# partial.lenses
**Repository Path**: mirrors_piotrwitek/partial.lenses
## Basic Information
- **Project Name**: partial.lenses
- **Description**: Partial lenses is a comprehensive, high-performance optics library for JavaScript
- **Primary Language**: Unknown
- **License**: MIT
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No
## Statistics
- **Stars**: 0
- **Forks**: 0
- **Created**: 2020-09-25
- **Last Updated**: 2026-05-17
## Categories & Tags
**Categories**: Uncategorized
**Tags**: None
## README
# [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#) Partial Lenses · [](https://gitter.im/calmm-js/chat) [](https://github.com/calmm-js/partial.lenses) [](https://www.npmjs.com/package/partial.lenses)
Lenses are basically an abstraction for simultaneously specifying operations to
[update](#L-modify) and [query](#L-get) [immutable](#on-immutability) data
structures. Lenses are [highly composable](#on-composability) and can be
[efficient](#benchmarks). This library provides a [rich
collection](#on-bundle-size-and-minification) of [partial](#on-partiality)
[isomorphisms](#isomorphisms), [lenses](#lenses), and [traversals](#traversals),
collectively known as [optics](#optics), for manipulating
[JSON](http://json.org/) and users [can](#L-toFunction) [write](#L-iso)
[new](#L-lens) [optics](#L-branch) for manipulating non-JSON objects, such as
[Immutable.js](#interfacing) 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!](https://calmm-js.github.io/partial.lenses/playground.html)
[](http://badge.fury.io/js/partial.lenses)
[](https://badge.fury.io/bo/partial.lenses)
[](https://travis-ci.org/calmm-js/partial.lenses)
[](https://codecov.io/github/calmm-js/partial.lenses?branch=master)
[](https://david-dm.org/calmm-js/partial.lenses)
[](https://david-dm.org/calmm-js/partial.lenses?type=dev)
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#contents) Contents
* [Tutorial](#tutorial)
* [Getting started](#getting-started)
* [A partial lens to access title texts](#a-partial-lens-to-access-titles)
* [Querying data](#querying-data)
* [Missing data can be expected](#missing-data-can-be-expected)
* [Updating data](#updating-data)
* [Inserting data](#inserting-data)
* [Removing data](#removing-data)
* [Exercises](#exercises)
* [Shorthands](#shorthands)
* [Systematic decomposition](#systematic-decomposition)
* [Manipulating multiple items](#manipulating-multiple-items)
* [Next steps](#next-steps)
* [The why of optics](#the-why-of-optics)
* [Reference](#reference)
* [Stable subset](#stable-subset)
* [Additional libraries](#additional-libraries)
* [Optics](#optics)
* [On partiality](#on-partiality)
* [On indexing](#on-indexing)
* [On immutability](#on-immutability)
* [On composability](#on-composability)
* [On lens laws](#on-lens-laws)
* [Myth: Partial Lenses are not lawful](#myth-partial-lenses-are-not-lawful)
* [Operations on optics](#operations-on-optics)
* [`L.assign(optic, object, maybeData) ~> maybeData`](#L-assign "L.assign: PLens s {p1: a1, ...ps, ...o} -> {p1: a1, ...ps} -> Maybe s -> Maybe s") v11.13.0
* [`L.modify(optic, (maybeValue, index) => maybeValue, maybeData) ~> maybeData`](#L-modify "L.modify: POptic s a -> ((Maybe a, Index) -> Maybe a) -> Maybe s -> Maybe s") v2.2.0
* [`L.remove(optic, maybeData) ~> maybeData`](#L-remove "L.remove: POptic s a -> Maybe s -> Maybe s") v2.0.0
* [`L.set(optic, maybeValue, maybeData) ~> maybeData`](#L-set "L.set: POptic s a -> Maybe a -> Maybe s -> Maybe s") v1.0.0
* [`L.traverse(algebra, (maybeValue, index) => operation, optic, maybeData) ~> operation`](#L-traverse "L.traverse: (Functor|Applicative|Monad) c -> ((Maybe a, Index) -> c b) -> POptic s t a b -> Maybe s -> c t") v10.0.0
* [Nesting](#nesting)
* [`L.compose(...optics) ~> optic`](#L-compose "L.compose: (POptic s s1, ...POptic sN a) -> POptic s a") or `[...optics]` v1.0.0
* [Recursing](#recursing)
* [`L.lazy(optic => optic) ~> optic`](#L-lazy "L.lazy: (POptic s a -> POptic s a) -> POptic s a") v5.1.0
* [Adapting](#adapting)
* [`L.choices(optic, ...optics) ~> optic`](#L-choices "L.choices: (POptic s a, ...POptic s a) -> POptic s a") v11.10.0
* [`L.choose((maybeValue, index) => optic) ~> optic`](#L-choose "L.choose: ((Maybe s, Index) -> POptic s a) -> POptic s a") v1.0.0
* [`L.cond(...[(maybeValue, index) => testable, consequentOptic][, [alternativeOptic]]) ~> optic`](#L-cond "L.cond: (...[(Maybe s, Index) -> Boolean, PLens s a][, [PLens s a]]) -> PLens s a") v13.1.0
* [`L.ifElse((maybeValue, index) => testable, optic, optic) ~> optic`](#L-ifElse "L.ifElse: ((Maybe s, Index) -> Boolean) -> POptic s a -> POptic s a -> POptic s a") v13.1.0
* ~~[`L.iftes((maybeValue, index) => testable, consequentOptic, ...[, alternativeOptic]) ~> optic`](#L-iftes "L.iftes: ((Maybe s, Index) -> Boolean) -> PLens s a -> PLens s a -> PLens s a") v11.14.0~~
* [`L.orElse(backupOptic, primaryOptic) ~> optic`](#L-orElse "L.orElse: (POptic s a, POptic s a) -> POptic s a") v2.1.0
* [Querying](#querying)
* [`L.chain((value, index) => optic, optic) ~> optic`](#L-chain "L.chain: ((a, Index) -> POptic s b) -> POptic s a -> POptic s b") v3.1.0
* [`L.choice(...optics) ~> optic`](#L-choice "L.choice: (...POptic s a) -> POptic s a") v2.1.0
* [`L.optional ~> optic`](#L-optional "L.optional: POptic a a") v3.7.0
* [`L.unless((maybeValue, index) => testable) ~> optic`](#L-unless "L.unless: ((Maybe a, Index) -> Boolean) -> POptic a a") v12.1.0
* [`L.when((maybeValue, index) => testable) ~> optic`](#L-when "L.when: ((Maybe a, Index) -> Boolean) -> POptic a a") v5.2.0
* [`L.zero ~> optic`](#L-zero "L.zero: POptic s a") v6.0.0
* [Debugging](#debugging)
* [`L.log(...labels) ~> optic`](#L-log "L.log: (...Any) -> POptic s s") v3.2.0
* [Internals](#internals)
* [`L.toFunction(optic) ~> optic`](#L-toFunction "L.toFunction: POptic s t a b -> (Maybe s, Index, (Functor|Applicative|Monad) c, (Maybe a, Index) -> c b) -> c t") v7.0.0
* [Transforms](#transforms)
* [Operations on transforms](#operations-on-transforms)
* [`L.transform(optic, maybeData) ~> maybeData`](#L-transform "L.transform: POptic s a -> Maybe s -> Maybe s") v11.7.0
* [Sequencing](#sequencing)
* [`L.seq(...transforms) ~> transform`](#L-seq "L.seq: (...PTransform s a) -> PTransform s a") v9.4.0
* [Transforming](#transforming)
* [`L.assignOp(object) ~> optic`](#L-assignOp "L.assignOp: {p1: a1, ...ps} -> POptic {p1: a1, ...ps, ...o} {p1: a1, ...ps}") v11.13.0
* [`L.modifyOp((maybeValue, index) => maybeValue) ~> optic`](#L-modifyOp "L.modifyOp: ((Maybe a, Index) -> Maybe a) -> POptic a a") v11.7.0
* [`L.removeOp ~> optic`](#L-removeOp "L.removeOp: POptic a a") v11.7.0
* [`L.setOp(maybeValue) ~> optic`](#L-setOp "L.setOp: Maybe a -> POptic a a") v11.7.0
* [Traversals](#traversals)
* [Creating new traversals](#creating-new-traversals)
* [`L.branch({prop: traversal, ...props}) ~> traversal`](#L-branch "L.branch: {p1: PTraversal s a, ...pts} -> PTraversal s a") v5.1.0
* [Traversals and combinators](#traversals-and-combinators)
* [`L.elems ~> traversal`](#L-elems "L.elems: PTraversal [a] a") v7.3.0
* [`L.entries ~> traversal`](#L-entries "L.entries: PTraversal {p: a, ...ps} [String, a]") v11.21.0
* [`L.flatten ~> traversal`](#L-flatten "L.flatten: PTraversal [...[a]...] a") v11.16.0
* [`L.keys ~> traversal`](#L-keys "L.keys: PTraversal {p: a, ...ps} String") v11.21.0
* [`L.matches(/.../g) ~> traversal`](#L-matches-g "L.matches: RegExp -> PTraversal String String") v10.4.0
* [`L.values ~> traversal`](#L-values "L.values: PTraversal {p: a, ...ps} a") v7.3.0
* [Folds over traversals](#folds-over-traversals)
* [`L.all((maybeValue, index) => testable, traversal, maybeData) ~> boolean`](#L-all "L.all: ((Maybe a, Index) -> Boolean) -> PTraversal s a -> Boolean") v9.6.0
* [`L.and(traversal, maybeData) ~> boolean`](#L-and "L.and: PTraversal s Boolean -> Boolean") v9.6.0
* [`L.any((maybeValue, index) => testable, traversal, maybeData) ~> boolean`](#L-any "L.any: ((Maybe a, Index) -> Boolean) -> PTraversal s a -> Boolean") v9.6.0
* [`L.collect(traversal, maybeData) ~> [...values]`](#L-collect "L.collect: PTraversal s a -> Maybe s -> [a]") v3.6.0
* [`L.collectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> [...values]`](#L-collectAs "L.collectAs: ((Maybe a, Index) -> Maybe b) -> PTraversal s a -> Maybe s -> [b]") v7.2.0
* [`L.concat(monoid, traversal, maybeData) ~> value`](#L-concat "L.concat: Monoid a -> (PTraversal s a -> Maybe s -> a)") v7.2.0
* [`L.concatAs((maybeValue, index) => value, monoid, traversal, maybeData) ~> value`](#L-concatAs "L.concatAs: ((Maybe a, Index) -> r) -> Monoid r -> (PTraversal s a -> Maybe s -> r)") v7.2.0
* [`L.count(traversal, maybeData) ~> number`](#L-count "L.count: PTraversal s a -> Number") v9.7.0
* [`L.countIf((maybeValue, index) => testable, traversal, maybeData) ~> number`](#L-countIf "L.countIf: ((Maybe a, Index) -> Boolean) -> PTraversal s a -> Number") v11.2.0
* [`L.counts(traversal, maybeData) ~> map`](#L-counts "L.counts: PTraversal s a -> Map Any Number") v11.21.0
* [`L.countsAs((maybeValue, index) => any, traversal, maybeData) ~> map`](#L-countsAs "L.countsAs: ((Maybe a, Index) -> Any) -> PTraversal s a -> Map Any Number") v11.21.0
* [`L.foldl((value, maybeValue, index) => value, value, traversal, maybeData) ~> value`](#L-foldl "L.foldl: ((r, Maybe a, Index) -> r) -> r -> PTraversal s a -> Maybe s -> r") v7.2.0
* [`L.foldr((value, maybeValue, index) => value, value, traversal, maybeData) ~> value`](#L-foldr "L.foldr: ((r, Maybe a, Index) -> r) -> r -> PTraversal s a -> Maybe s -> r") v7.2.0
* [`L.forEach((maybeValue, index) => undefined, traversal, maybeData) ~> undefined`](#L-forEach "L.forEach: ((Maybe a, Index) -> Undefined) -> PTraversal s a -> Maybe s -> Undefined") v11.20.0
* [`L.isDefined(traversal, maybeData) ~> boolean`](#L-isDefined "L.isDefined: PTraversal s a -> Maybe s -> Boolean") v11.8.0
* [`L.isEmpty(traversal, maybeData) ~> boolean`](#L-isEmpty "L.isEmpty: PTraversal s a -> Maybe s -> Boolean") v11.5.0
* [`L.join(string, traversal, maybeData) ~> string`](#L-join "L.join: String -> PTraversal s a -> Maybe s -> String") v11.2.0
* [`L.joinAs((maybeValue, index) => maybeString, string, traversal, maybeData) ~> string`](#L-joinAs "L.joinAs: ((Maybe a, Index) -> Maybe String) -> String -> PTraversal s a -> Maybe s -> String") v11.2.0
* [`L.maximum(traversal, maybeData) ~> maybeValue`](#L-maximum "L.maximum: Ord a => PTraversal s a -> Maybe s -> Maybe a") v7.2.0
* [`L.maximumBy((maybeValue, index) => maybeKey, traversal, maybeData) ~> maybeValue`](#L-maximumBy "L.maximumBy: Ord k => ((Maybe a, Index) -> Maybe k) -> PTraversal s a -> Maybe s -> Maybe a") v11.2.0
* [`L.mean(traversal, maybeData) ~> number`](#L-mean "L.mean: PTraversal s Number -> Maybe s -> Number") v11.17.0
* [`L.meanAs((maybeValue, index) => maybeNumber, traversal, maybeData) ~> number`](#L-meanAs "L.meanAs: ((Maybe a, Index) -> Maybe Number) -> PTraversal s a -> Maybe s -> Number") v11.17.0
* [`L.minimum(traversal, maybeData) ~> maybeValue`](#L-minimum "L.minimum: Ord a => PTraversal s a -> Maybe s -> Maybe a") v7.2.0
* [`L.minimumBy((maybeValue, index) => maybeKey, traversal, maybeData) ~> maybeValue`](#L-minimumBy "L.minimumBy: Ord k => ((Maybe a, Index) -> Maybe k) -> PTraversal s a -> Maybe s -> Maybe a") v11.2.0
* [`L.none((maybeValue, index) => testable, traversal, maybeData) ~> boolean`](#L-none "L.none: ((Maybe a, Index) -> Boolean) -> PTraversal s a -> Boolean") v11.6.0
* [`L.or(traversal, maybeData) ~> boolean`](#L-or "L.or: PTraversal s Boolean -> Boolean") v9.6.0
* [`L.product(traversal, maybeData) ~> number`](#L-product "L.product: PTraversal s Number -> Maybe s -> Number") v7.2.0
* [`L.productAs((maybeValue, index) => number, traversal, maybeData) ~> number`](#L-productAs "L.productAs: ((Maybe a, Index) -> Number) -> PTraversal s a -> Maybe s -> Number") v11.2.0
* [`L.select(traversal, maybeData) ~> maybeValue`](#L-select "L.select: PTraversal s a -> Maybe s -> Maybe a") v9.8.0
* [`L.selectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> maybeValue`](#L-selectAs "L.selectAs: ((Maybe a, Index) -> Maybe b) -> PTraversal s a -> Maybe s -> Maybe b") v9.8.0
* [`L.sum(traversal, maybeData) ~> number`](#L-sum "L.sum: PTraversal s Number -> Maybe s -> Number") v7.2.0
* [`L.sumAs((maybeValue, index) => number, traversal, maybeData) ~> number`](#L-sumAs "L.sumAs: ((Maybe a, Index) -> Number) -> PTraversal s a -> Maybe s -> Number") v11.2.0
* [Lenses](#lenses)
* [Operations on lenses](#operations-on-lenses)
* [`L.get(lens, maybeData) ~> maybeValue`](#L-get "L.get: PLens s a -> Maybe s -> Maybe a") v2.2.0
* [Creating new lenses](#creating-new-lenses)
* [`L.lens((maybeData, index) => maybeValue, (maybeValue, maybeData, index) => maybeData) ~> lens`](#L-lens "L.lens: ((Maybe s, Index) -> Maybe a) -> ((Maybe a, Maybe s, Index) -> Maybe s) -> PLens s a") v1.0.0
* [`L.setter((maybeValue, maybeData, index) => maybeData) ~> lens`](#L-setter "L.setter: ((Maybe a, Maybe s, Index) -> Maybe s) -> PLens s a") v10.3.0
* [`L.foldTraversalLens((traversal, maybeData) ~> maybeValue, traversal) ~> lens`](#L-foldTraversalLens "L.foldTraversalLens: (PTraversal s a -> Maybe s -> Maybe a) -> PTraversal s a -> PLens s a") v11.5.0
* [Enforcing invariants](#enforcing-invariants)
* [`L.defaults(valueIn) ~> lens`](#L-defaults "L.defaults: s -> PLens s s") v2.0.0
* [`L.define(value) ~> lens`](#L-define "L.define: s -> PLens s s") v1.0.0
* [`L.normalize((value, index) => maybeValue) ~> lens`](#L-normalize "L.normalize: ((s, Index) -> Maybe s) -> PLens s s") v1.0.0
* [`L.required(valueOut) ~> lens`](#L-required "L.required: s -> PLens s s") v1.0.0
* [`L.reread((valueIn, index) => maybeValueIn) ~> lens`](#L-reread "L.reread: ((s, Index) -> Maybe s) -> PLens s s") v11.21.0
* [`L.rewrite((valueOut, index) => maybeValueOut) ~> lens`](#L-rewrite "L.rewrite: ((s, Index) -> Maybe s) -> PLens s s") v5.1.0
* [Lensing array-like objects](#array-like)
* [`L.append ~> lens`](#L-append "L.append: PLens [a] a") v1.0.0
* [`L.filter((maybeValue, index) => testable) ~> lens`](#L-filter "L.filter: ((Maybe a, Index) -> Boolean) -> PLens [a] [a]") v1.0.0
* [`L.find((maybeValue, index, {hint: index}) => testable[, {hint: index}]) ~> lens`](#L-find "L.find: ((Maybe a, Index, {hint: Index}) -> Boolean[, {hint: Index}]) -> PLens [a] a") v1.0.0
* [`L.findWith(optic[, {hint: index}]) ~> optic`](#L-findWith "L.findWith: (POptic s a[, {hint: Index}]) -> POptic [s] a") v1.0.0
* [`L.first ~> lens`](#L-first "L.first: PLens [a] a") v13.1.0
* [`L.index(elemIndex) ~> lens`](#L-index "L.index: Integer -> PLens [a] a") or `elemIndex` v1.0.0
* [`L.last ~> lens`](#L-last "L.last: PLens [a] a") v9.8.0
* [`L.prefix(maybeBegin) ~> lens`](#L-prefix "L.prefix: Maybe Number -> PLens [a] [a]") v11.12.0
* [`L.slice(maybeBegin, maybeEnd) ~> lens`](#L-slice "L.slice: Maybe Number -> Maybe Number -> PLens [a] [a]") v8.1.0
* [`L.suffix(maybeEnd) ~> lens`](#L-suffix "L.suffix: Maybe Number -> PLens [a] [a]") v11.12.0
* [Lensing objects](#lensing-objects)
* [`L.pickIn({prop: lens, ...props}) ~> lens`](#L-pickIn "L.pickIn: {p1: PLens s1 a1, ...pls} -> PLens {p1: s1, ...pls} {p1: a1, ...pls}") v11.11.0
* [`L.prop(propName) ~> lens`](#L-prop "L.prop: (p: a) -> PLens {p: a, ...ps} a") or `propName` v1.0.0
* [`L.props(...propNames) ~> lens`](#L-props "L.props: (p1: a1, ...ps) -> PLens {p1: a1, ...ps, ...o} {p1: a1, ...ps}") v1.4.0
* [`L.propsOf(object) ~> lens`](#L-propsOf "L.propsOf: {p1: a1, ...ps} -> PLens {p1: a1, ...ps, ...o} {p1: a1, ...ps}") v11.13.0
* [`L.removable(...propNames) ~> lens`](#L-removable "L.removable: (p1: a1, ...ps) -> PLens {p1: a1, ...ps, ...o} {p1: a1, ...ps, ...o}") v9.2.0
* [Lensing strings](#lensing-strings)
* [`L.matches(/.../) ~> lens`](#L-matches "L.matches: RegExp -> PLens String String") v10.4.0
* [Providing defaults](#providing-defaults)
* [`L.valueOr(valueOut) ~> lens`](#L-valueOr "L.valueOr: s -> PLens s s") v3.5.0
* [Transforming data](#transforming-data)
* [`L.pick({prop: lens, ...props}) ~> lens`](#L-pick "L.pick: {p1: PLens s a1, ...pls} -> PLens s {p1: a1, ...pls}") v1.2.0
* [`L.replace(maybeValueIn, maybeValueOut) ~> lens`](#L-replace "L.replace: Maybe s -> Maybe s -> PLens s s") v1.0.0
* [Isomorphisms](#isomorphisms)
* [Operations on isomorphisms](#operations-on-isomorphisms)
* [`L.getInverse(isomorphism, maybeData) ~> maybeData`](#L-getInverse "L.getInverse: PIso a b -> Maybe b -> Maybe a") v5.0.0
* [Creating new isomorphisms](#creating-new-isomorphisms)
* [`L.iso(maybeData => maybeValue, maybeValue => maybeData) ~> isomorphism`](#L-iso "L.iso: (Maybe s -> Maybe a) -> (Maybe a -> Maybe s) -> PIso s a") v5.3.0
* [Isomorphism combinators](#isomorphism-combinators)
* [`L.array(isomorphism) ~> isomorphism`](#L-array "L.array: PIso a b -> PIso [a] [b]") v11.19.0
* [`L.inverse(isomorphism) ~> isomorphism`](#L-inverse "L.inverse: PIso a b -> PIso b a") v4.1.0
* [Basic isomorphisms](#basic-isomorphisms)
* [`L.complement ~> isomorphism`](#L-complement "L.complement: PIso Boolean Boolean") v9.7.0
* [`L.identity ~> isomorphism`](#L-identity "L.identity: PIso s s") v1.3.0
* [`L.indexed ~> isomorphism`](#L-indexed "L.indexed: PIso [a] [[Integer, a]]") v11.21.0
* [`L.is(value) ~> isomorphism`](#L-is "L.is: v -> PIso v Boolean") v11.1.0
* [`L.keyed ~> isomorphism`](#L-keyed "L.keyed: PIso {p: a, ...ps} [[String, a]]") v11.21.0
* [`L.reverse ~> isomorphism`](#L-reverse "L.reverse: PIso [a] [a]") v11.22.0
* [`L.singleton ~> isomorphism`](#L-singleton "L.singleton: PIso [a] a") v11.18.0
* [Standard isomorphisms](#standard-isomorphisms)
* [`L.uri ~> isomorphism`](#L-uri "L.uri: PIso String String") v11.3.0
* [`L.uriComponent ~> isomorphism`](#L-uriComponent "L.uriComponent: PIso String String") v11.3.0
* [`L.json({reviver, replacer, space}) ~> isomorphism`](#L-json "L.json: {reviver, replacer, space} -> PIso String JSON") v11.3.0
* [Interop](#interop)
* [`L.pointer(jsonPointer) ~> lens`](#L-pointer "L.pointer: JSONPointer s a -> PLens s a") v11.21.0
* [Auxiliary](#auxiliary)
* [`L.seemsArrayLike(anything) ~> boolean`](#L-seemsArrayLike "L.seemsArrayLike: any -> Boolean") v11.4.0
* [Examples](#examples)
* [An array of ids as boolean flags](#an-array-of-ids-as-boolean-flags)
* [Dependent fields](#dependent-fields)
* [Collection toggle](#collection-toggle)
* [BST as a lens](#bst-as-a-lens)
* [BST traversal](#bst-traversal)
* [Interfacing with Immutable.js](#interfacing)
* [`List` indexing](#list-indexing)
* [Interfacing traversals](#interfacing-traversals)
* [Deepening topics](#deepening-topics)
* [Understanding `L.filter`, `L.find`, `L.select`, and `L.when`](#understanding-filter-find-select-and-when)
* [Advanced topics](#advanced-topics)
* [Performance tips](#performance-tips)
* [Nesting traversals does not create intermediate aggregates](#nesting-traversals-does-not-create-intermediate-aggregates)
* [Avoid reallocating optics in `L.choose`](#avoid-reallocating-optics-in-l-choose)
* [On bundle size and minification](#on-bundle-size-and-minification)
* [Background](#background)
* [Motivation](#motivation)
* [Design choices](#design-choices)
* [Partiality](#partiality)
* [Focus on JSON](#focus-on-json)
* [Use of `undefined`](#use-of-undefined)
* [Allowing strings and integers as optics](#allowing-strings-and-integers-as-optics)
* [Treating an array of optics as a composition of optics](#treating-an-array-of-optics-as-a-composition-of-optics)
* [Applicatives](#applicatives)
* [Combinators for creating new optics](#combinators-for-creating-new-optics)
* [Indexing](#indexing)
* [Static Land](#static-land)
* [Performance](#performance)
* [Benchmarks](#benchmarks)
* [Lenses all the way](#lenses-all-the-way)
* [Related work](#related-work)
* [Papers and other introductory material](#papers-and-other-introductory-material)
* [JavaScript / TypeScript / Flow libraries](#javascript-typescript-flow-libraries)
* [Libraries for other languages](#libraries-for-other-languages)
* [Contributing](#contributing)
* [Building](#building)
* [Testing](#testing)
* [Documentation](#documentation)
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#tutorial) Tutorial
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:
```js
const sampleTitles = {titles: [{language: 'en', text: 'Title'},
{language: 'sv', text: 'Rubrik'}]}
```
We ultimately want to present the user with a rich enough editor, with features
such as undo-redo and validation, for manipulating the content represented by
those JSON objects. The `titles` property is really just one tiny part of the
data model, but, in this tutorial, we only look at it, because it is sufficient
for introducing most of the basic ideas.
So, what we'd like to have is a way to access the `text` of titles in a given
language. Given a language, we want to be able to
* get the corresponding text,
* update the corresponding text,
* insert a new text and the immediately surrounding object in a new language, and
* remove an existing text and the immediately surrounding object.
Furthermore, when updating, inserting, and removing texts, we'd like the
operations to treat the JSON as [immutable](#on-immutability) 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](https://en.wikipedia.org/wiki/Domain-specific_language)
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`](#L-get) and [`set`](#L-set), on the element that the
lens focuses on.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#getting-started) Getting started
Let's first import the libraries
```jsx
import * as L from 'partial.lenses'
import * as R from 'ramda'
```
and [▶ play](https://calmm-js.github.io/partial.lenses/#getting-started) just a
bit with lenses.
> Note that links with the [▶
> play](https://calmm-js.github.io/partial.lenses/#getting-started) 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](https://calmm-js.github.io/partial.lenses/playground.html)
> 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)`](#L-prop), to access a named property of an object, and
[`L.index(elemIndex)`](#L-index), to access an element at a given index in an
array, and compose the path using [`L.compose(...lenses)`](#L-compose).
So, to just [get](#L-get) at the `titles` array of the `sampleTitles` we can use
the lens [`L.prop('titles')`](#L-prop):
```js
L.get(L.prop('titles'),
sampleTitles)
// [{ language: 'en', text: 'Title' },
// { language: 'sv', text: 'Rubrik' }]
```
To focus on the first element of the `titles` array, we compose with
the [`L.index(0)`](#L-index) lens:
```js
L.get(L.compose(L.prop('titles'),
L.index(0)),
sampleTitles)
// { language: 'en', text: 'Title' }
```
Then, to focus on the `text`, we compose with [`L.prop('text')`](#L-prop):
```js
L.get(L.compose(L.prop('titles'),
L.index(0),
L.prop('text')),
sampleTitles)
// 'Title'
```
We can then use the same composed lens to also [set](#L-set) the `text`:
```js
L.set(L.compose(L.prop('titles'),
L.index(0),
L.prop('text')),
'New title',
sampleTitles)
// { titles: [{ language: 'en', text: 'New title' },
// { language: 'sv', text: 'Rubrik' }] }
```
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](#L-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.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#a-partial-lens-to-access-titles) A partial lens to access title texts
Let's then just [compose](#L-compose) a parameterized lens for accessing the
`text` of titles:
```js
const textIn = language => L.compose(L.prop('titles'),
L.normalize(R.sortBy(L.get('language'))),
L.find(R.whereEq({language})),
L.valueOr({language, text: ''}),
L.removable('text'),
L.prop('text'))
```
Take a moment to read through the above definition line by line. Each part
either specifies a step in the path to select the desired element or a way in
which the data structure must be treated at that point. The
[`L.prop(...)`](#L-prop) parts are already familiar. The other parts we will
mention below.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#querying-data) Querying data
Thanks to the parameterized search part,
[`L.find(R.whereEq({language}))`](#L-find), of the lens composition, we can use
it to query titles:
```js
L.get(textIn('sv'), sampleTitles)
// 'Rubrik'
```
The [`L.find`](#L-find) lens is a 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`](http://ramdajs.com/docs/#whereEq) function
that creates an equality predicate from a given template object.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#missing-data-can-be-expected) Missing data can be expected
Partial lenses can generally deal with missing data. In this case, when
[`L.find`](#L-find) doesn't find an element, it instead works like a lens to
[append](#L-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:
```js
L.get(textIn('fi'), sampleTitles)
// ''
```
We get this value, rather than `undefined`, thanks to the [`L.valueOr({language,
text: ''})`](#L-valueOr) 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`:
```js
L.get(textIn('fi'), undefined)
// ''
```
With partial lenses, `undefined` is the equivalent of non-existent.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#updating-data) Updating data
As with ordinary lenses, we can use the same lens to update titles:
```js
L.set(textIn('en'), 'The title', sampleTitles)
// { titles: [ { language: 'en', text: 'The title' },
// { language: 'sv', text: 'Rubrik' } ] }
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#inserting-data) Inserting data
The same partial lens also allows us to insert new titles:
```js
L.set(textIn('fi'), 'Otsikko', sampleTitles)
// { titles: [ { language: 'en', text: 'Title' },
// { language: 'fi', text: 'Otsikko' },
// { language: 'sv', text: 'Rubrik' } ] }
```
There are 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:
''})`](#L-valueOr) 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')))`](#L-normalize) part of our lens.
The [`L.normalize`](#L-normalize) lens transforms the data when either read or
written with the given function. In this case we used Ramda's
[`R.sortBy`](http://ramdajs.com/docs/#sortBy) to specify that we want the titles
to be kept sorted by language.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#removing-data) Removing data
Finally, we can use the same partial lens to remove titles:
```js
L.set(textIn('sv'), undefined, sampleTitles)
// { titles: [ { language: 'en', text: 'Title' } ] }
```
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')`](#L-removable) 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:
```js
L.set(L.seq(textIn('sv'),
textIn('en')),
undefined,
sampleTitles)
// { titles: [] }
```
Above we use [`L.seq`](#L-seq) to run the [`L.set`](#L-set) operation over both
of the focused titles.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#exercises) Exercises
Take out one (or more) [`L.normalize(...)`](#L-normalize),
[`L.valueOr(...)`](#L-valueOr) or [`L.removable(...)`](#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.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#shorthands) Shorthands
For clarity, the previous code snippets avoided some of the shorthands that this
library supports. In particular,
* [`L.compose(...)`](#L-compose) can be abbreviated as an array
[`[...]`](#L-compose),
* [`L.prop(propName)`](#L-prop) can be abbreviated as [`propName`](#L-prop), and
* [`L.set(l, undefined, s)`](#L-set) can be abbreviated as [`L.remove(l,
s)`](#L-remove).
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#systematic-decomposition) 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:
```jsx
L.compose(L.prop('titles'),
L.normalize(R.sortBy(L.get('language'))),
L.find(R.whereEq({language})),
L.valueOr({language, text: ''}),
L.removable('text'),
L.prop('text'))
```
Following the structure or schema of the JSON, we could break this into three
separate lenses:
* a lens for accessing the titles of a model object,
* a parameterized lens for querying a title object from titles, and
* a lens for accessing the text of a title object.
Furthermore, we could organize the lenses to reflect the structure of the JSON
model:
```js
const Title = {
text: [L.removable('text'), 'text']
}
const Titles = {
titleIn: language => [L.find(R.whereEq({language})),
L.valueOr({language, text: ''})]
}
const Model = {
titles: ['titles',
L.normalize(R.sortBy(L.get('language')))],
textIn: language => [Model.titles,
Titles.titleIn(language),
Title.text]
}
```
We can now say:
```js
L.get(Model.textIn('sv'), sampleTitles)
// 'Rubrik'
```
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.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#manipulating-multiple-items) Manipulating multiple items
So far we have used a lens to manipulate individual items. This library also
supports [traversals](#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:
```js
const texts = [Model.titles,
L.elems,
Title.text]
```
What makes the above a traversal is the [`L.elems`](#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`](#L-collect) all the texts:
```js
L.collect(texts, sampleTitles)
// [ 'Title', 'Rubrik' ]
```
More generally, we can [map and fold](#L-concatAs) over texts. For example, we
could use [`L.maximumBy`](#L-maximumBy) to find a title with the maximum length:
```js
L.maximumBy(R.length, texts, sampleTitles)
// 'Rubrik'
```
Of course, we can also modify texts. For example, we could uppercase all the
titles:
```js
L.modify(texts, R.toUpper, sampleTitles)
// { titles: [ { language: 'en', text: 'TITLE' },
// { language: 'sv', text: 'RUBRIK' } ] }
```
We can also manipulate texts selectively. For example, we could remove all
the texts that are longer than 5 characters:
```js
L.remove([texts, L.when(t => t.length > 5)],
sampleTitles)
// { titles: [ { language: 'en', text: 'Title' } ] }
```
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#next-steps) Next steps
This concludes the tutorial. The reference documentation contains lots of tiny
examples and a few [more involved examples](#L-lazy). The [examples](#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](#bst-as-a-lens). The
[wiki](https://github.com/calmm-js/partial.lenses/wiki) contains further
examples and playground links. Last, but perhaps not least, there is also a
page of [Partial Lenses
Exercises](https://calmm-js.github.io/partial.lenses/exercises.html) to solve.
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#the-why-of-optics) 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](#tutorial) problem without
optics. One could, for example, write a collection of operations like
`getText`, `setText`, `addText`, and `remText`:
```js
const getEntry = R.curry((language, data) =>
data.titles.find(R.whereEq({language})))
const hasText = R.pipe(getEntry, Boolean)
const getText = R.pipe(getEntry, R.defaultTo({}), R.prop('text'))
const mapProp = R.curry((fn, prop, obj) =>
R.assoc(prop, fn(R.prop(prop, obj)), obj))
const mapText = R.curry((language, fn, data) =>
mapProp(R.map(R.ifElse(R.whereEq({language}),
mapProp(fn, 'text'),
R.identity)),
'titles',
data))
const remText = R.curry((language, data) =>
mapProp(R.filter(R.complement(R.whereEq({language}))),
'titles'))
const addText = R.curry((language, text, data) =>
mapProp(R.append({language, text}), 'titles', data))
const 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](#tutorial) and due to the separation of concerns
that tends to give you a lot of robust functionality in [a small amount of
code](#a-partial-lens-to-access-titles).
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#reference) Reference
The [combinators](https://wiki.haskell.org/Combinator) provided by this library
are available as named imports. Typically one just imports the library as:
```jsx
import * as L from 'partial.lenses'
```
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#stable-subset) 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:
* [`L.compose(...optics) ~> optic`](#L-compose) is stable with the exception
that one must not depend on being able to compose optics with ordinary
functions. Also, the use of arrays to denote composition is not part of the
stable subset. Note that [`L.compose()`](#L-compose) is guaranteed to be
equivalent to the [`L.identity`](#L-identity) optic.
* [`L.get(lens, maybeData) ~> maybeValue`](#L-get) is stable without
limitations.
* [`L.lens(maybeData => maybeValue, (maybeValue, maybeData) => maybeData) ~>
lens`](#L-lens) is stable with the exception that one must not depend on the
user specified getter and setter functions being passed more than 1 and 2
arguments, respectively, and one must make no assumptions about any extra
parameters being passed.
* [`L.modify(optic, maybeValue => maybeValue, maybeData) ~>
maybeData`](#L-modify) is stable with the exception that one must not depend
on the user specified function being passed more than 1 argument and one must
make no assumptions about any extra parameters being passed.
* [`L.remove(optic, maybeData) ~> maybeData`](#L-remove) is stable without
limitations.
* [`L.set(optic, maybeValue, maybeData) ~> maybeData`](#L-set) is stable without
limitations.
The main intention behind the stable subset is to enable a dependent library to
make basic use of lenses created by client code using the dependent library.
In retrospect, the stable subset has existed since version 2.2.0.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#additional-libraries) 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](https://github.com/polytypic/infestines) library,
which is mainly used for the currying helpers it provides, are not provided.
Currently the following additional Partial Lenses libraries exist:
* [Partial Lenses Validation](https://github.com/calmm-js/partial.lenses.validation)
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#optics) Optics
The abstractions, [traversals](#traversals), [lenses](#lenses), and
[isomorphisms](#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](#L-inverse).
In addition to basic bidirectional optics, this library also supports more
arbitrary [transforms](#transforms) using optics with [sequencing](#L-seq) and
[transform ops](#transforming). 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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#on-partiality) On partiality
By [definition](https://en.wikipedia.org/wiki/Partial_function), 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`](#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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#on-indexing) On indexing
Optics in this library support a simple unnested form of indexing. When
focusing on an array element or a 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:
```js
L.get([L.find(R.equals('bar')), (value, index) => ({value, index})],
['foo', 'bar', 'baz'])
// {value: 'bar', index: 1}
```
```js
L.modify(L.values, (value, key) => ({key, value}), {x: 1, y: 2})
// {x: {key: 'x', value: 1}, y: {key: 'y', value: 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 focus. For example, [`L.when`](#L-when)
doesn't have an index by itself, but it passes through the index provided by the
preceding optic:
```js
L.collectAs((value, index) => ({value, index}),
[L.elems, L.when(x => x > 2)],
[3, 1, 4, 1])
// [{value: 3, index: 0}, {value: 4, index: 2}]
```
```js
L.collectAs((value, key) => ({value, key}),
[L.values, L.when(x => x > 2)],
{x: 3, y: 1, z: 4, w: 1})
// [{value: 3, key: 'x'}, {value: 4, key: 'z'}]
```
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 define
combinators to construct paths. The reason for not collecting paths by default
is that doing so would be relatively expensive due to additional allocations.
The [`L.choose`](#L-choose) combinator can be useful in cases where there is a
need to access some index or context along the path to a focus.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#on-immutability) On immutability
Starting with version [10.0.0](./CHANGELOG.md#1000), to strongly guide away from
mutating data structures, optics call
[`Object.freeze`](https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#on-composability) On composability
A lot of libraries these days claim to be
[composable](https://en.wikipedia.org/wiki/Composability). 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:
| | Operation(s) | Semantics
| ------------------------- | ----------------------------------------------------------------------------------- | -----------------------------------------------------------------------------------------
| [Nesting](#nesting) | [`L.compose(...optics)`](#L-compose) or `[...optics]` | [Monoid](https://en.wikipedia.org/wiki/Monoid) over [unityped](http://cs.stackexchange.com/questions/18847/if-dynamically-typed-languages-are-truly-statically-typed-unityped-languages-w) [optics](#optics)
| [Recursing](#recursing) | [`L.lazy(optic => optic)`](#L-lazy) | [Fixed point](https://en.wikipedia.org/wiki/Fixed-point_combinator)
| [Adapting](#adapting) | [`L.choices(optic, ...optics)`](#L-choices) | [Semigroup](https://en.wikipedia.org/wiki/Semigroup) over [optics](#optics)
| [Querying](#querying) | [`L.choice(...optics)`](#L-choice) and [`L.chain(value => optic, optic)`](#L-chain) | [MonadPlus](https://en.wikibooks.org/wiki/Haskell/Alternative_and_MonadPlus) over [optics](#optics)
| Picking | [`L.pick({...prop:lens})`](#L-pick) | Product of [lenses](#lenses)
| Branching | [`L.branch({...prop:traversal})`](#L-branch) | [Coproduct](https://en.wikipedia.org/wiki/Coproduct) of [traversals](#traversals)
| [Sequencing](#sequencing) | [`L.seq(...transforms)`](#L-seq) | Monad over [transforms](#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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#on-lens-laws) 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](http://sebfisch.github.io/research/pub/Fischer+MPC15.pdf), 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*:
```js
function test(actual, expected) {
return R.equals(actual, expected) || {actual, expected}
}
const 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'
})
// { GetSet: true, SetGet: true, SetSet: true }
```
You might want to [▶
play](https://calmm-js.github.io/partial.lenses/#on-lens-laws) 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.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#myth-partial-lenses-are-not-lawful) Myth: Partial Lenses are not lawful
For some reason there seems to be a persistent myth that partial lenses cannot
obey [lens laws](http://sebfisch.github.io/research/pub/Fischer+MPC15.pdf). 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`](#L-find) combinator. The truth is that it doesn't by
itself obey lens laws. Here is an example:
```js
L.get(L.find(R.equals(1)),
L.set(L.find(R.equals(1)), 2, []))
// undefined
```
As you can see, [`L.find(R.equals(1))`](#L-find) does not obey the `SetGet` aka
`Put-Get` law. Does this make the [`L.find`](#L-find) combinator useless? Far
from it.
Consider the following lens:
```js
const 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:
```js
const sampleAssoc = [{key: 'x', val: 42}, {key: 'y', val: 24}]
L.set(valOf('x'), 101, [])
// [{key: 'x', val: 101}]
```
```js
L.get(valOf('x'), sampleAssoc)
// 42
```
```js
L.get(valOf('z'), sampleAssoc)
// undefined
```
```js
L.set(valOf('x'), undefined, sampleAssoc)
// [{key: 'y', val: 24}]
```
```js
L.set(valOf('x'), 13, sampleAssoc)
// [{key: 'x', val: 13}, {key: 'y', val: 24}]
```
It obeys lens laws:
```js
VeryWellBehavedLens({
elemA: 2,
elemB: 3,
data: [{key: 'x', val: 13}],
lens: valOf('x')
})
```
Before you try to break it, note that a lens returned by `valOf(key)` is only
supposed to work on valid association arrays. A valid association array must
not contain duplicate keys, `undefined` is not valid `val`, and the order of
elements is not significant. (Note that you could also add
[`L.rewrite(R.sortBy(L.get('key')))`](#L-rewrite) 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`](#L-find)
results in a lawful partial lens is that the lenses composed after it restrict
the scope of the lens so that one cannot modify the `key`.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#operations-on-optics) Operations on optics
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-assign) [`L.assign(optic, object, maybeData) ~> maybeData`](#L-assign "L.assign: PLens s {p1: a1, ...ps, ...o} -> {p1: a1, ...ps} -> Maybe s -> Maybe s") 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:
```js
L.assign(L.elems, {y: 1}, [{x: 3, y: 2}, {x: 4}])
// [ { x: 3, y: 1 }, { x: 4, y: 1 } ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-modify) [`L.modify(optic, (maybeValue, index) => maybeValue, maybeData) ~> maybeData`](#L-modify "L.modify: POptic s a -> ((Maybe a, Index) -> Maybe a) -> Maybe s -> Maybe s") v2.2.0
`L.modify` allows one to map over the elements focused on by the given optic.
For example:
```js
L.modify(['elems', 0, 'x'], R.inc, {elems: [{x: 1, y: 2}, {x: 3, y: 4}]})
// { elems: [ { x: 2, y: 2 }, { x: 3, y: 4 } ] }
```
```js
L.modify(['elems', L.elems, 'x'],
R.dec,
{elems: [{x: 1, y: 2}, {x: 3, y: 4}]})
// { elems: [ { x: 0, y: 2 }, { x: 2, y: 4 } ] }
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-remove) [`L.remove(optic, maybeData) ~> maybeData`](#L-remove "L.remove: POptic s a -> Maybe s -> Maybe s") v2.0.0
`L.remove` allows one to remove the elements focused on by the given optic.
For example:
```js
L.remove([0, L.defaults({}), 'x'], [{x: 1}, {x: 2}, {x: 3}])
// [ { x: 2 }, { x: 3 } ]
```
```js
L.remove([L.elems, 'x', L.when(x => x > 1)], [{x: 1}, {x: 2, y: 1}, {x: 3}])
// [ { x: 1 }, { y: 1 }, {} ]
```
Note that `L.remove(optic, maybeData)` is equivalent to [`L.set(lens, undefined,
maybeData)`](#L-set). With partial lenses, setting to `undefined` typically has
the effect of removing the focused element.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-set) [`L.set(optic, maybeValue, maybeData) ~> maybeData`](#L-set "L.set: POptic s a -> Maybe a -> Maybe s -> Maybe s") v1.0.0
`L.set` allows one to replace the elements focused on by the given optic with
the specified value.
For example:
```js
L.set(['a', 0, 'x'], 11, {id: 'z'})
// {a: [{x: 11}], id: 'z'}
```
```js
L.set([L.elems, 'x', L.when(x => x > 1)], -1, [{x: 1}, {x: 2, y: 1}, {x: 3}])
// [ { x: 1 }, { x: -1, y: 1 }, { x: -1 } ]
```
Note that `L.set(lens, maybeValue, maybeData)` is equivalent to [`L.modify(lens,
R.always(maybeValue), maybeData)`](#L-modify).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-traverse) [`L.traverse(algebra, (maybeValue, index) => operation, optic, maybeData) ~> operation`](#L-traverse "L.traverse: (Functor|Applicative|Monad) c -> ((Maybe a, Index) -> c b) -> POptic s t a b -> Maybe s -> c t") 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`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#algebra)
argument must be either a
[`Functor`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#functor),
[`Applicative`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#applicative),
or
[`Monad`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#monad)
depending on the optic as specified in [`L.toFunction`](#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:
```js
const 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
}
const count = x => x2n => {
const k = `${x}`
const n = (x2n[k] || 0) + 1
return {result: n, state: L.set(k, n, x2n)}
}
State.run({}, L.traverse(State, count, L.elems, [1, 2, 1, 1, 2, 3, 4, 3, 4, 5]))
// [1, 1, 2, 3, 2, 1, 1, 2, 2, 1]
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#nesting) Nesting
The [`L.compose`](#L-compose) combinator allows one to build optics that deal
with nested data structures.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-compose) [`L.compose(...optics) ~> optic`](#L-compose "L.compose: (POptic s s1, ...POptic sN a) -> POptic s a") 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.
The following equations characterize composition:
```jsx
L.compose() = L.identity
L.compose(l) = l
L.modify(L.compose(o, ...os)) = R.compose(L.modify(o), ...os.map(L.modify))
L.get(L.compose(o, ...os)) = R.pipe(L.get(o), ...os.map(L.get))
```
Furthermore, in this library, an array of optics `[...optics]` is treated as a
composition `L.compose(...optics)`. Using the array notation, the above
equations can be written as:
```jsx
[] = L.identity
[l] = l
L.modify([o, ...os]) = R.compose(L.modify(o), ...os.map(L.modify))
L.get([o, ...os]) = R.pipe(L.get(o), ...os.map(L.get))
```
For example:
```js
L.set(['a', 1], 'a', {a: ['b', 'c']})
// { a: [ 'b', 'a' ] }
```
```js
L.get(['a', 1], {a: ['b', 'c']})
// 'c'
```
You can also directly compose optics with ordinary functions. The result of
such a composition is a read-only optic.
For example:
```js
L.get(['x', x => x + 1], {x: 1})
// 2
```
```js
L.set(['x', x => x + 1], 3, {x: 1})
// { 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](./CHANGELOG.md#1100) 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`](http://ramdajs.com/docs/#compose) is not the same as
`L.compose`.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#recursing) Recursing
The [`L.lazy`](#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](#transforms) with loops.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-lazy) [`L.lazy(optic => optic) ~> optic`](#L-lazy "L.lazy: (POptic s a -> POptic s a) -> POptic s a") 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](#L-compose)
or [presequenced](#L-seq) 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:
```js
const primitives = [
L.optional,
L.lazy(rec => L.cond([R.is(Array), [L.elems, rec]],
[R.is(Object), [L.values, rec]],
[ L.identity]))]
```
Note that the above creates a cyclic representation of the traversal.
Now, for example:
```js
L.collect(primitives, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
// [ 1, 2, 3, 4, 5, 6 ]
```
```js
L.modify(primitives, x => x+1, [[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
// [ [ [ 2 ], 3 ], { y: 4 }, [ { l: 5, r: [ 6 ] }, { x: 7 } ] ]
```
```js
L.remove([primitives, L.when(x => 3 <= x && x <= 4)],
[[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
// [ [ [ 1 ], 2 ], {}, [ { r: [ 5 ] }, { x: 6 } ] ]
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#adaptning) Adapting
Adapting combinators allow one to build optics that adapt to their input.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-choices) [`L.choices(optic, ...optics) ~> optic`](#L-choices "L.choices: (POptic s a, ...POptic s a) -> POptic s a") 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.choice`](#L-choice).
For example:
```js
L.set([L.elems, L.choices('a', 'd')], 3, [{R: 1}, {a: 1}, {d: 2}])
// [ { R: 1, d: 3 }, { a: 3 }, { d: 3 } ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-choose) [`L.choose((maybeValue, index) => optic) ~> optic`](#L-choose "L.choose: ((Maybe s, Index) -> POptic s a) -> POptic s a") 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`](#L-cond).
For example:
```js
const majorAxis =
L.choose(({x, y} = {}) => Math.abs(x) < Math.abs(y) ? 'y' : 'x')
L.get(majorAxis, {x: -3, y: 1})
// -3
```
```js
L.modify(majorAxis, R.negate, {x: -3, y: 1})
// { x: 3, y: 1 }
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-cond) [`L.cond(...[(maybeValue, index) => testable, consequentOptic][, [alternativeOptic]]) ~> optic`](#L-cond "L.cond: (...[(Maybe s, Index) -> Boolean, PLens s a][, [PLens s a]]) -> PLens s a") 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.choose`](#L-choose) and
[`L.ifElse`](#L-ifElse).
```jsx
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 a
`[alternative]` singleton, where the *alternative* is an optic to be used in
case none of the predicates return true. If all predicates return false and
there is no alternative, `L.cond` acts like [`L.zero`](#L-zero).
For example:
```js
const minorAxis =
L.cond([({x, y} = {}) => Math.abs(y) < Math.abs(x), 'y'], ['x'])
L.get(minorAxis, {x: -3, y: 1})
// 1
```
```js
L.modify(minorAxis, R.negate, {x: -3, y: 1})
// { x: -3, y: -1 }
```
Note that it is better to omit the predicate from the alternative
```jsx
L.cond(..., [alternative])
```
than to use a catch all predicate like [`R.T`](http://ramdajs.com/docs/#T)
```jsx
L.cond(..., [R.T, alternative])
```
because in the latter case `L.cond` cannot determinate that a user defined
predicate will always be true and has to construct a more expensive optic.
Note that `L.cond` can be implemented using [`L.choose`](#L-choose), but not
vice versa. [`L.choose`](#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.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-ifElse) [`L.ifElse((maybeValue, index) => testable, optic, optic) ~> optic`](#L-ifElse "L.ifElse: ((Maybe s, Index) -> Boolean) -> POptic s a -> POptic s a -> POptic s a") v13.1.0
`L.ifElse` creates an optic whose operation is selected based on the given
predicate from the two given optics. If the predicates 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`](#L-cond).
For example:
```js
L.modify(L.ifElse(Array.isArray, L.elems, L.values), R.inc, [1, 2, 3])
// [ 2, 3, 4 ]
```
```js
L.modify(L.ifElse(Array.isArray, L.elems, L.values), R.inc, {x: 1, y: 2, z: 3})
// {x: 2, y: 3, z: 4}
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-iftes) ~~[`L.iftes((maybeValue, index) => testable, consequentOptic, ...[, alternativeOptic]) ~> optic`](#L-iftes "L.iftes: ((Maybe s, Index) -> Boolean) -> PLens s a -> PLens s a -> PLens s a") v11.14.0~~
**WARNING: `L.iftes` has been obsoleted. Use [`L.ifElse`](#L-ifElse) or
[`L.cond`](#L-cond) instead. See [CHANGELOG](./CHANGELOG.md#1310) for
details.**
`L.iftes` creates an optic whose operation is selected from the given optics and
predicates on the underlying view.
```jsx
L.iftes( predicate, consequent
[ , ... ]
[ , alternative ] )
```
`L.iftes` is not curried unlike most functions in this library. `L.iftes`
requires at least two arguments and successive arguments form *predicate* -
*consequent* pairs. The predicates are functions on the underlying view and are
tested sequentially. The consequents are optics and `L.iftes` acts like the
consequent corresponding to the first predicate that returns true. If `L.iftes`
is given an odd number of arguments, the last argument is the *alternative*
taken in case none of the predicates returns true. If all predicates return
false and there is no alternative, `L.iftes` acts like [`L.zero`](#L-zero).
For example:
```js
const minorAxis =
L.iftes(({x, y} = {}) => Math.abs(y) < Math.abs(x), 'y', 'x')
L.get(minorAxis, {x: -3, y: 1})
// 1
```
```js
L.modify(minorAxis, R.negate, {x: -3, y: 1})
// { x: -3, y: -1 }
```
Note that `L.iftes` can be implemented using [`L.choose`](#L-choose).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-orElse) [`L.orElse(backupOptic, primaryOptic) ~> optic`](#L-orElse "L.orElse: (POptic s a, POptic s a) -> POptic s a") v2.1.0
`L.orElse(backupOptic, primaryOptic)` acts like `primaryOptic` when its view is
not `undefined` and otherwise like `backupOptic`.
Note that [`L.choice(...optics)`](#L-choice) is equivalent to
`optics.reduceRight(L.orElse, L.zero)` and [`L.choices(...optics)`](#L-choices)
is equivalent to `optics.reduce(L.orElse)`.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#querying) Querying
Querying combinators allow one to use optics to query data structures. Querying
is distinguished from [adapting](#adapting) in that querying defaults to an
empty or read-only [zero](#L-zero).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-chain) [`L.chain((value, index) => optic, optic) ~> optic`](#L-chain "L.chain: ((a, Index) -> POptic s b) -> POptic s a -> POptic s b") v3.1.0
`L.chain` provides a monadic
[chain](https://github.com/rpominov/static-land/blob/master/docs/spec.md#chain)
combinator for querying with optics. `L.chain(toOptic, optic)` is equivalent to
```jsx
L.compose(optic, L.choose((maybeValue, index) =>
maybeValue === undefined
? L.zero
: toOptic(maybeValue, index)))
```
Note that with the [`R.always`](http://ramdajs.com/docs/#always), `L.chain`,
[`L.choice`](#L-choice) and [`L.zero`](#L-zero) combinators, one can consider
optics as subsuming the maybe monad.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-choice) [`L.choice(...optics) ~> optic`](#L-choice "L.choice: (...POptic s a) -> POptic s a") 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
[`L.zero`](#L-zero), which is the identity element of `L.choice`. See also
[`L.choices`](#L-choices).
For example:
```js
L.modify([L.elems, L.choice('a', 'd')], R.inc, [{R: 1}, {a: 1}, {d: 2}])
// [ { R: 1 }, { a: 2 }, { d: 3 } ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-optional) [`L.optional ~> optic`](#L-optional "L.optional: POptic a a") 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:
```js
L.set([L.elems, 'x'], 3, [{x: 1}, {y: 2}])
// [ { x: 3 }, { y: 2, x: 3 } ]
```
and:
```js
L.set([L.elems, 'x', L.optional], 3, [{x: 1}, {y: 2}])
// [ { x: 3 }, { y: 2 } ]
```
Note that `L.optional` is equivalent to [`L.when(x => x !==
undefined)`](#L-when).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-unless) [`L.unless((maybeValue, index) => testable) ~> optic`](#L-unless "L.unless: ((Maybe a, Index) -> Boolean) -> POptic a a") v12.1.0
`L.unless` allows one to selectively skip elements within a traversal or to
selectively turn a lens into a read-only lens whose view is `undefined`. See
also [`L.when`](#L-when).
For example:
```js
L.modify([L.elems, L.unless(x => x < 0)], R.negate, [0, -1, 2, -3, 4])
// [ -0, -1, -2, -3, -4 ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-when) [`L.when((maybeValue, index) => testable) ~> optic`](#L-when "L.when: ((Maybe a, Index) -> Boolean) -> POptic a a") v5.2.0
`L.when` allows one to selectively skip elements within a traversal or to
selectively turn a lens into a read-only lens whose view is `undefined`. See
also [`L.unless`](#L-unless).
For example:
```js
L.modify([L.elems, L.when(x => x > 0)], R.negate, [0, -1, 2, -3, 4])
// [ 0, -1, -2, -3, -4 ]
```
Note that `L.when(p)` is equivalent to [`L.choose((x, i) => p(x, i) ?
L.identity : L.zero)`](#L-choose).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-zero) [`L.zero ~> optic`](#L-zero "L.zero: POptic s a") v6.0.0
`L.zero` is the identity element of [`L.choice`](#L-choice) and
[`L.chain`](#L-chain). As a traversal, `L.zero` is a traversal of no elements
and as a lens, i.e. when used with [`L.get`](#L-get), `L.zero` is a read-only
lens whose view is always `undefined`.
For example:
```js
L.collect([L.elems,
L.cond([R.is(Array), L.elems],
[R.is(Object), 'x'],
[L.zero])],
[1, {x: 2}, [3, 4]])
// [ 2, 3, 4 ]
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#debugging) Debugging
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-log) [`L.log(...labels) ~> optic`](#L-log "L.log: (...Any) -> POptic s s") v3.2.0
`L.log(...labels)` is an identity optic that outputs
[`console.log`](https://developer.mozilla.org/en-US/docs/Web/API/Console/log)
messages with the given labels (or [format in
Node.js](https://nodejs.org/api/console.html#console_console_log_data)) when
data flows in either direction, `get` or `set`, through the lens.
For example:
```js
L.set(['x', L.log('x')], '11', {x: 10})
// x get 10
// x set 11
// { x: '11' }
```
```js
L.set(['x', L.log('%s x: %j')], '11', {x: 10})
// get x: 10
// set x: '11'
// { x: '11' }
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#internals) Internals
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-toFunction) [`L.toFunction(optic) ~> optic`](#L-toFunction "L.toFunction: POptic s t a b -> (Maybe s, Index, (Functor|Applicative|Monad) c, (Maybe a, Index) -> c b) -> c t") v7.0.0
`L.toFunction` converts a given optic, which can be a [string](#L-prop), an
[integer](#L-index), an [array](#L-compose), or a function to a 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`](#L-traverse).
For [isomorphisms](#isomorphisms) and [lenses](#lenses), the returned function
will have the signature
```jsx
(Maybe s, Index, Functor c, (Maybe a, Index) -> c b) -> c t
```
for [traversals](#traversals) the signature will be
```jsx
(Maybe s, Index, Applicative c, (Maybe a, Index) -> c b) -> c t
```
and for [transforms](#transforms) the signature will be
```jsx
(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`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#functor),
[`Applicative`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#applicative),
and
[`Monad`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#monad)
arguments are expected to conform to their [Static
Land](https://github.com/rpominov/static-land/blob/master/docs/spec.md)
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`](#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`](#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.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#transforms) Transforms
Ordinary [optics](#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](#L-modifyOp) data structures. Such operations are called *transforms*
in this library.
Unlike ordinary optics, transforms allow for monadic [sequencing](#L-seq), 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](#lenses) have a single focus and [traversals](#traversals)
have multiple focuses that can then be operated upon using various operations
such as [`L.modify`](#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](#transforming), that act as traversals of no
elements, can, and perhaps preferably should, be [empty](#L-isEmpty) and should
be executed using [`L.transform`](#L-transform), which, unlike
[`L.modify`](#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](#transforming)
within an ordinary optic definition. Furthermore, it is also possible to use
[sequencing](#L-seq) 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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#operations-on-transforms) Operations on transforms
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-transform) [`L.transform(optic, maybeData) ~> maybeData`](#L-transform "L.transform: POptic s a -> Maybe s -> Maybe s") v11.7.0
`L.transform(o, s)` is shorthand for [`L.modify(o, x => x, s)`](#L-modify) and
is intended for running [transforms](#transforms) defined using [transform
ops](#transforming).
Note that
* [`L.assign(o, x, s)`](#L-assign) is equivalent to [`L.transform([o,
L.assignOp(x)], s)`](#L-assignOp),
* [`L.modify(o, f, s)`](#L-modify) is equivalent to [`L.transform([o,
L.modifyOp(f)], s)`](#L-modifyOp),
* [`L.set(o, x, s)`](#L-set) is equivalent to [`L.transform([o, L.setOp(x)],
s)`](#L-setOp), and
* [`L.remove(o, s)`](#L-remove) is equivalent to [`L.transform([o, L.removeOp],
s)`](#L-removeOp).
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#sequencing) Sequencing
The [`L.seq`](#L-seq) combinator allows one to build [transforms](#transforms)
that modify their focus more than once.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-seq) [`L.seq(...transforms) ~> transform`](#L-seq "L.seq: (...PTransform s a) -> PTransform s a") 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:
```js
const everywhere = [
L.optional,
L.lazy(rec => L.cond([R.is(Array), L.seq([L.elems, rec], L.identity)],
[R.is(Object), L.seq([L.values, rec], L.identity)],
[ L.identity]))]
```
The above `everywhere` transform is similar to the
[`F.everywhere`](https://github.com/polytypic/fastener#F-everywhere) transform
of the [`fastener`](https://github.com/polytypic/fastener) zipper-library. Note
that the above `everywhere` and the [`primitives`](#L-lazy) example differ in
that `primitives` only targets the non-object and non-array elements of the data
structure while `everywhere` also targets those.
```js
L.modify(everywhere, x => [x], {xs: [{x: 1}, {x: 2}]})
// [ {xs: [ [ [ { x: [ 1 ] } ], [ { x: [ 2 ] } ] ] ] } ]
```
Note that `L.seq`, [`L.choose`](#L-choose), and [`L.setOp`](#L-setOp) can be
combined together as a
[`Monad`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#monad)
```jsx
chain(x2t, t) = L.seq(t, L.choose(x2t))
of(x) = L.setOp(x)
```
which is not the same as the [querying monad](#L-chain).
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#transforming) Transforming
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-assignOp) [`L.assignOp(object) ~> optic`](#L-assignOp "L.assignOp: {p1: a1, ...ps} -> POptic {p1: a1, ...ps, ...o} {p1: a1, ...ps}") v11.13.0
`L.assignOp` creates an optic that merges the given object into the object in
focus.
For example:
```js
L.transform([L.elems, L.assignOp({y: 1})], [{x: 3}, {x: 4, y: 5}])
// [ { x: 3, y: 1 }, { x: 4, y: 1 } ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-modifyOp) [`L.modifyOp((maybeValue, index) => maybeValue) ~> optic`](#L-modifyOp "L.modifyOp: ((Maybe a, Index) -> Maybe a) -> POptic a a") v11.7.0
`L.modifyOp` creates an optic that maps the focus with the given function. When
used as a traversal, `L.modifyOp` acts as a traversal of no elements. When used
as a lens, `L.modifyOp` acts as a read-only lens whose view is the mapped focus.
Usually, however, `L.modifyOp` is used within [transforms](#transforms).
For example:
```js
L.transform(L.branch({xs: [L.elems, L.modifyOp(R.inc)],
z: [L.optional, L.modifyOp(R.negate)],
ys: [L.elems, L.modifyOp(R.dec)]}),
{xs: [1, 2, 3],
ys: [1, 2, 3]})
// { xs: [ 2, 3, 4 ],
// ys: [ 0, 1, 2 ] }
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-removeOp) [`L.removeOp ~> optic`](#L-removeOp "L.removeOp: POptic a a") v11.7.0
`L.removeOp` is shorthand for [`L.setOp(undefined)`](#L-setOp).
Here is an example based on a question from a user:
```js
const sampleToFilter = {elements: [{time: 1, subelements: [1, 2, 3, 4]},
{time: 2, subelements: [1, 2, 3, 4]},
{time: 3, subelements: [1, 2, 3, 4]}]}
L.transform(['elements',
L.elems,
L.seq([L.when(elem => elem.time < 2), L.removeOp],
['subelements', L.elems, L.when(i => i < 3), L.removeOp])],
sampleToFilter)
// { elements: [ { time: 2, subelements: [ 3, 4 ] },
// { time: 3, subelements: [ 3, 4 ] } ] }
```
The idea is to filter the data both by `time` and by `subelements`.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-setOp) [`L.setOp(maybeValue) ~> optic`](#L-setOp "L.setOp: Maybe a -> POptic a a") v11.7.0
`L.setOp(x)` is shorthand for [`L.modifyOp(R.always(x))`](#L-modifyOp).
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#traversals) Traversals
A traversal operates over a collection of non-overlapping focuses that are
visited only once and can, for example, be [collected](#L-collect),
[folded](#L-concatAs), [modified](#L-modify), [set](#L-set) and
[removed](#L-remove). Put in another way, a traversal specifies a set of paths
to elements in a data structure.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#creating-new-traversals) Creating new traversals
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-branch) [`L.branch({prop: traversal, ...props}) ~> traversal`](#L-branch "L.branch: {p1: PTraversal s a, ...pts} -> PTraversal s a") 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:
```js
L.collect(L.branch({first: L.elems, second: {value: L.identity}}),
{first: ['x'], second: {value: 'y'}})
// [ 'x', 'y' ]
```
The use of [`L.identity`](#L-identity) above might be puzzling at first.
[`L.identity`](#L-identity) essentially specifies an empty path. So, when a
property is mapped to [`L.identity`](#L-identity) in the template given to
`L.branch`, it means that the element is to be visited by the resulting
traversal.
Note that you can also compose `L.branch` with other optics. For example, you
can compose with [`L.pick`](#L-pick) to create a traversal over specific
elements of an array:
```js
L.modify([L.pick({z: 2, x: 0}),
L.branch({x: L.identity, z: L.identity})],
R.negate,
[1, 2, 3])
// [ -1, 2, -3 ]
```
See the [BST traversal](#bst-traversal) section for a more meaningful example.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#traversals-and-combinators) Traversals and combinators
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-elems) [`L.elems ~> traversal`](#L-elems "L.elems: PTraversal [a] a") v7.3.0
`L.elems` is a traversal over the elements of an [array-like](#array-like)
object. When written through, `L.elems` always produces an `Array`.
For example:
```js
L.modify(['xs', L.elems, 'x'], R.inc, {xs: [{x: 1}, {x: 2}]})
// { xs: [ { x: 2 }, { x: 3 } ] }
```
Just like with other optics operating on [array-like](#array-like) objects, when
manipulating non-`Array` objects, [`L.rewrite`](#L-rewrite) can be used to
convert the result to the desired type, if necessary:
```js
L.modify([L.rewrite(xs => Int8Array.from(xs)), L.elems],
R.inc,
Int8Array.from([-1, 4, 0, 2, 4]))
// Int8Array [ 0, 5, 1, 3, 5 ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-entries) [`L.entries ~> traversal`](#L-entries "L.entries: PTraversal {p: a, ...ps} [String, a]") v11.21.0
`L.entries` is a traversal over the entries, or `[key, value]` pairs, of an
object.
For example:
```js
L.modify(L.entries, ([k, v]) => [v, k], {x: 'a', y: 'b'})
// { a: 'x', b: 'y' }
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-flatten) [`L.flatten ~> traversal`](#L-flatten "L.flatten: PTraversal [...[a]...] a") v11.16.0
`L.flatten` is a traversal over the elements of arbitrarily nested arrays.
Other [array-like](#array-like) objects are treated as elements by `L.flatten`.
In case the immediate target of `L.flatten` is not an array, it is traversed.
For example:
```js
L.join(' ', L.flatten, [[[1]], ['2'], 3])
// '1 2 3'
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-keys) [`L.keys ~> traversal`](#L-keys "L.keys: PTraversal {p: a, ...ps} String") v11.21.0
`L.keys` is a traversal over the keys of an object.
For example:
```js
L.modify(L.keys, R.toUpper, {x: 1, y: 2})
// { X: 1, Y: 2 }
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-matches-g) [`L.matches(/.../g) ~> traversal`](#L-matches-g "L.matches: RegExp -> PTraversal String String") v10.4.0
`L.matches`, when given a regular expression with the
[`global`](https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/RegExp/global)
flag, `/.../g`, is a partial traversal over the matches that the regular
expression gives over the focused string. See also [`L.matches`](#L-matches).
For example:
```js
L.collect([L.matches(/[^&=?]+=[^&=]+/g),
L.pick({name: L.matches(/^[^=]+/),
value: L.matches(/[^=]+$/)})],
'?first=foo&second=bar')
// [ { name: 'first', value: 'foo' },
// { name: 'second', value: 'bar' } ]
```
Note that an empty match terminates the traversal. It is possible to make use
of that feature, but it is also possible that an empty match is due to an
incorrect regular expression that can match the empty string.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-values) [`L.values ~> traversal`](#L-values "L.values: PTraversal {p: a, ...ps} a") v7.3.0
`L.values` is a traversal over the values of an `instanceof Object`. When
written through, `L.values` always produces an `Object`.
For example:
```js
L.modify(L.values, R.negate, {a: 1, b: 2, c: 3})
// { a: -1, b: -2, c: -3 }
```
When manipulating objects with a non-`Object` constructor
```js
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`](#L-rewrite) can be used to convert the result to the desired type,
if necessary:
```js
const 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))
// XYZ { x: -1, y: -2, z: -3 }
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#folds-over-traversals) Folds over traversals
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-all) [`L.all((maybeValue, index) => testable, traversal, maybeData) ~> boolean`](#L-all "L.all: ((Maybe a, Index) -> Boolean) -> PTraversal s a -> Boolean") v9.6.0
`L.all` determines whether all of the elements focused on by the given traversal
satisfy the given predicate.
For example:
```js
L.all(x => 1 <= x && x <= 6,
primitives,
[[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
// true
```
See also: [`L.any`](#L-any), [`L.none`](#L-none), and
[`L.selectAs`](#L-selectAs).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-and) [`L.and(traversal, maybeData) ~> boolean`](#L-and "L.and: PTraversal s Boolean -> Boolean") v9.6.0
`L.and` determines whether all of the elements focused on by the given traversal
are truthy.
For example:
```js
L.and(L.elems, [])
// true
```
Note that `L.and` is equivalent to [`L.all(x => x)`](#L-all). See also:
[`L.or`](#L-or).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-any) [`L.any((maybeValue, index) => testable, traversal, maybeData) ~> boolean`](#L-any "L.any: ((Maybe a, Index) -> Boolean) -> PTraversal s a -> Boolean") v9.6.0
`L.any` determines whether any of the elements focused on by the given traversal
satisfy the given predicate.
For example:
```js
L.any(x => x > 5,
primitives,
[[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
// true
```
See also: [`L.all`](#L-all), [`L.none`](#L-none), and
[`L.selectAs`](#L-selectAs).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-collect) [`L.collect(traversal, maybeData) ~> [...values]`](#L-collect "L.collect: PTraversal s a -> Maybe s -> [a]") 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.
For example:
```js
L.collect(['xs', L.elems, 'x'], {xs: [{x: 1}, {x: 2}]})
// [ 1, 2 ]
```
Note that `L.collect` is equivalent to [`L.collectAs(x => x)`](#L-collectAs).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-collectAs) [`L.collectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> [...values]`](#L-collectAs "L.collectAs: ((Maybe a, Index) -> Maybe b) -> PTraversal s a -> Maybe s -> [b]") v7.2.0
`L.collectAs` returns an array of the elements focused on by the given traversal
or lens from a data structure and mapped by the given function to a
non-`undefined` value.
For example:
```js
L.collectAs(R.negate, ['xs', L.elems, 'x'], {xs: [{x: 1}, {x: 2}]})
// [ -1, -2 ]
```
`L.collectAs(toMaybe, traversal, maybeData)` is equivalent to
[`L.concatAs(toCollect, Collect, [traversal, toMaybe], maybeData)`](#L-concatAs)
where `Collect` and `toCollect` are defined as follows:
```js
const Collect = {empty: R.always([]), concat: R.concat}
const toCollect = x => x !== undefined ? [x] : []
```
So:
```js
L.concatAs(toCollect,
Collect,
['xs', L.elems, 'x', R.negate],
{xs: [{x: 1}, {x: 2}]})
// [ -1, -2 ]
```
The internal implementation of `L.collectAs` is optimized and faster than the
above naïve implementation.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-concat) [`L.concat(monoid, traversal, maybeData) ~> value`](#L-concat "L.concat: Monoid a -> (PTraversal s a -> Maybe s -> a)") 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](https://github.com/rpominov/static-land/blob/master/docs/spec.md#monoid)
over the values focused on by `t`.
For example:
```js
const Sum = {empty: () => 0, concat: (x, y) => x + y}
L.concat(Sum, L.elems, [1, 2, 3])
// 6
```
Note that `L.concat` is staged so that after given the first argument,
`L.concat(m)`, a computation step is performed.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-concatAs) [`L.concatAs((maybeValue, index) => value, monoid, traversal, maybeData) ~> value`](#L-concatAs "L.concatAs: ((Maybe a, Index) -> r) -> Monoid r -> (PTraversal s a -> Maybe s -> r)") 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](https://github.com/rpominov/static-land/blob/master/docs/spec.md#monoid)
over the values returned by `xMi2r`.
For example:
```js
L.concatAs(x => x, Sum, L.elems, [1, 2, 3])
// 6
```
Note that `L.concatAs` is staged so that after given the first two arguments,
`L.concatAs(f, m)`, a computation step is performed.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-count) [`L.count(traversal, maybeData) ~> number`](#L-count "L.count: PTraversal s a -> 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:
```js
L.count([L.elems, 'x'], [{x: 11}, {y: 12}])
// 1
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-countIf) [`L.countIf((maybeValue, index) => testable, traversal, maybeData) ~> number`](#L-countIf "L.countIf: ((Maybe a, Index) -> Boolean) -> PTraversal s a -> 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:
```js
L.countIf(L.isDefined('x'), L.elems, [{x: 11}, {y: 12}])
// 1
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-counts) [`L.counts(traversal, maybeData) ~> map`](#L-counts "L.counts: PTraversal s a -> Map Any Number") v11.21.0
`L.counts` returns a
[map](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Map)
of the counts of distinct values, including `undefined`, focused on by the given
traversal.
For example:
```js
Array.from(L.counts(L.elems, [3, 1, 4, 1]).entries())
// [[3, 1], [1, 2], [4, 1]]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-countsAs) [`L.countsAs((maybeValue, index) => any, traversal, maybeData) ~> map`](#L-countsAs "L.countsAs: ((Maybe a, Index) -> Any) -> PTraversal s a -> Map Any Number") v11.21.0
`L.countsAs` returns a
[map](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/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:
```js
Array.from(L.countsAs(Math.abs, L.elems, [3, -1, 4, 1]).entries())
// [[3, 1], [1, 2], [4, 1]]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-foldl) [`L.foldl((value, maybeValue, index) => value, value, traversal, maybeData) ~> value`](#L-foldl "L.foldl: ((r, Maybe a, Index) -> r) -> r -> PTraversal s a -> Maybe s -> r") v7.2.0
`L.foldl` performs a fold from left over the elements focused on by the given
traversal.
For example:
```js
L.foldl((x, y) => x + y, 0, L.elems, [1, 2, 3])
// 6
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-foldr) [`L.foldr((value, maybeValue, index) => value, value, traversal, maybeData) ~> value`](#L-foldr "L.foldr: ((r, Maybe a, Index) -> r) -> r -> PTraversal s a -> Maybe s -> r") v7.2.0
`L.foldr` performs a fold from right over the elements focused on by the given
traversal.
For example:
```js
L.foldr((x, y) => x * y, 1, L.elems, [1, 2, 3])
// 6
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-forEach) [`L.forEach((maybeValue, index) => undefined, traversal, maybeData) ~> undefined`](#L-forEach "L.forEach: ((Maybe a, Index) -> Undefined) -> PTraversal s a -> Maybe s -> Undefined") v11.20.0
`L.forEach` calls the given function for each focus of the traversal.
For example:
```js
L.forEach(console.log, [L.elems, 'x', L.elems], [{x: [3]}, {x: [1, 4]}, {x: [1]}])
// 3 0
// 1 0
// 4 1
// 1 0
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-isDefined) [`L.isDefined(traversal, maybeData) ~> boolean`](#L-isDefined "L.isDefined: PTraversal s a -> Maybe s -> 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`](#L-isEmpty).
For example:
```js
L.isDefined('x', {y: 1})
// false
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-isEmpty) [`L.isEmpty(traversal, maybeData) ~> boolean`](#L-isEmpty "L.isEmpty: PTraversal s a -> Maybe s -> 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`](#L-isDefined).
For example:
```js
L.isEmpty(L.flatten, [[], [[[], []], []]])
// true
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-join) [`L.join(string, traversal, maybeData) ~> string`](#L-join "L.join: String -> PTraversal s a -> Maybe s -> 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:
```js
L.join(', ', [L.elems, 'x'], [{x: 1}, {y: 2}, {x: 3}])
// '1, 3'
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-joinAs) [`L.joinAs((maybeValue, index) => maybeString, string, traversal, maybeData) ~> string`](#L-joinAs "L.joinAs: ((Maybe a, Index) -> Maybe String) -> String -> PTraversal s a -> Maybe s -> 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:
```js
L.joinAs(JSON.stringify, ', ', L.elems, [{x: 1}, {y: 2}])
// '{'x':1}, {'y':2}'
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-maximum) [`L.maximum(traversal, maybeData) ~> maybeValue`](#L-maximum "L.maximum: Ord a => PTraversal s a -> Maybe s -> Maybe a") v7.2.0
`L.maximum` computes a maximum of the optional elements targeted by the
traversal.
For example:
```js
L.maximum(L.elems, [1, 2, 3])
// 3
```
Note that elements are ordered according to the `>` operator.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-maximumBy) [`L.maximumBy((maybeValue, index) => maybeKey, traversal, maybeData) ~> maybeValue`](#L-maximumBy "L.maximumBy: Ord k => ((Maybe a, Index) -> Maybe k) -> PTraversal s a -> Maybe s -> Maybe a") 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:
```js
L.maximumBy(R.length, L.elems, ['first', 'second', '--||--', 'third'])
// 'second'
```
Note that keys are ordered according to the `>` operator.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-mean) [`L.mean(traversal, maybeData) ~> number`](#L-mean "L.mean: PTraversal s Number -> Maybe s -> Number") v11.17.0
`L.mean` computes the arithmetic mean of the optional numbers targeted by the
traversal.
For example:
```js
L.mean([L.elems, 'x'], [{x: 1}, {ignored: 3}, {x: 2}])
// 1.5
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-meanAs) [`L.meanAs((maybeValue, index) => maybeNumber, traversal, maybeData) ~> number`](#L-meanAs "L.meanAs: ((Maybe a, Index) -> Maybe Number) -> PTraversal s a -> Maybe s -> 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:
```js
L.meanAs((x, i) => x <= i ? undefined : x, L.elems, [3, 1, 4, 1])
// 3.5
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-minimum) [`L.minimum(traversal, maybeData) ~> maybeValue`](#L-minimum "L.minimum: Ord a => PTraversal s a -> Maybe s -> Maybe a") v7.2.0
`L.minimum` computes a minimum of the optional elements targeted by the
traversal.
For example:
```js
L.minimum(L.elems, [1, 2, 3])
// 1
```
Note that elements are ordered according to the `<` operator.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-minimumBy) [`L.minimumBy((maybeValue, index) => maybeKey, traversal, maybeData) ~> maybeValue`](#L-minimumBy "L.minimumBy: Ord k => ((Maybe a, Index) -> Maybe k) -> PTraversal s a -> Maybe s -> Maybe a") 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:
```js
L.minimumBy(L.get('x'), L.elems, [{x: 1}, {x: -3}, {x: 2}])
// {x: -3}
```
Note that keys are ordered according to the `<` operator.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-none) [`L.none((maybeValue, index) => testable, traversal, maybeData) ~> boolean`](#L-none "L.none: ((Maybe a, Index) -> Boolean) -> PTraversal s a -> Boolean") v11.6.0
`L.none` determines whether none of the elements focused on by the given
traversal satisfy the given predicate.
For example:
```js
L.none(x => x > 5,
primitives,
[[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
// false
```
See also: [`L.all`](#L-all), [`L.any`](#L-any), and [`L.selectAs`](#L-selectAs).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-or) [`L.or(traversal, maybeData) ~> boolean`](#L-or "L.or: PTraversal s Boolean -> Boolean") v9.6.0
`L.or` determines whether any of the elements focused on by the given traversal
is truthy.
For example:
```js
L.or(L.elems, [])
// false
```
Note that `L.or` is equivalent to [`L.any(x => x)`](#L-any). See also:
[`L.and`](#L-and).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-product) [`L.product(traversal, maybeData) ~> number`](#L-product "L.product: PTraversal s Number -> Maybe s -> Number") v7.2.0
`L.product` computes the product of the optional numbers targeted by the
traversal.
For example:
```js
L.product(L.elems, [1, 2, 3])
// 6
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-productAs) [`L.productAs((maybeValue, index) => number, traversal, maybeData) ~> number`](#L-productAs "L.productAs: ((Maybe a, Index) -> Number) -> PTraversal s a -> Maybe s -> 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:
```js
L.productAs((x, i) => x + i, L.elems, [3, 2, 1])
// 27
```
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`.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-select) [`L.select(traversal, maybeData) ~> maybeValue`](#L-select "L.select: PTraversal s a -> Maybe s -> Maybe a") v9.8.0
`L.select` goes lazily over the elements focused on by the given traversal and
returns the first non-`undefined` element.
```js
L.select([L.elems, 'y'], [{x:1}, {y:2}, {z:3}])
// 2
```
Note that `L.select` is equivalent to [`L.selectAs(x => x)`](#L-selectAs).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-selectAs) [`L.selectAs((maybeValue, index) => maybeValue, traversal, maybeData) ~> maybeValue`](#L-selectAs "L.selectAs: ((Maybe a, Index) -> Maybe b) -> PTraversal s a -> Maybe s -> Maybe b") v9.8.0
`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.
```js
L.selectAs(x => x > 3 ? -x : undefined, L.elems, [3, 1, 4, 1, 5])
// -4
```
`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:
```js
const all = (p, t, s) => !L.selectAs(x => p(x) ? undefined : true, t, s)
```
Now:
```js
all(x => x < 9,
primitives,
[[[1], 2], {y: 3}, [{l: 4, r: [5]}, {x: 6}]])
// true
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-sum) [`L.sum(traversal, maybeData) ~> number`](#L-sum "L.sum: PTraversal s Number -> Maybe s -> Number") v7.2.0
`L.sum` computes the sum of the optional numbers targeted by the traversal.
For example:
```js
L.sum(L.elems, [1, 2, 3])
// 6
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-sumAs) [`L.sumAs((maybeValue, index) => number, traversal, maybeData) ~> number`](#L-sumAs "L.sumAs: ((Maybe a, Index) -> Number) -> PTraversal s a -> Maybe s -> 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:
```js
L.sumAs((x, i) => x + i, L.elems, [3, 2, 1])
// 9
```
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`.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#lenses) Lenses
Lenses always have a single focus which can be [viewed](#L-get) directly. Put
in another way, a lens specifies a path to a single element in a data structure.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#operations-on-lenses) Operations on lenses
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-get) [`L.get(lens, maybeData) ~> maybeValue`](#L-get "L.get: PLens s a -> Maybe s -> Maybe a") v2.2.0
`L.get` returns the element focused on by a [lens](#lenses) from a data
structure.
For example:
```js
L.get('y', {x: 112, y: 101})
// 101
```
Note that `L.get` does not work on [traversals](#traversals).
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#creating-new-lenses) Creating new lenses
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-lens) [`L.lens((maybeData, index) => maybeValue, (maybeValue, maybeData, index) => maybeData) ~> lens`](#L-lens "L.lens: ((Maybe s, Index) -> Maybe a) -> ((Maybe a, Maybe s, Index) -> Maybe s) -> PLens s a") 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](http://momentjs.com/), to bidirectionally
convert a pair of `start` and `end` times to a duration:
```js
const timesAsDuration = L.lens(
({start, end} = {}) => {
if (undefined === start)
return undefined
if (undefined === end)
return 'Infinity'
return moment.duration(moment(end).diff(moment(start))).toJSON()
},
(duration, {start = moment().toJSON()} = {}) => {
if (undefined === duration || 'Infinity' === duration) {
return {start}
} else {
return {
start,
end: moment(start).add(moment.duration(duration)).toJSON()
}
}
}
)
```
Now, for example:
```js
L.get(timesAsDuration,
{start: '2016-12-07T09:39:02.451Z',
end: moment('2016-12-07T09:39:02.451Z').add(10, 'hours').toISOString()})
// 'PT10H'
```
```js
L.set(timesAsDuration,
'PT10H',
{start: '2016-12-07T09:39:02.451Z',
end: '2016-12-07T09:39:02.451Z'})
// { end: '2016-12-07T19:39:02.451Z',
// start: '2016-12-07T09:39:02.451Z' }
```
When composed with [`L.pick`](#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](http://momentjs.com/).
See the [Interfacing with Immutable.js](#interfacing) section for another
example of using `L.lens`.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-setter) [`L.setter((maybeValue, maybeData, index) => maybeData) ~> lens`](#L-setter "L.setter: ((Maybe a, Maybe s, Index) -> Maybe s) -> PLens s a") v10.3.0
`L.setter(set)` is shorthand for [`L.lens(x => x, set)`](#L-lens).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-foldTraversalLens) [`L.foldTraversalLens((traversal, maybeData) ~> maybeValue, traversal) ~> lens`](#L-foldTraversalLens "L.foldTraversalLens: (PTraversal s a -> Maybe s -> Maybe a) -> PTraversal s a -> PLens s a") 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.
For example:
```js
L.get(L.foldTraversalLens(L.minimum, L.elems), [3, 1, 4])
// 1
```
```js
L.set(L.foldTraversalLens(L.minimum, L.elems), 2, [3, 1, 4])
// [ 2, 2, 2 ]
```
See the [Collection toggle](#collection-toggle) section for a more interesting
example.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#enforcing-invariants) Enforcing invariants
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-defaults) [`L.defaults(valueIn) ~> lens`](#L-defaults "L.defaults: s -> PLens s s") 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.
For example:
```js
L.get(['items', L.defaults([])], {})
// []
```
```js
L.get(['items', L.defaults([])], {items: [1, 2, 3]})
// [ 1, 2, 3 ]
```
```js
L.set(['items', L.defaults([])], [], {items: [1, 2, 3]})
// {}
```
Note that `L.defaults(valueIn)` is equivalent to [`L.replace(undefined,
valueIn)`](#L-replace).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-define) [`L.define(value) ~> lens`](#L-define "L.define: s -> PLens s s") 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.
```js
L.get(['x', L.define(null)], {y: 10})
// null
```
```js
L.set(['x', L.define(null)], undefined, {y: 10})
// { y: 10, x: null }
```
Note that `L.define(value)` is equivalent to `[L.required(value),
L.defaults(value)]`.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-normalize) [`L.normalize((value, index) => maybeValue) ~> lens`](#L-normalize "L.normalize: ((s, Index) -> Maybe s) -> PLens s s") 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)`](#L-reread) and [`L.rewrite(fn)`](#L-rewrite).
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`](http://ramdajs.com/docs/#equals) comparison will do.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-required) [`L.required(valueOut) ~> lens`](#L-required "L.required: s -> PLens s s") 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:
```js
L.remove(['item'], {item: 1})
// {}
```
```js
L.remove(['item', L.required(null)], {item: 1})
// { item: null }
```
Note that `L.required(valueOut)` is equivalent to [`L.replace(valueOut,
undefined)`](#L-replace).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-reread) [`L.reread((valueIn, index) => maybeValueIn) ~> lens`](#L-reread "L.reread: ((s, Index) -> Maybe s) -> PLens s s") v11.21.0
`L.reread` maps the value with the given transform on read and implicitly maps
`undefined` to `undefined`. See also [`L.normalize`](#L-normalize).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-rewrite) [`L.rewrite((valueOut, index) => maybeValueOut) ~> lens`](#L-rewrite "L.rewrite: ((s, Index) -> Maybe s) -> PLens s s") v5.1.0
`L.rewrite` maps the value with the given transform when written and implicitly
maps `undefined` to `undefined`. See also [`L.normalize`](#L-normalize).
One use case for `rewrite` is to re-establish data structure invariants after
changes.
See the [BST as a lens](#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`](#L-seemsArrayLike).
When writing through a lens or traversal that operates on array-like objects,
the result is always a plain `Array`. For example:
```js
L.set(1, 'a', 'LoLa')
// [ 'L', 'a', 'L', 'a' ]
```
It may seem like the result should be of the same type as the object being
manipulated, but that is problematic, because
* the focus of a *partial* optic is always optional, so there might not be
an original array-like object whose type to use, and
* manipulation of the elements can change their types, so they may no longer be
compatible with the type of the original array-like object.
Therefore, instead, when manipulating strings or array-like non-`Array` objects,
[`L.rewrite`](#L-rewrite) can be used to explicitly convert the result to the
desired type, if necessary. For example:
```js
L.set([L.rewrite(R.join('')), 1], 'a', 'LoLa')
// 'LaLa'
```
Also, when manipulating array-like objects, partial lenses generally ignore
everything but the `length` property and the integer properties from `0` to
`length-1`.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-append) [`L.append ~> lens`](#L-append "L.append: PLens [a] a") v1.0.0
`L.append` is a write-only lens that can be used to append values to an
[array-like](#array-like) object. The view of `L.append` is always `undefined`.
For example:
```js
L.get(L.append, ['x'])
// undefined
```
```js
L.set(L.append, 'x', undefined)
// [ 'x' ]
```
```js
L.set(L.append, 'x', ['z', 'y'])
// [ 'z', 'y', 'x' ]
```
Note that `L.append` is equivalent to [`L.index(i)`](#L-index) with the index
`i` set to the length of the focused array or 0 in case the focus is not a
defined array.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-filter) [`L.filter((maybeValue, index) => testable) ~> lens`](#L-filter "L.filter: ((Maybe a, Index) -> Boolean) -> PLens [a] [a]") v1.0.0
`L.filter` operates on [array-like](#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:
```js
L.set(L.filter(x => x <= '2'), 'abcd', '3141592')
// [ 'a', 'b', 'c', 'd', '3', '4', '5', '9' ]
```
**NOTE**: If you are merely modifying a data structure, and don't need to limit
yourself to lenses, consider using the [`L.elems`](#L-elems) traversal composed
with [`L.when`](#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](https://en.wikipedia.org/wiki/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`](#L-normalize) or [`L.rewrite`](#L-rewrite) would be preferable.
Also, the [`L.elems`](#L-elems) traversal composed with [`L.when`](#L-when) will
retain order of elements.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-find) [`L.find((maybeValue, index, {hint: index}) => testable[, {hint: index}]) ~> lens`](#L-find "L.find: ((Maybe a, Index, {hint: Index}) -> Boolean[, {hint: Index}]) -> PLens [a] a") v1.0.0
`L.find` operates on [array-like](#array-like) objects like
[`L.index`](#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-append).
```js
L.remove(L.find(x => x <= 2), [3, 1, 4, 1, 5, 9, 2])
// [ 3, 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:
```js
L.modify([L.find(R.whereEq({id: 2}), {hint: 2}), 'value'],
R.toUpper,
[{id: 3, value: 'a'},
{id: 2, value: 'b'},
{id: 1, value: 'c'},
{id: 4, value: 'd'},
{id: 5, value: 'e'}])
// [{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](#myth-partial-lenses-are-not-lawful) for discussion and an example.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-findWith) [`L.findWith(optic[, {hint: index}]) ~> optic`](#L-findWith "L.findWith: (POptic s a[, {hint: Index}]) -> POptic [s] a") v1.0.0
`L.findWith` chooses an index from an [array-like](#array-like) object through
which the given optic has a non-`undefined` view and then returns an optic that
focuses on that.
For example:
```js
L.get(L.findWith('x'), [{z: 6}, {x: 9}, {y: 6}])
// 9
```
```js
L.set(L.findWith('x'), 3, [{z: 6}, {x: 9}, {y: 6}])
// [ { z: 6 }, { x: 3 }, { y: 6 } ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-first) [`L.first ~> lens`](#L-first "L.first: PLens [a] a") v13.1.0
`L.first` is a synonym for [`L.index(0)`](#L-index) or [`0`](#L-index) and
focuses on the first element of an [array-like](#array-like) object or works
like [`L.append`](#L-append) in case no such element exists. See also
[`L.last`](#L-last).
For example:
```js
L.get(L.first, ['a', 'b'])
// 'a'
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-index) [`L.index(elemIndex) ~> lens`](#L-index "L.index: Integer -> PLens [a] a") or `elemIndex` v1.0.0
`L.index(elemIndex)` or just `elemIndex` focuses on the element at specified
index of an [array-like](#array-like) object.
* When not viewing an index with a defined element, the result is `undefined`.
* When setting to `undefined`, the element is removed from the resulting array,
shifting all higher indices down by one.
* When setting a defined value to an index that is higher than the length of the
array-like object, the missing elements will be filled with `undefined`.
For example:
```js
L.set(2, 'z', ['x', 'y', 'c'])
// [ 'x', 'y', 'z' ]
```
```js
L.remove(0, ['x'])
// [ ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-last) [`L.last ~> lens`](#L-last "L.last: PLens [a] a") v9.8.0
`L.last` focuses on the last element of an [array-like](#array-like) object or
works like [`L.append`](#L-append) in case no such element exists. See also
[`L.first`](#L-first).
Focusing on an empty array or `undefined` results in returning `undefined`. For
example:
```js
L.get(L.last, [1, 2, 3])
// 3
```
```js
L.get(L.last, [])
// undefined
```
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:
```js
L.set(L.last, 5, [1, 2, 3])
// [1, 2, 5]
```
```js
L.set(L.last, 1, [])
// [1]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-prefix) [`L.prefix(maybeBegin) ~> lens`](#L-prefix "L.prefix: Maybe Number -> PLens [a] [a]") v11.12.0
`L.prefix` focuses on a range of elements of an [array-like](#array-like) object
starting from the beginning of the object. `L.prefix` is a special case of
[`L.slice`](#L-slice).
The end of the range is determined as follows:
- non-negative values are relative to the beginning of the array-like object,
- `Infinity` is the end of the array-like object,
- negative values are relative to the end of the array-like object,
- `-Infinity` is the beginning of the array-like object, and
- `undefined` is the end of the array-like object.
For example:
```js
L.set(L.prefix(0), [1], [2, 3])
// [ 1, 2, 3 ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-slice) [`L.slice(maybeBegin, maybeEnd) ~> lens`](#L-slice "L.slice: Maybe Number -> Maybe Number -> PLens [a] [a]") v8.1.0
`L.slice` focuses on a specified range of elements of an
[array-like](#array-like) object. See also [`L.prefix`](#L-prefix) and
[`L.suffix`](#L-suffix).
The range is determined like with the standard
[`slice`](https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/Array/slice)
method of arrays:
- non-negative values are relative to the beginning of the array-like object,
- `Infinity` is the end of the array-like object,
- negative values are relative to the end of the array-like object,
- `-Infinity` is the beginning of the array-like object, and
- `undefined` gives the defaults: 0 for the begin and length for the end.
For example:
```js
L.get(L.slice(1, -1), [1, 2, 3, 4])
// [ 2, 3 ]
```
```js
L.set(L.slice(-2, undefined), [0], [1, 2, 3, 4])
// [ 1, 2, 0 ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-suffix) [`L.suffix(maybeEnd) ~> lens`](#L-prefix "L.prefix: Maybe Number -> PLens [a] [a]") v11.12.0
`L.suffix` focuses on a range of elements of an [array-like](#array-like) object
starting from the end of the object. `L.suffix` is a special case of
[`L.slice`](#L-slice).
The beginning of the range is determined as follows:
- non-negative values are relative to the end of the array-like object,
- `Infinity` is the beginning of the array-like object,
- negative values are relative to the beginning of the array-like object,
- `-Infinity` is the end of the array-like object, and
- `undefined` is the beginning of the array-like object.
Note that the rules above are different from the rules for determining the
beginning of [`L.slice`](#L-slice).
For example:
```js
L.set(L.suffix(1), [4, 1], [3, 1, 3])
// [ 3, 1, 4, 1 ]
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#lensing-objects) 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:
```js
function Custom(gold, silver, bronze) {
this.gold = gold
this.silver = silver
this.bronze = bronze
}
L.set('silver', -2, new Custom(1, 2, 3))
// { gold: 1, silver: -2, bronze: 3 }
```
When manipulating objects whose constructor is not `Object`,
[`L.rewrite`](#L-rewrite) can be used to convert the result to the desired type,
if necessary:
```js
L.set([L.rewrite(objectTo(Custom)), 'silver'], -2, new Custom(1, 2, 3))
// Custom { gold: 1, silver: -2, bronze: 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:
```js
for (const k in L.set('silver', -2, new Custom(1, 2, 3)))
console.log(k)
// gold
// silver
// bronze
```
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.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-pickIn) [`L.pickIn({prop: lens, ...props}) ~> lens`](#L-pickIn "L.pickIn: {p1: PLens s1 a1, ...pls} -> PLens {p1: s1, ...pls} {p1: a1, ...pls}") v11.11.0
`L.pickIn` creates a lens from the given possibly nested object template of
lenses similar to [`L.pick`](#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`](#L-props).
For example:
```js
L.get(L.pickIn({meta: {file: [], ext: []}}),
{meta: {file: './foo.txt', base: 'foo', ext: 'txt'}})
// { meta: { file: './foo.txt', ext: 'txt' } }
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-prop) [`L.prop(propName) ~> lens`](#L-prop "L.prop: (p: a) -> PLens {p: a, ...ps} a") or `propName` v1.0.0
`L.prop(propName)` or just `propName` focuses on the specified object property.
* When not viewing a defined object property, the result is `undefined`.
* When writing to a property, the result is always an `Object`.
* When setting property to `undefined`, the property is removed from the result.
When setting or removing properties, the order of keys is preserved.
For example:
```js
L.get('y', {x: 1, y: 2, z: 3})
// 2
```
```js
L.set('y', -2, {x: 1, y: 2, z: 3})
// { x: 1, y: -2, z: 3 }
```
When manipulating objects whose constructor is not `Object`,
[`L.rewrite`](#L-rewrite) can be used to convert the result to the desired type,
if necessary:
```js
L.set([L.rewrite(objectTo(XYZ)), 'z'], 3, new XYZ(3, 1, 4))
// XYZ { x: 3, y: 1, z: 3 }
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-props) [`L.props(...propNames) ~> lens`](#L-props "L.props: (p1: a1, ...ps) -> PLens {p1: a1, ...ps, ...o} {p1: a1, ...ps}") 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`](#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.
```js
L.set(L.props('x', 'y'), {x: 4}, {x: 1, y: 2, z: 3})
// { x: 4, z: 3 }
```
Note that `L.props(k1, ..., kN)` is equivalent to [`L.pick({[k1]: k1, ..., [kN]:
kN})`](#L-pick) and [`L.pickIn({[k1]: [], ..., [kN]: []})`](#L-pickIn).
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-propsOf) [`L.propsOf(object) ~> lens`](#L-propsOf "L.propsOf: {p1: a1, ...ps} -> PLens {p1: a1, ...ps, ...o} {p1: a1, ...ps}") v11.13.0
`L.propsOf(o)` is shorthand for [`L.props(...Object.keys(o))`](#L-props)
allowing one to focus on the properties specified via the given sample object.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-removable) [`L.removable(...propNames) ~> lens`](#L-removable "L.removable: (p1: a1, ...ps) -> PLens {p1: a1, ...ps, ...o} {p1: a1, ...ps, ...o}") 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:
```js
L.remove('x', {x: 1, y: 2})
// { y: 2 }
```
```js
L.remove([L.removable('x'), 'x'], {x: 1, y: 2})
// undefined
```
Also note that, in a composition, `L.removable` is likely preceded by
[`L.valueOr`](#L-valueOr) (or [`L.defaults`](#L-defaults)) like in the
[tutorial](#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`](#L-defaults) can
replace such a pair.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#lensing-strings) Lensing strings
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-matches) [`L.matches(/.../) ~> lens`](#L-matches "L.matches: RegExp -> PLens String String") v10.4.0
`L.matches`, when given a regular expression without the
[`global`](https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/RegExp/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`](#L-matches-g).
For example:
```js
L.set(L.matches(/\.[^./]+$/),
'.txt',
'/dir/file.ext')
// '/dir/file.txt'
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#providing-defaults) Providing defaults
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-valueOr) [`L.valueOr(valueOut) ~> lens`](#L-valueOr "L.valueOr: s -> PLens s s") 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.
For example:
```js
L.get(L.valueOr(0), null)
// 0
```
```js
L.set(L.valueOr(0), 0, 1)
// 0
```
```js
L.remove(L.valueOr(0), 1)
// undefined
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#transforming-data) Transforming data
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-pick) [`L.pick({prop: lens, ...props}) ~> lens`](#L-pick "L.pick: {p1: PLens s a1, ...pls} -> PLens s {p1: a1, ...pls}") 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`](#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:
```js
const 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:
```js
const 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:
```js
L.get(sanitize, sampleFlat)
// { pos: { x: 1, y: 2 }, vel: { x: 1, y: 0 } }
```
That works in both directions:
```js
L.modify([sanitize, 'pos', 'x'], R.add(5), sampleFlat)
// { px: 6, py: 2, vx: 1, vy: 0 }
```
**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](#isomorphisms) between the "flat" and "nested" forms of the data.
It can even be inverted using [`L.inverse`](#L-inverse):
```js
L.get(L.inverse(sanitize), {pos: {x: 1, y: 2}, vel: {x: 1, y: 0}})
// { px: 1, py: 2, vx: 1, vy: 0 }
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-replace) [`L.replace(maybeValueIn, maybeValueOut) ~> lens`](#L-replace "L.replace: Maybe s -> Maybe s -> PLens s s") v1.0.0
`L.replace(maybeValueIn, maybeValueOut)`, when viewed, replaces the value
`maybeValueIn` with `maybeValueOut` and vice versa when set.
For example:
```js
L.get(L.replace(1, 2), 1)
// 2
```
```js
L.set(L.replace(1, 2), 2, 0)
// 1
```
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`](#L-defaults), [`required`](#L-required) and
[`define`](#L-define).
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#isomorphisms) Isomorphisms
[Isomorphisms](https://en.wikipedia.org/wiki/Isomorphism) are [lenses](#lenses)
with a kind of [inverse](#L-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:
```jsx
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`](#L-pick), can also be used to create isomorphisms. On the other
hand, some forms of optic composition, particularly [adapting](#adapting) and
[querying](#querying), do not work properly on (inverted) isomorphisms.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#operations-on-isomorphisms) Operations on isomorphisms
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-getInverse) [`L.getInverse(isomorphism, maybeData) ~> maybeData`](#L-getInverse "L.getInverse: PIso a b -> Maybe b -> Maybe a") v5.0.0
`L.getInverse` views through an isomorphism in the inverse direction.
For example:
```js
const expect = (p, f) => x => p(x) ? f(x) : undefined
const offBy1 = L.iso(expect(R.is(Number), R.inc),
expect(R.is(Number), R.dec))
L.getInverse(offBy1, 1)
// 0
```
Note that `L.getInverse(iso, data)` is equivalent to [`L.set(iso, data,
undefined)`](#L-set).
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:
```js
L.getInverse('meaning', 42)
// { meaning: 42 }
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#creating-new-isomorphisms) Creating new isomorphisms
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-iso) [`L.iso(maybeData => maybeValue, maybeValue => maybeData) ~> isomorphism`](#L-iso "L.iso: (Maybe s -> Maybe a) -> (Maybe a -> Maybe s) -> PIso s a") 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:
```js
const reverseString = L.iso(expect(R.is(String), R.reverse),
expect(R.is(String), R.reverse))
L.modify([L.uriComponent,
L.json(),
'bottle',
0,
reverseString,
L.rewrite(R.join('')),
0],
R.toUpper,
'%7B%22bottle%22%3A%5B%22egassem%22%5D%7D')
// '%7B%22bottle%22%3A%22egasseM%22%7D'
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#isomorphism-combinators) Isomorphism combinators
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-array) [`L.array(isomorphism) ~> isomorphism`](#L-array "L.array: PIso a b -> PIso [a] [b]") v11.19.0
`L.array` lifts an isomorphism between elements, `a ≅ b`, to an isomorphism
between an [array-like](#array-like) object and an array of elements, `[a] ≅
[b]`.
For example:
```js
L.getInverse(L.array(L.pick({x: 'y', z: 'x'})), [{x:2, z:1}, {x:4, z:3}])
// [{x:1, y:2}, {x:3, y:4}]
```
Elements mapped to `undefined` by the isomorphism on elements are removed from
the resulting array in both directions.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-inverse) [`L.inverse(isomorphism) ~> isomorphism`](#L-inverse "L.inverse: PIso a b -> PIso b a") v4.1.0
`L.inverse` returns the inverse of the given isomorphism. Note that this
operation only makes sense on isomorphisms.
For example:
```js
L.get(L.inverse(offBy1), 1)
// 0
```
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#basic-isomorphisms) Basic isomorphisms
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-complement) [`L.complement ~> isomorphism`](#L-complement "L.complement: PIso Boolean Boolean") 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:
```js
L.set([L.complement, L.log()],
'Could be anything truthy',
'Also converted to bool')
// get false
// set 'Could be anything truthy'
// false
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-identity) [`L.identity ~> isomorphism`](#L-identity "L.identity: PIso s s") 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
[`[]`](#L-compose). The following equations characterize `L.identity`:
```jsx
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
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-indexed) [`L.indexed ~> isomorphism`](#L-indexed "L.indexed: PIso [a] [[Integer, a]]") v11.21.0
`L.indexed` is an isomorphism between an [array-like](#array-like) object and an
array of `[index, value]` pairs.
For example:
```js
L.modify([L.rewrite(R.join('')),
L.indexed,
L.normalize(R.sortBy(L.get(1))),
0,
1],
R.toUpper,
'optics')
// 'optiCs'
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-is) [`L.is(value) ~> isomorphism`](#L-is "L.is: v -> PIso v Boolean") v11.1.0
`L.is` reads the given value as `true` and everything else as `false` and writes
`true` as the given value and everything else as `undefined`. See
[here](#an-array-of-ids-as-boolean-flags) for an example.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-keyed) [`L.keyed ~> isomorphism`](#L-keyed "L.keyed: PIso {p: a, ...ps} [[String, a]]") v11.21.0
`L.keyed` is an isomorphism between an object and an array of `[key, value]`
pairs.
For example:
```js
L.get(L.keyed, {a: 1, b: 2})
// [ ['a', 1], ['b', 2] ]
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-reverse) [`L.reverse ~> isomorphism`](#L-reverse "L.reverse: PIso [a] [a]") v11.22.0
`L.reverse` is an isomorphism between an [array-like](#array-like) object
and its reverse.
For example:
```js
L.join(', ', [L.reverse, L.elems], 'abc')
// 'c, b, a'
```
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-singleton) [`L.singleton ~> isomorphism`](#L-singleton "L.singleton: PIso [a] a") v11.18.0
`L.singleton` is a partial isomorphism between an [array-like](#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:
```js
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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#standard-isomorphisms) Standard isomorphisms
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-uri) [`L.uri ~> isomorphism`](#L-uri "L.uri: PIso String String") v11.3.0
`L.uri` is an isomorphism based on the standard
[`decodeURI`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURI)
and
[`encodeURI`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/encodeURI)
functions.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-uriComponent) [`L.uriComponent ~> isomorphism`](#L-uriComponent "L.uriComponent: PIso String String") v11.3.0
`L.uriComponent` is an isomorphism based on the standard
[`decodeURIComponent`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent)
and
[`encodeURIComponent`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/encodeURIComponent)
functions.
##### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-json) [`L.json({reviver, replacer, space}) ~> isomorphism`](#L-json "L.json: {reviver, replacer, space} -> PIso String JSON") v11.3.0
`L.json({reviver, replacer, space})` returns an isomorphism based on the
standard
[`JSON.parse`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/JSON/parse)
and
[`JSON.stringify`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/JSON/stringify)
functions. The optional `reviver` is passed to
[`JSON.parse`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/JSON/parse)
and the optional `replacer` and `space` are passed to
[`JSON.stringify`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/JSON/stringify).
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#interop) Interop
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-pointer) [`L.pointer(jsonPointer) ~> lens`](#L-pointer "L.pointer: JSONPointer s a -> PLens s a") v11.21.0
`L.pointer` converts a valid [JSON Pointer](https://tools.ietf.org/html/rfc6901)
(string) into a bidirectional lens. Works with [JSON
String](https://tools.ietf.org/html/rfc6901#section-5) and [URI Fragment
Identifier](https://tools.ietf.org/html/rfc6901#section-6) representations.
For Example:
```js
L.get(L.pointer('/foo/0'), {foo: [1, 2]})
// 1
```
```js
L.modify(L.pointer('#/foo/1'), x => x + 1, {foo: [1, 2]})
// {foo: [1, 3]}
```
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#auxiliary) Auxiliary
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#L-seemsArrayLike) [`L.seemsArrayLike(anything) ~> boolean`](#L-seemsArrayLike "L.seemsArrayLike: any -> 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](#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](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array),
[typed
arrays](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays),
and
[strings](https://developer.mozilla.org/en/docs/Web/JavaScript/Reference/Global_Objects/String).
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.
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#examples) Examples
Note that if you are new to lenses, then you probably want to start with the
[tutorial](#tutorial).
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#an-array-of-ids-as-boolean-flags) 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:
```js
const sampleFlags = ['id-19', 'id-76']
```
Here is a parameterized lens that does just that:
```js
const flag = id => [L.normalize(R.sortBy(R.identity)),
L.find(R.equals(id)),
L.is(id)]
```
Now we can treat individual constants as boolean flags:
```js
L.get(flag('id-69'), sampleFlags)
// false
```
```js
L.get(flag('id-76'), sampleFlags)
// true
```
In both directions:
```js
L.set(flag('id-69'), true, sampleFlags)
// ['id-19', 'id-69', 'id-76']
```
```js
L.set(flag('id-76'), false, sampleFlags)
// ['id-19']
```
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#dependent-fields) 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`](#L-props)
(or, in more complex cases, [`L.pick`](#L-pick)) to limit the set of properties
to deal with, and [`L.rewrite`](#L-rewrite) to insert the desired restriction
logic. Here is how it could look like for the `maximum`:
```js
const maximum = [
L.props('maximum', 'initial'),
L.rewrite(props => {
const {maximum, initial} = props
if (maximum < initial)
return {maximum, initial: maximum}
else
return props
}),
'maximum']
```
Now:
```js
L.set(maximum,
5,
{maximum: 10, initial: 8, something: 'else'})
// {maximum: 5, initial: 5, something: 'else'}
```
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#collection-toggle) 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](http://todomvc.com/) spec includes [such a
checkbox](https://github.com/tastejs/todomvc/blob/master/app-spec.md#mark-all-as-complete).
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:
```js
const sampleTodos = [{completed: true}, {completed: false}, {completed: true}]
```
We can address those flags with a traversal:
```js
const completedFlags = [L.elems, 'completed']
```
To compute a single boolean out of a traversal over booleans we can use the
[`L.and`](#L-and) fold and use that to define a lens parameterized over flag
traversals using [`L.foldTraversalLens`](#L-foldTraversalLens):
```js
const selectAll = L.foldTraversalLens(L.and)
```
Now we can say, for example:
```js
L.get(selectAll(completedFlags), sampleTodos)
// false
```
```js
L.set(selectAll(completedFlags), true, sampleTodos)
// [{completed: true}, {completed: true}, {completed: true}]
```
As an exercise define `unselectAll` using the [`L.or`](#L-or) fold. How does it
differ from `selectAll`?
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#bst-as-a-lens) 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`](#L-cond) combinator allows for dynamic selection of
lenses based on examining the data structure being manipulated. Using
[`L.cond`](#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:
```js
const searchAttempt = key => L.lazy(rec => [
L.cond([n => !n || key === n.key, L.defaults({key})],
[n => key < n.key, ['smaller', rec]],
[ ['greater', rec]])])
const valueOfAttempt = key => [searchAttempt(key), 'value']
```
Note that we also make use of the [`L.lazy`](#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:
```js
const fromPairs =
R.reduce((t, [k, v]) => L.set(valueOfAttempt(k), v, t), undefined)
```
Now:
```js
const sampleBST = fromPairs([[3, 'g'], [2, 'a'], [1, 'm'], [4, 'i'], [5, 'c']])
sampleBST
// { key: 3,
// value: 'g',
// smaller: { key: 2, value: 'a', smaller: { key: 1, value: 'm' } },
// greater: { key: 4, value: 'i', greater: { key: 5, value: 'c' } } }
```
However, the above `searchAttempt` lens constructor does not maintain the BST
structure when values are being removed:
```js
L.remove(valueOfAttempt(3), sampleBST)
// { key: 3,
// smaller: { key: 2, value: 'a', smaller: { key: 1, value: 'm' } },
// greater: { key: 4, value: 'i', greater: { key: 5, value: 'c' } } }
```
How do we fix this? We could check and transform the data structure to a BST
after changes. The [`L.rewrite`](#L-rewrite) combinator can be used for that
purpose. Here is a naïve rewrite to fix a tree after value removal:
```js
const 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:
```js
const search = key => L.lazy(rec => [
naiveBST,
L.cond([n => !n || key === n.key, L.defaults({key})],
[n => key < n.key, ['smaller', rec]],
[ ['greater', rec]])])
const valueOf = key => [search(key), 'value']
```
Now we can also remove values from a binary tree:
```js
L.remove(valueOf(3), sampleBST)
// { key: 4,
// value: 'i',
// greater: { key: 5, value: 'c' },
// smaller: { key: 2, value: 'a', smaller: { key: 1, value: 'm' } } }
```
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](https://en.wikipedia.org/wiki/AVL_tree) or
[Red-Black](https://en.wikipedia.org/wiki/Red%E2%80%93black_tree). Another
worthy exercise would be to make it so that the empty binary tree is `null`
rather than `undefined`.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#bst-traversal) BST traversal
What about [traversals](#traversals) over BSTs? We can use the
[`L.branch`](#L-branch) combinator to define an in-order traversal over the
values of a BST:
```js
const values = L.lazy(rec => [
L.optional,
naiveBST,
L.branch({smaller: rec,
value: L.identity,
greater: rec})])
```
Given a binary tree `sampleBST` we can now manipulate it as a whole. For
example:
```js
L.join('-', values, sampleBST)
// 'm-a-g-i-c'
```
```js
L.modify(values, R.toUpper, sampleBST)
// { key: 3,
// value: 'G',
// smaller: { key: 2, value: 'A', smaller: { key: 1, value: 'M' } },
// greater: { key: 4, value: 'I', greater: { key: 5, value: 'C' } } }
```
```js
L.remove([values, L.when(x => x > 'e')], sampleBST)
// { key: 5, value: 'c', smaller: { key: 2, value: 'a' } }
```
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#interfacing) Interfacing with Immutable.js
[Immutable.js](http://facebook.github.io/immutable-js/) is a popular library
providing immutable data structures. As argued in [Lenses with
Immutable.js](https://medium.com/@drboolean/lenses-with-immutable-js-9bda85674780#.kzq41xgw3)
it can be useful to be able to manipulate Immutable.js data structures using
[optics](#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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#list-indexing) `List` indexing
Here is a primitive partial lens for indexing
[`List`](http://facebook.github.io/immutable-js/docs/#/List) written using
[`L.lens`](#L-lens):
```js
const getList = i => xs => Immutable.List.isList(xs) ? xs.get(i) : undefined
const setList = i => (x, xs) => {
if (!Immutable.List.isList(xs))
xs = Immutable.List()
if (x !== undefined)
return xs.set(i, x)
return xs.delete(i)
}
const idxList = i => L.lens(getList(i), setList(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`.
We can now view existing elements:
```js
const sampleList = Immutable.List(['a', 'l', 'i', 's', 't'])
L.get(idxList(2), sampleList)
// 'i'
```
Update existing elements:
```js
L.modify(idxList(1), R.toUpper, sampleList)
// List [ 'a', 'L', 'i', 's', 't' ]
```
And remove existing elements:
```js
L.remove(idxList(0), sampleList)
// List [ 'l', 'i', 's', 't' ]
```
We can also create lists from non-lists:
```js
L.set(idxList(0), 'x', undefined)
// List [ 'x' ]
```
And we can also append new elements:
```js
L.set(idxList(5), '!', sampleList)
// List [ 'a', 'l', 'i', 's', 't', '!' ]
```
Consider what happens when the index given to `idxList` points further beyond
the last element. Both the [`L.index`](#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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#interfacing-traversals) Interfacing traversals
Fortunately we do not need Immutable.js data structures to provide a compatible
*partial*
[`traverse`](https://github.com/rpominov/static-land/blob/master/docs/spec.md#traversable)
function to support [traversals](#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](#isomorphisms) between `List` and arrays:
```js
const fromList = xs => Immutable.List.isList(xs) ? xs.toArray() : undefined
const toList = xs => R.is(Array, xs) && xs.length ? Immutable.List(xs) : undefined
const isoList = L.iso(fromList, toList)
```
So, now we can [compose](#L-compose) a traversal over `List` as:
```js
const seqList = [isoList, L.elems]
```
And all the usual operations work as one would expect, for example:
```js
L.remove([seqList, L.when(c => c < 'i')], sampleList)
// List [ 'l', 's', 't' ]
```
And:
```js
L.joinAs(R.toUpper,
'',
[seqList, L.when(c => c <= 'i')],
sampleList)
// 'AI'
```
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#deepening-topics) Deepening topics
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#understanding-filter-find-select-and-when) Understanding [`L.filter`](#L-filter), [`L.find`](#L-find), [`L.select`](#L-select), and [`L.when`](#L-when)
The [`L.filter`](#L-filter), [`L.find`](#L-find), [`L.select`](#L-select), and
[`L.when`](#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.select(traversal, data) ~> value` | `L.select: 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`](#L-filter) and [`L.find`](#L-find)
introduce lenses, [`L.select`](#L-select) eliminates a traversal, and
[`L.when`](#L-when) introduces an optic, which will always be a traversal in
this section. We can also read that [`L.filter`](#L-filter) and
[`L.find`](#L-find) operate on arrays, while [`L.select`](#L-select) and
[`L.when`](#L-when) operate on arbitrary traversals. Yet another thing to make
note of is that both [`L.find`](#L-find) and [`L.select`](#L-select) are
many-to-one while both [`L.filter`](#L-filter) and [`L.when`](#L-when) retain
cardinality.
The following equations relate the operations in the read direction:
```jsx
L.get([L.filter(p), 0]) = L.get(L.find(p))
L.select([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`](#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`](#L-find)
is probably not what one should use to generally search for something in a data
structure.
[`L.select`](#L-select) (and [`L.selectAs`](#L-selectAs)) 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`](#L-when) to filter elements
or to limit the traversal.
[`L.filter`](#L-filter) can be used to create a bidirectional view of a subset
of elements of an array matching a given predicate. [`L.filter`](#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`](#L-elems) and [`L.when`](#L-when), because then [no intermediate
array of the elements is
computed](#nesting-traversals-does-not-create-intermediate-aggregates).
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#advanced-topics) Advanced topics
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#performance-tips) Performance tips
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#nesting-traversals-does-not-create-intermediate-aggregates) 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](http://ramdajs.com/):
```js
const sumPositiveXs = R.pipe(R.flatten,
R.map(R.prop('x')),
R.filter(R.lt(0)),
R.sum)
const sampleXs = [[{x: 1}], [{x: -2}, {x: 2}]]
sumPositiveXs(sampleXs)
// 3
```
A performance problem in the above naïve `sumPositiveXs` function is that aside
from the last step, `R.sum`, every step of the computation, `R.flatten`,
`R.map(R.prop('x'))`, and `R.filter(R.lt(0))`, creates an intermediate array
that is only used by the next step of the computation and is then thrown away.
When dealing with large amounts of data this kind of composition can cause
performance issues.
Please note that the above example is *intentionally naïve*. In Ramda [one can
use transducers to avoid building such intermediate
results](http://simplectic.com/blog/2015/ramda-transducers-logs/) although in
this particular case the use of [`R.flatten`](http://ramdajs.com/docs/#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
```js
L.sum([L.flatten, 'x', L.when(R.lt(0))], sampleXs)
// 3
```
and, thankfully, it doesn't create intermediate arrays. This is the case with
traversals in general.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#avoid-reallocating-optics-in-l-choose) Avoid reallocating optics in [`L.choose`](#L-choose)
The function given to [`L.choose`](#L-choose) is called each time the optic is
used and any allocations done by the function are consequently repeated.
Consider the following example:
```jsx
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`](#L-choose):
```jsx
const 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`](#L-cond)
combinator:
```jsx
L.cond([Array.isArray, [L.elems, 'data']], ['data'])
```
This has the advantage that the optics are constructed only once.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#on-bundle-size-and-minification) On bundle size and minification
The distribution of this library includes a [prebuilt and minified browser
bundle](https://unpkg.com/partial.lenses/dist/partial.lenses.min.js). However,
this library is not designed to be primarily used via that bundle. Rather, this
library is bundled with [Rollup](https://rollupjs.org/), uses `/*#__PURE__*/`
annotations to help [UglifyJS](https://github.com/mishoo/UglifyJS2) 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](https://github.com/rollup/rollup-plugin-replace) and
[uglify](https://github.com/TrySound/rollup-plugin-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:
```jsx
import replace from 'rollup-plugin-replace'
import uglify from 'rollup-plugin-uglify'
// ...
export default {
plugins: [
replace({
'process.env.NODE_ENV': JSON.stringify('production')
}),
// ...
uglify({
compress: {
passes: 3
}
})
]
}
```
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#background) Background
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#motivation) Motivation
In late 2015, while implementing UIs for manipulating fairly complex JSON
objects, we wrote a module of additional lens combinators on top of
[Ramda](http://ramdajs.com)'s lenses. Lenses allowed us to operate on nested
objects in a [compositional](#on-composability) manner and, thanks to treating
data as [immutable](#on-immutability), 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:
```jsx
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](#L-get) and [set](#L-set), we also wanted
to have the ability to [insert](#L-append) and [remove](#L-remove). In other
words, we wanted full [CRUD](https://en.wikipedia.org/wiki/CRUD) semantics,
because that is what our UIs also had to provide.
We also wanted lenses to have the ability to [search](#L-find) for things,
because we often had to deal with e.g. arrays containing objects with unique IDs
aka [association lists](#myth-partial-lenses-are-not-lawful).
All of these considerations give rise to a notion of
[partiality](#on-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](#benchmarks), [optics](#optics) library, supporting not only
partial [lenses](#lenses), but also [isomorphisms](#isomorphisms),
[traversals](#traversals), and also a notion of [transforms](#transforms).
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#design-choices) 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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#partiality) Partiality
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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#focus-on-json) 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](#on-immutability)
collections and back).
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#use-of-undefined) Use of `undefined`
`undefined` is a natural choice in JavaScript, especially when dealing with
JSON, to represent nothingness. Some libraries use `null`, but that is arguably
a poor choice, because `null` is a valid JSON value. Some libraries implement
special `Maybe` types, but the benefits do not seem worth the trouble. First of
all, `undefined` already exists in JavaScript and is not a valid JSON value.
Inventing a new value to represent nothingness doesn't seem to add much. OTOH,
wrapping values with `Just` objects introduces a significant performance
overhead due to extra allocations. Operations with optics do not otherwise
necessarily require large numbers of allocations and can be made highly
efficient.
Not having an explicit `Just` object means that dealing with values such as
`Just Nothing` requires special consideration.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#allowing-strings-and-integers-as-optics) Allowing [strings](#L-prop) and [integers](#L-index) 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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#treating-an-array-of-optics-as-a-composition-of-optics) Treating an [array of optics as a composition](#L-compose) 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`](http://ramdajs.com/docs/#assocPath) and
[`dissocPath`](http://ramdajs.com/docs/#dissocPath) for performance reasons.
Client code can also manipulate such simple paths as data.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#applicatives) Applicatives
One interesting consequence of partiality is that it becomes possible to [invert
isomorphisms](#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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#combinators-for-creating-new-optics) Combinators for creating new optics
By providing combinators for creating new [traversals](#L-branch),
[lenses](#L-lens) and [isomorphisms](#L-iso), client code need not depend on the
internal implementation of optics. The current version of this library exposes
the internal implementation via [`L.toFunction`](#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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#indexing) Indexing
[Indexing](#on-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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#static-land) Static Land
The algebraic structures used in partial lenses follow the [Static
Land](https://github.com/rpominov/static-land) specification rather than the
[Fantasy Land](https://github.com/fantasyland/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](https://github.com/rpominov/static-land/issues/36#issuecomment-285938602)
for switching to use Static Land was that correct implementation of
[`traverse`](#L-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.
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#performance) Performance
Concern for performance has been a part of the work on partial lenses for some
time. The basic principles can be summarized in order of importance:
* Minimize overheads
* Micro-optimize for common cases
* Avoid stack overflows
* Avoid [quadratic algorithms](http://accidentallyquadratic.tumblr.com/)
* Avoid optimizations that require large amounts of code
* Run [benchmarks](#benchmarks) continuously to detect performance regressions
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#benchmarks) Benchmarks
Here are a few benchmark results on partial lenses (as `L` version 12.0.0) and
some roughly equivalent operations using [Ramda](http://ramdajs.com/) (as `R`
version 0.24.1), [Ramda Lens](https://github.com/ramda/ramda-lens) (as `P`
version 0.1.2), [Flunc Optics](https://github.com/flunc/optics) (as `O` version
0.0.2), [Optika](https://github.com/phadej/optika) (as `K` version 0.0.2), and
[lodash.get](https://www.npmjs.com/package/lodash.get) (as `_get` version
4.4.2). As always with benchmarks, you should take these numbers with a pinch
of salt and preferably try and measure your actual use cases!
```jsx
25,687,744/s 1.00 L.get(L_find_id_5000, ids)
6,481,640/s 1.00 R.reduceRight(add, 0, xs100)
645,685/s 10.04 L.foldr(add, 0, L.elems, xs100)
212,023/s 30.57 xs100.reduceRight(add, 0)
3,764/s 1721.80 O.Fold.foldrOf(O.Traversal.traversed, addC, 0, xs100)
11,219/s 1.00 R.reduceRight(add, 0, xs100000)
344/s 32.59 L.foldr(add, 0, L.elems, xs100000)
63/s 178.68 xs100000.reduceRight(add, 0)
0/s Infinity O.Fold.foldrOf(O.Traversal.traversed, addC, 0, xs100000) -- STACK OVERFLOW
1,072,743/s 1.00 L.foldl(add, 0, L.elems, xs100)
1,011,495/s 1.06 xs100.reduce(add, 0)
43,635/s 24.58 R.reduce(add, 0, xs100)
2,870/s 373.74 O.Fold.foldlOf(O.Traversal.traversed, addC, 0, xs100)
4,317,541/s 1.00 L.sum(L.elems, xs100)
1,757,844/s 2.46 K.traversed().sumOf(xs100)
781,977/s 5.52 xs100.reduce((a, b) => a + b, 0)
562,042/s 7.68 L.concat(Sum, L.elems, xs100)
40,359/s 106.98 R.sum(xs100)
24,498/s 176.24 P.sumOf(P.traversed, xs100)
4,427/s 975.27 O.Fold.sumOf(O.Traversal.traversed, xs100)
672,740/s 1.00 L.maximum(L.elems, xs100)
3,150/s 213.57 O.Fold.maximumOf(O.Traversal.traversed, xs100)
160,545/s 1.00 L.sum([L.elems, L.elems, L.elems], xsss100)
158,749/s 1.01 L.concat(Sum, [L.elems, L.elems, L.elems], xsss100)
4,342/s 36.97 P.sumOf(R.compose(P.traversed, P.traversed, P.traversed), xsss100)
924/s 173.83 O.Fold.sumOf(R.compose(O.Traversal.traversed, O.Traversal.traversed, O.Traversal.traversed), xsss100)
4,026,492/s 1.00 K.traversed().arrayOf(xs100)
884,327/s 4.55 L.collect(L.elems, xs100)
674,081/s 5.97 xs100.map(I.id)
3,389/s 1188.15 O.Fold.toListOf(O.Traversal.traversed, xs100)
261,183/s 1.00 L.collect([L.elems, L.elems, L.elems], xsss100)
45,543/s 5.73 K.traversed().traversed().traversed().arrayOf(xsss100)
39,917/s 6.54 {let acc=[]; xsss100.forEach(x0 => {x0.forEach(x1 => {acc = acc.concat(x1)})}); return acc}
9,483/s 27.54 R.chain(R.chain(R.identity), xsss100)
808/s 323.18 O.Fold.toListOf(R.compose(O.Traversal.traversed, O.Traversal.traversed, O.Traversal.traversed), xsss100)
73,101/s 1.00 L.collect(L.flatten, xsss100)
20,728/s 3.53 R.flatten(xsss100)
17,181,707/s 1.00 L.modify(L.elems, inc, xs)
12,345,707/s 1.39 xs.map(inc)
3,362,832/s 5.11 R.map(inc, xs)
1,201,219/s 14.30 K.traversed().over(xs, inc)
514,727/s 33.38 O.Setter.over(O.Traversal.traversed, inc, xs)
320,319/s 53.64 P.over(P.traversed, inc, xs)
537,524/s 1.00 L.modify(L.elems, inc, xs1000)
86,351/s 6.22 R.map(inc, xs1000)
67,524/s 7.96 xs1000.map(inc)
62,750/s 8.57 K.traversed().over(xs1000, inc)
386/s 1393.46 O.Setter.over(O.Traversal.traversed, inc, xs1000) -- QUADRATIC
350/s 1533.96 P.over(P.traversed, inc, xs1000) -- QUADRATIC
181,879/s 1.00 L.modify([L.elems, L.elems, L.elems], inc, xsss100)
42,069/s 4.32 K.traversed().traversed().traversed().over(xsss100, inc)
39,798/s 4.57 xsss100.map(x0 => x0.map(x1 => x1.map(inc)))
12,152/s 14.97 R.map(R.map(R.map(inc)), xsss100)
3,547/s 51.28 O.Setter.over(R.compose(O.Traversal.traversed, O.Traversal.traversed, O.Traversal.traversed), inc, xsss100)
2,833/s 64.21 P.over(R.compose(P.traversed, P.traversed, P.traversed), inc, xsss100)
56,785,329/s 1.00 L.get(1, xs)
33,964,648/s 1.67 _get(xs, 1)
13,337,651/s 4.26 R.nth(1, xs)
2,009,575/s 28.26 R.view(l_1, xs)
1,292,644/s 43.93 K.idx(1).get(xs)
135,916,645/s 1.00 L_get_1(xs)
20,726,712/s 6.56 L.get(1)(xs)
4,928,473/s 27.58 R_nth_1(xs)
3,102,858/s 43.80 R.nth(1)(xs)
34,306,843/s 1.00 L.set(1, 0, xs)
8,463,425/s 4.05 xs.map((x, i) => i === 1 ? 0 : x)
7,620,992/s 4.50 {let ys = xs.slice(); ys[1] = 0; return ys}
3,110,983/s 11.03 R.update(1, 0, xs)
846,762/s 40.52 K.idx(1).set(xs, 0)
825,091/s 41.58 R.set(l_1, 0, xs)
38,054,495/s 1.00 L.get('y', xyz)
22,503,604/s 1.69 R.prop('y', xyz)
16,064,531/s 2.37 _get(xyz, 'y')
1,904,551/s 19.98 R.view(l_y, xyz)
1,298,160/s 29.31 K.key('y').get(xyz)
55,510,303/s 1.00 L_get_y(xyz)
16,108,081/s 3.45 L.get('y')(xyz)
5,755,079/s 9.65 R_prop_y(xyz)
3,426,127/s 16.20 R.prop('y')(xyz)
7,304,713/s 1.00 L.set('y', 0, xyz)
7,067,585/s 1.03 R.assoc('y', 0, xyz)
962,102/s 7.59 R.set(l_y, 0, xyz)
893,527/s 8.18 K.key('y').set(xyz, 0)
14,057,181/s 1.00 L.get([0, 'x', 0, 'y'], axay)
10,564,131/s 1.33 _get(axay, [0, 'x', 0, 'y'])
10,401,902/s 1.35 R.path([0, 'x', 0, 'y'], axay)
1,807,011/s 7.78 R.view(l_0x0y, axay)
768,044/s 18.30 K_0_x_0_y.get(axay)
533,320/s 26.36 R.view(l_0_x_0_y, axay)
3,673,407/s 1.00 L.set([0, 'x', 0, 'y'], 0, axay)
783,511/s 4.69 R.assocPath([0, 'x', 0, 'y'], 0, axay)
526,253/s 6.98 K_0_x_0_y.set(axay, 0)
420,175/s 8.74 R.set(l_0x0y, 0, axay)
268,101/s 13.70 R.set(l_0_x_0_y, 0, axay)
3,600,477/s 1.00 L.modify([0, 'x', 0, 'y'], inc, axay)
553,966/s 6.50 K_0_x_0_y.over(axay, inc)
481,177/s 7.48 R.over(l_0x0y, inc, axay)
286,049/s 12.59 R.over(l_0_x_0_y, inc, axay)
34,538,589/s 1.00 L.remove(1, xs)
3,707,371/s 9.32 R.remove(1, 1, xs)
8,109,050/s 1.00 L.remove('y', xyz)
2,277,988/s 3.56 R.dissoc('y', xyz)
17,364,173/s 1.00 _get(xyzn, ['x', 'y', 'z'])
14,492,570/s 1.20 L.get(['x', 'y', 'z'], xyzn)
11,267,296/s 1.54 R.path(['x', 'y', 'z'], xyzn)
1,846,108/s 9.41 R.view(l_xyz, xyzn)
802,010/s 21.65 K_xyz.get(xyzn)
735,724/s 23.60 R.view(l_x_y_z, xyzn)
149,892/s 115.84 O.Getter.view(o_x_y_z, xyzn)
3,954,161/s 1.00 L.set(['x', 'y', 'z'], 0, xyzn)
1,120,288/s 3.53 R.assocPath(['x', 'y', 'z'], 0, xyzn)
639,504/s 6.18 K_xyz.set(xyzn, 0)
524,245/s 7.54 R.set(l_xyz, 0, xyzn)
428,160/s 9.24 R.set(l_x_y_z, 0, xyzn)
202,344/s 19.54 O.Setter.set(o_x_y_z, 0, xyzn)
1,334,454/s 1.00 R.find(x => x > 3, xs100)
1,078,015/s 1.24 L.selectAs(x => x > 3 ? x : undefined, L.elems, xs100)
2,639/s 505.62 O.Fold.findOf(O.Traversal.traversed, x => x > 3, xs100)
10,289,501/s 1.00 L.selectAs(x => x < 3 ? x : undefined, L.elems, xs100)
4,869,112/s 2.11 R.find(x => x < 3, xs100)
2,642/s 3895.21 O.Fold.findOf(O.Traversal.traversed, x => x < 3, xs100) -- NO SHORTCUT EVALUATION
11,873/s 1.00 L.sum([L.elems, x => x+1, x => x*2, L.when(x => x%2 === 0)], xs1000)
3,939/s 3.01 R.transduce(R.compose(R.map(x => x+1), R.map(x => x*2), R.filter(x => x%2 === 0)), (x, y) => x+y, 0, xs1000)
3,208/s 3.70 R.pipe(R.map(x => x+1), R.map(x => x*2), R.filter(x => x%2 === 0), R.sum)(xs1000)
227,524/s 1.00 R.forEach(I.id, xs1000)
191,623/s 1.19 L.forEach(I.id, L.elems, xs1000)
115,242/s 1.97 xs1000.forEach(I.id)
274,800/s 1.00 L.forEach(I.id, [L.elems, L.elems, L.elems], xsss100)
98,020/s 2.80 xsss100.forEach(xss100 => xss100.forEach(xs100 => xs100.forEach(I.id)))
27,571/s 9.97 R.forEach(R.forEach(R.forEach(I.id)), xsss100)
7,522/s 1.00 L.minimumBy(x => -x, L.elems, xs10000)
6,074/s 1.24 L.minimum(L.elems, xs10000)
3,628/s 2.07 R.reduce(R.min, -Infinity, xs10000)
135,501/s 1.00 L.mean(L.elems, xs1000)
3,972/s 34.11 R.mean(xs1000)
6,004,793/s 1.00 L.remove(50, xs100)
1,822,682/s 3.29 R.remove(50, 1, xs100)
5,351,194/s 1.00 L.set(50, 2, xs100)
1,481,221/s 3.61 R.update(50, 2, xs100)
701,500/s 7.63 K.idx(50).set(xs100, 2)
588,315/s 9.10 R.set(l_50, 2, xs100)
74,693/s 1.00 L.remove(5000, xs10000)
41,819/s 1.79 R.remove(5000, 1, xs10000)
62,035/s 1.00 L.set(5000, 2, xs10000)
25,243/s 2.46 R.update(5000, 2, xs10000)
6,066,473/s 1.00 L.modify(L.values, inc, xyz)
371,930/s 1.00 L.modify(L.values, inc, xs10o)
45,104/s 8.25 L.modify(L.values, inc, xs100o)
4,729/s 78.65 L.modify(L.values, inc, xs1000o)
457/s 813.95 L.modify(L.values, inc, xs10000o)
627,104/s 1.00 L.modify(flatten, inc, nested)
372,220/s 1.68 L.modify(everywhere, incNum, nested)
910,205/s 1.00 L.modify(flatten, inc, xs10)
797,621/s 1.14 L.modify(everywhere, incNum, xs10)
149,226/s 1.00 L.modify(flatten, inc, xs100)
148,868/s 1.00 L.modify(everywhere, incNum, xs100)
16,650/s 1.00 L.modify(flatten, inc, xs1000)
16,568/s 1.00 L.modify(everywhere, incNum, xs1000)
1,649,943/s 1.00 L.set(xyzs, 1, undefined)
1,146,574/s 1.44 L.set(L.seq('x', 'y', 'z'), 1, undefined)
258,867/s 1.00 L.modify(values, x => x + x, bst)
461,117/s 1.00 L.collect(values, bst)
99,026/s 1.00 fromPairs(bstPairs)
55,185/s 1.00 L.get(L.slice(100, -100), xs10000)
44,500/s 1.24 R.slice(100, -100, xs10000)
6,285,532/s 1.00 L.get(L.slice(1, -1), xs)
5,630,115/s 1.12 R.slice(1, -1, xs)
3,258,908/s 1.00 L.get(L.slice(10, -10), xs100)
2,631,005/s 1.24 R.slice(10, -10, xs100)
10,587,077/s 1.00 L.get(L.defaults(1), 2)
10,292,488/s 1.03 L.get(L.defaults(1), undefined)
32,798,020/s 1.00 L.get(defaults1, undefined)
32,514,817/s 1.01 L.get(defaults1, 2)
12,695,440/s 1.00 L.get(L.define(1), 2)
11,844,087/s 1.07 L.get(L.define(1), undefined)
59,263,791/s 1.00 L.get(define1, undefined)
58,069,337/s 1.02 L.get(define1, 2)
18,295,242/s 1.00 L.get(L.valueOr(1), null)
17,945,092/s 1.02 L.get(L.valueOr(1), undefined)
17,647,953/s 1.04 L.get(L.valueOr(1), 2)
62,939,499/s 1.00 L.get(valueOr1, 2)
61,951,497/s 1.02 L.get(valueOr1, undefined)
61,774,643/s 1.02 L.get(valueOr1, null)
58,659/s 1.00 L.concatAs(toList, List, L.elems, xs100)
60,600/s 1.00 L.modify(L.flatten, inc, xsss100)
8,020,941/s 1.00 L.selectAs(x => x > 3 ? x : undefined, L.elems, pi)
4,490,772/s 1.79 R.find(x => x > 3, pi)
36,548/s 219.46 O.Fold.findOf(O.Traversal.traversed, x => x > 3, pi)
6,463,455/s 1.00 L.get(L.find(x => x !== 1, {hint: 0}), xs)
6,354,515/s 1.02 L.get(L.find(x => x !== 1), xs)
4,771,136/s 1.35 R.find(x => x !== 1, xs)
1,349,545/s 1.00 R.find(x => x !== 1, xs100)
922,586/s 1.46 L.get(L.find(x => x !== 1), xs100)
920,802/s 1.47 L.get(L.find(x => x !== 1, {hint: 0}), xs100)
178,559/s 1.00 R.find(x => x !== 1, xs1000)
109,454/s 1.63 L.get(L.find(x => x !== 1), xs1000)
108,734/s 1.64 L.get(L.find(x => x !== 1, {hint: 0}), xs1000)
4,573,676/s 1.00 L.get(valueOr0x0y, axay)
4,403,047/s 1.04 L.get(define0x0y, axay)
4,042,229/s 1.13 L.get(defaults0x0y, axay)
866,539/s 1.00 L.set(valueOr0x0y, 1, undefined)
834,961/s 1.04 L.set(define0x0y, 1, undefined)
801,436/s 1.08 L.set(defaults0x0y, 1, undefined)
1,205,594/s 1.00 L.set(L.findWith('x'), 2, axay)
7,245,673/s 1.00 L.get(aEb, {x: 1})
6,798,963/s 1.07 L.get(abS, {x: 1})
4,350,745/s 1.67 L.get(abM, {x: 1})
3,248,524/s 2.23 L.get(L.orElse('a', 'b'), {x: 1})
2,322,918/s 3.12 L.get(L.choices('a', 'b'), {x: 1})
4,032,504/s 1.00 L.get(abcS, {x: 1})
3,904,677/s 1.03 L.get(aEbEc, {x: 1})
3,505,278/s 1.15 L.get(abcM, {x: 1})
1,406,931/s 2.87 L.get(L.choices('a', 'b', 'c'), {x: 1})
989,032/s 4.08 L.get(L.choice('a', 'b', 'c'), {x: 1})
1,271,972/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](./bench/bench.js) for details.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#lenses-all-the-way) Lenses all the way
As said in the first sentence of this document, lenses are convenient for
performing updates on individual elements of [immutable](#on-immutability) data
structures. Having abilities such as [nesting](#L-compose),
[adapting](#L-choose), [recursing](#L-lazy) and [restructuring](#L-pick) using
lenses makes the notion of an individual element quite flexible and, even
further, [traversals](#traversals) make it possible to [selectively](#L-when)
target zero or more elements of [non-trivial](#L-branch) 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](https://github.com/polytypic/fastener), for example, are, in some
ways, less principled and can implement queries and transforms that are outside
the scope of lenses and traversals.
One type of use case which we've ran into multiple times and falls out of the
sweet spot of lenses is performing uniform transforms over data structures. For
example, we've run into the following use cases:
* Eliminate all references to an object with a particular id.
* Transform all instances of certain objects over many paths.
* Filter out extra fields from objects of varying shapes and paths.
One approach to making such whole data structure spanning updates is to use a
simple bottom-up transform. Here is a simple implementation for JSON based on
ideas from the [Uniplate](https://github.com/ndmitchell/uniplate) library:
``` js
const descend = (w2w, w) => R.is(Object, w) ? R.map(w2w, w) : w
const substUp = (h2h, w) => descend(h2h, descend(w => substUp(h2h, w), w))
const 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:
``` js
const sampleBloated = {
just: 'some',
extra: 'crap',
that: [
'we',
{want: 'to',
filter: ['out'],
including: {the: 'following',
extra: true,
fields: 1}}]
}
```
We can now remove the `extra` `fields` like this:
``` js
transform(R.ifElse(R.allPass([R.is(Object), R.complement(R.is(Array))]),
L.remove(L.props('extra', 'fields')),
R.identity),
sampleBloated)
// { just: 'some',
// that: [ 'we', { want: 'to',
// filter: ['out'],
// including: {the: 'following'} } ] }
```
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#related-work) 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!
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#papers-and-other-introductory-material) Papers and other introductory material
* [A Little Lens Starter Tutorial](https://www.schoolofhaskell.com/school/to-infinity-and-beyond/pick-of-the-week/a-little-lens-starter-tutorial)
* [A clear picture of lens laws](http://sebfisch.github.io/research/pub/Fischer+MPC15.pdf)
* [An Introduction Into Lenses In JavaScript](https://medium.com/javascript-inside/an-introduction-into-lenses-in-javascript-e494948d1ea5#.777juzfcw)
* [Functional Lenses, How Do They Work](https://medium.com/@dtipson/functional-lenses-d1aba9e52254#.qja55h7uh)
* [Lenses with Immutable.js](https://medium.com/@drboolean/lenses-with-immutable-js-9bda85674780#.4irzg5u1q)
* [Polymorphic Update with van Laarhoven Lenses](http://r6.ca/blog/20120623T104901Z.html)
* [Profunctor Optics: Modular Data Accessors](https://arxiv.org/abs/1703.10857)
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#javascript-typescript-flow-libraries) JavaScript / TypeScript / Flow libraries
* [5outh/nanoscope](https://github.com/5outh/nanoscope)
* [DrBoolean/lenses](https://github.com/DrBoolean/lenses)
* [fantasyland/fantasy-lenses](https://github.com/fantasyland/fantasy-lenses)
* [flunc/optics](https://github.com/flunc/optics)
* [gcanti/monocle-ts](https://github.com/gcanti/monocle-ts)
* [hallettj/safety-lens](https://github.com/hallettj/safety-lens)
* [ochafik/es6-lenses](https://github.com/ochafik/es6-lenses)
* [phadej/optika](https://github.com/phadej/optika)
* [ramda/ramda-lens](https://github.com/ramda/ramda-lens)
* [thisismN/lentil](https://github.com/thisismN/lentil)
#### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#libraries-for-other-languages) Libraries for other languages
* [ekmett/lens](https://github.com/ekmett/lens)
* [julien-truffaut/Monocle](https://github.com/julien-truffaut/Monocle)
* [purescript-contrib/purescript-profunctor-lenses](https://github.com/purescript-contrib/purescript-profunctor-lenses)
* [xyncro/aether](https://github.com/xyncro/aether)
## [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#contributing) Contributing
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](https://gitter.im/calmm-js/chat) 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](https://help.github.com/articles/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.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#building) Building
The `prepare` script is the usual way to build after changes:
```bash
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:
```bash
npm run watch
```
It starts watching the source files and runs dist and docs builds and tests
after changes.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#testing) Testing
The [tests](./test/tests.js) in this library are written in an atypical manner.
First of all, the tests are written as strings that are `eval`ed. 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`](./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 need to also add a type contract
and a shadow implementation for the primitive.
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`.
### [≡](#contents) [▶](https://calmm-js.github.io/partial.lenses/#documentation) Documentation
The `docs` folder contains the generated documentation. You can open the file
locally:
```bash
open docs/index.html
```
To actually build the docs (translate the markdown to html), you can run
```bash
npm run docs
```
or you can use the watch
```bash
npm run watch
```
which builds the docs if you save `README.md`. The watch also runs
[LiveReload](http://livereload.com/) so if you have the plugin, your browser
will refresh automatically after changes.