaults(valueIn) ~> lens v2.0.0

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 v1.0.0

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 v1.0.0

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 v1.0.0

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 v11.21.0

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 v5.1.0

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.

Lensing array-like objects

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

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 v1.0.0

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 v14.3.0

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 v1.0.0

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 v1.0.0

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.find(R.whereEq({id: 2}), {hint: 2}), 'value'],
    {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 v1.0.0

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 v13.1.0

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 v1.0.0

L.index(elemIndex) or just elemIndex focuses on the element at specified index of an array-like object.

For example:

L.set(2, 'z', ['x', 'y', 'c'])
L.remove(0, ['x'])
L.last ~> lens v9.8.0

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 v11.12.0

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:

For example:

L.set(L.prefix(0), [1], [2, 3])
L.slice(maybeBegin, maybeEnd) ~> lens v8.1.0

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:

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 v11.12.0

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:

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])

Lensing objects

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) { = 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)))

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 v11.11.0

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.pickIn({meta: {file: [], ext: []}}),
  {meta: {file: './foo.txt', base: 'foo', ext: 'txt'}}
L.prop(propName) ~> lens or propName v1.0.0

L.prop(propName) or just propName focuses on the specified object property.

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 v1.4.0

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 v11.13.0

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 v9.2.0

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.

Lensing strings

L.matches(/.../) ~> lens v10.4.0

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')

Providing defaults

L.valueOr(valueOut) ~> lens v3.5.0

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).

Transforming data

L.pick({prop: lens, ...props}) ~> lens v1.2.0

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 v1.0.0

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.

Operations on isomorphisms

L.getInverse(isomorphism, maybeData) ~> maybeData v5.0.0

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(,, expect(, 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)

Creating new isomorphisms

L.iso(maybeData => maybeValue, maybeValue => maybeData) ~> isomorphism v5.3.0

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.reverse),
  expect(, R.reverse)

L.mapping([patternFwd, patternBwd] | (...variables) => [patternFwd, patternBwd]) ~> isomorphism v14.8.0

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.mapping((x, y) => [[x, L._, ...y], {x, y}]),
  ['a', 'b', 'c', 'd']
      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 v14.8.0

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 v14.8.0

L.mappings is a shorthand for multiple L.mapping L.alternatives.


L.mappings((...variables) => [patternPair1, ..., patternPairN])

is equivalent to

  L.mappings((...variables) => patternPair1),
  L.mappings((...variables) => patternPairN)

For example:

  L.array(L.mappings((x, y) => [[[x, y], {x, y}], [{x, y}, [x, y]]])),
  [['a', 'b'], {x: 1, y: 2}]

Isomorphism combinators

L.alternatives(isomorphism, ...isomorphisms) ~> isomorphism v14.7.0

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.applyAt(elementsOptic, isomorphism) ~> isomorphism v14.9.0

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 v11.19.0

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 v14.9.0

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 v4.1.0

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 v14.3.0

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 v14.7.0

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).

Basic isomorphisms

L.complement ~> isomorphism v9.7.0

L.complement is an isomorphism that performs logical negation of any non-undefined value when either read or written through.

For example:

  [L.complement, L.log()],
  'Could be anything truthy',
  'Also converted to bool'
L.identity ~> isomorphism v1.3.0

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 ~> isomorphism v11.1.0 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 v14.3.0

L.subset returns an isomorphism that acts like the identity when the data passes the given predicate and otherwise maps the data to undefined.

Array isomorphisms

L.indexed ~> isomorphism v11.21.0

L.indexed is an isomorphism between an array-like object and an array of [index, value] pairs.

For example:

L.reverse ~> isomorphism v11.22.0

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 v11.18.0

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.

Object isomorphisms

L.disjoint(propName => propName) ~> isomorphism v13.13.0

L.disjoint divides an object into disjoint subsets based on the given function that maps keys to group keys.

For example:

  L.lazy(rec => L.cond(
    [, [L.elems, rec]],
    [, [
      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 v11.21.0

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 v14.1.0

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.replaces('+', '%20'),
L.get(querystring, '?foo=bar&abc=xyz&abc=123')
  [querystring, 'foo'],

Standard isomorphisms

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.json({reviver, replacer, space}) ~> isomorphism v11.3.0

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.json(), 'foo', L.elems, L.modifyOp(R.negate)],
L.uri ~> isomorphism v11.3.0

L.uri is an isomorphism based on the standard decodeURI and encodeURI functions. Decoding errors are caught and passed as results.

L.uriComponent ~> isomorphism v11.3.0

L.uriComponent is an isomorphism based on the standard decodeURIComponent and encodeURIComponent functions. Decoding errors are caught and passed as results.

Standardish isomorphisms

L.querystring ~> isomorphism v14.2.0

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: '' })

String isomorphisms

L.dropPrefix(prefix) ~> isomorphism v13.8.0

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 v13.8.0

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'), '')
L.getInverse(L.dropSuffix('.bar'), 'foo')
L.replaces(substringIn, substringOut) ~> isomorphism v13.8.0

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 v13.8.0

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 v13.8.0

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', ''])

Arithmetic isomorphisms

L.add(number) ~> isomorphism v13.9.0

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 v13.9.0

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 v13.9.0

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 v13.9.0

L.negate negates the number in focus when either read or written through.

For example:

L.get(L.negate, 2)
L.subtract(number) ~> isomorphism v13.9.0

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)


Fantasy Land

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 v14.5.0

L.FantasyFunctor is a Static Land compatible functor that dispatches to the fantasy-land/map method.

L.fromFantasy(TypeRep) ~> Functor|Applicative|Monad v14.5.0

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 v14.5.0

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 v14.5.0

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.

JSON Pointer

L.pointer(jsonPointer) ~> lens v11.21.0

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 v11.4.0

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.

An array of ids as boolean flags

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 => [

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)

Dependent fields

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}
      return props


L.set(maximum, 5, {maximum: 10, initial: 8, something: 'else'})

Collection toggle

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?

BST as a lens

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 => [
    [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),


var sampleBST = fromPairs([[3, 'g'], [2, 'a'], [1, 'm'], [4, 'i'], [5, 'c']])

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 => [
    [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.

BST traversal

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.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)

Interfacing with Immutable.js

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 indexing

Here 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.

Interfacing traversals

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 =>, 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)


  [seqList, L.when(c => c <= 'i')],

Deepening topics

Understanding 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.

Advanced topics

Performance tips

Nesting traversals does not create intermediate aggregates

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(

var sampleXs = [[{x: 1}], [{x: -2}, {x: 2}]]


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,'x')), and R.filter(, 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(], sampleXs)

and, thankfully, it doesn't create intermediate arrays. This is the case with traversals in general.

Avoid reallocating optics in 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.

On bundle size and minification

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: [
      'process.env.NODE_ENV': JSON.stringify('production')
    // ...
      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.

Design choices

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.

Focus on JSON

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).

Use of undefined

undefined is arguably a natural choice in JavaScript to represent nothingness:

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.

Allowing strings and integers as optics

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.

Treating an array of optics as a composition of optics

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.

Combinators for creating new optics

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.

Static Land

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:


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
       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
  14,296,101/s     1.10   L.modify(L.elems, inc, xs)
   2,992,297/s     5.25, 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
      85,445/s     6.22, 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 => =>
      11,834/s    16.39, 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, 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( => x+1), => x*2), R.filter(x => x%2 === 0)), (x, y) => x+y, 0, xs1000)
       3,166/s     3.19   R.pipe( => x+1), => x*2), R.filter(x => x%2 === 0), R.sum)(xs1000)

     216,761/s     1.00   R.forEach(, xs1000)
     190,861/s     1.14   L.forEach(, L.elems, xs1000)
     115,582/s     1.88   xs1000.forEach(

     252,911/s     1.00   L.forEach(, L_e_e_e, xsss100)
     237,600/s     1.06   L.forEach(, [L.elems, L.elems, L.elems], xsss100)
      99,597/s     2.54   xsss100.forEach(xss100 => xss100.forEach(xs100 => xs100.forEach(
      29,031/s     8.71   R.forEach(R.forEach(R.forEach(, 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.

Lenses all the way

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:

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) =>, w) ?, 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: [
      want: 'to',
      filter: ['out'],
      including: {the: 'following', extra: true, fields: 1}

We can now remove the extra fields like this:

    R.allPass([, R.complement(]),
    L.remove(L.props('extra', 'fields')),

Related work

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!

Papers and other introductory material

JavaScript / TypeScript / Flow libraries

Libraries for other languages


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(( - startTime)/1000));