partial.lenses

[ Tutorial | Reference | Background ]

This library provides a collection of Ramda compatible partial lenses. While an ordinary lens can be used to view and update an existing part of a data structure, a partial lens can view optional data, insert new data, update existing data and delete existing data and can provide default values and maintain required data structure parts.

In JavaScript, missing data can be mapped to undefined, which is what partial lenses also do. When a part of a data structure is missing, an attempt to view it returns undefined. When a part is missing, setting it to a defined value inserts the new part. Setting an existing part to undefined deletes it. Partial lenses are defined in such a way that operations compose and one can conveniently and robustly operate on deeply nested data structures.

Tutorial

Let's work with the following sample JSON object:

const data = { contents: [ { language: "en", text: "Title" },
                           { language: "sv", text: "Rubrik" } ] }

First we import libraries

import L from "partial.lenses"
import R from "ramda"

and compose a parameterized lens for accessing texts:

const textIn = language =>
  L.compose(L.prop("contents"),
            L.required([]),
            L.normalize(R.sortBy(R.prop("language"))),
            L.find(R.whereEq({language})),
            L.default({language}),
            L.prop("text"),
            L.default(""))

Take a moment to read through the above definition line by line. Each line has a specific purpose. The purpose of the L.prop(...) lines is probably obvious. The other lines we will mention below.

Querying data

Thanks to the parameterized search part, L.find(R.whereEq({language})), of the lens composition, we can use it to query texts:

> L.view(textIn("sv"), data)
"Rubrik"
> L.view(textIn("en"), data)
"Title"

Partial lenses can deal with missing data. If we use the partial lens to query a text that does not exist, we get the default:

> L.view(textIn("fi"), data)
""

We get this default, rather than undefined, thanks to the last part, L.default(""), of our lens composition. We get the default even if we query from undefined:

> L.view(textIn("fi"), undefined)
""

With partial lenses, undefined is the equivalent of empty or non-existent.

Updating data

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

> L.set(textIn("en"), "The title", data)
{ contents: [ { language: "en", text: "The title" },
              { language: "sv", text: "Rubrik" } ] }

Inserting data

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

> L.set(textIn("fi"), "Otsikko", data)
{ contents: [ { language: "en", text: "Title" },
              { language: "fi", text: "Otsikko" },
              { language: "sv", text: "Rubrik" } ] }

Note the position into which the new text was inserted. The array of texts is kept sorted thanks to the L.normalize(R.sortBy(R.prop("language"))) part of our lens.

Deleting data

Finally, we can use the same partial lens to delete texts:

> L.set(textIn("sv"), undefined, data)
{ contents: [ { language: "en", text: "Title" } ] }

Note that a single 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.default({language}) part of our lens composition. A L.default(value) lens works symmetrically. When set with value, the result is undefined, which means that the focus of the lens is to be deleted.

If we delete all of the texts, we get the required value:

> R.pipe(L.set(textIn("sv"), undefined),
         L.set(textIn("en"), undefined))(data)
{ contents: [] }

The contents property is not removed thanks to the L.required([]) part of our lens composition. L.required is the dual of L.default. L.default replaces undefined values when viewed and L.required replaces undefined values when set.

Note that unless required and default values are explicitly specified as part of the lens, they will both be undefined.

Exercise

Take out one (or more) L.required(...), L.normalize(...) or L.default(...) 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.

Shorthands

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

• L.compose(...) can be abbreviated as L(...),
• L.prop(string) can be abbreviated as string, and
• L.set(l, undefined, s) can be abbreviated as L.delete(l, s).

Systematic decomposition

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

const textIn = language =>
  L.compose(L.prop("contents"),
            L.required([]),
            L.normalize(R.sortBy(R.prop("language"))),
            L.find(R.whereEq({language})),
            L.default({language}),
            L.prop("text"),
            L.default(""))

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

• a lens for accessing the contents of a data object,
• a parameterized lens for querying a content object from contents, and
• a lens for accessing the text of a content object.

Furthermore, we could organize the lenses into an object following the structure of the JSON:

const M = {
  data: {
    contents: L("contents",
                L.required([]),
                L.normalize(R.sortBy(R.prop("language"))))
  },
  contents: {
    contentIn: language => L(L.find(R.whereEq({language})),
                             L.default({language}))
  },
  content: {
    text: L("text", L.default(""))
  }
}

Using the above object, we could rewrite the parameterized textIn lens as:

const textIn = language => L(M.data.contents,
                             M.contents.contentIn(language),
                             M.content.text)

This style of organizing lenses is overkill for our toy example. In a more realistic case the data object would contain many more properties. Also, rather than composing a lens, like 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.

Food for thought: BST as a lens

The previous example is based on an actual use case. In this section we look at a more involved example: BST, binary search tree, as a lens.

Binary search may initially seem to be outside the scope of definable lenses. However, the L.choose lens allows for dynamic construction of lenses based on examining the data structure being manipulated. Inside L.choose 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:

const binarySearch = key =>
  L(L.default({key}),
    L.choose(node =>
             key < node.key ? L("smaller", binarySearch(key)) :
             node.key < key ? L("greater", binarySearch(key)) :
                              L.identity))

const valueOf = key => L(binarySearch(key), "value")

This actually works to a degree. We can use the valueOf lens constructor to build a binary tree:

> const t = R.reduce((tree, item) => L.set(valueOf(item.key), item.value, tree),
                     undefined,
                     [{key: "c", value: 1},
                      {key: "a", value: 2},
                      {key: "b", value: 3}])
> t
{ smaller: { greater: { value: 3, key: 'b' }, value: 2, key: 'a' },
  value: 1,
  key: 'c' }

However, the above binarySearch lens constructor does not maintain the BST structure when values are being deleted:

> L.delete(valueOf('c'), t)
{ smaller: { greater: { value: 3, key: 'b' },
             value: 2,
             key: 'a' },
  key: 'c' }

How do we fix this? What we need is to normalize the data structure after changes. The L.normalize lens can be used for that purpose. Here is the updated binarySearch definition:

const binarySearch = key =>
  L(L.default({key}),
    L.normalize(node => {
      if ("value" in node)
        return node
      if (!("greater" in node) && "smaller" in node)
        return node.smaller
      if (!("smaller" in node) && "greater" in node)
        return node.greater
      return node
    }),
    L.choose(node =>
             key < node.key ? L("smaller", binarySearch(key)) :
             node.key < key ? L("greater", binarySearch(key)) :
                              L.identity))

Now we can also delete values from a binary tree:

> L.delete(valueOf('c'), t)
{ greater: { value: 3, key: 'b' }, value: 2, key: 'a' }

As an exercise you could improve the normalization to maintain some balance condition such as AVL.

Reference

Usage

The lenses and operations on lenses are accessed via the default import:

import L from "partial.lenses"

Operations on lenses

You can access basic operations on lenses via the default import L:

L.compose(l, ...ls)

L(l, ...ls) and L.compose(l, ...ls) both are the same as R.compose(lift(l), ...ls.map(lift)) (see compose) and compose a lens from a path of lenses.

For example:

> L.view(L("a", 1), {a: ["b", "c"]})
"c"

L.lens(get, set)

L.lens(get, set) is the same as R.lens(get, set) (see lens) and creates a new primitive lens.

L.over(l, x2x, s)

L.over(l, x2x, s) is the same as R.over(lift(l), x2x, s) (see over) and allows one to map over the focused element of a data structure.

For example:

> L.over("elems", R.map(L.delete("x")), {elems: [{x: 1, y: 2}, {x: 3, y: 4}]})
{elems: [{y: 2}, {y: 4}]}

L.set(l, x, s)

L.set(l, x, s) is the same as R.set(lift(l), x, s) (see set) and is also equivalent to L.over(l, () => x, s).

For example:

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

L.view(l, s)

L.view(l, s) is the same as R.view(lift(l), s) (see view) and returns the focused element from a data structure.

For example:

> L.view("y", {x: 112, y: 101})
101

Lifting

The idempotent lift operation is defined as

const lift = l => {
  switch (typeof l) {
  case "string": return L.prop(l)
  case "number": return L.index(l)
  default:       return l
  }
}

and is available as a non-default export. All operations in this library that take lenses as arguments implicitly lift them.

L.delete(l, s)

L.delete(l, s) is equivalent to L.set(l, undefined, s). With partial lenses, setting to undefined typically has the effect of removing the focused element.

For example:

> L.delete(L("a", "b"), {a: {b: 1}, x: {y: 2}})
{x: {y: 2}}

L.deleteAll(l, s)

L.deleteAll(l, s) deletes all the non undefined items targeted by the lens l from s. This only makes sense for a lens that

• can potentially focus on more than one item and
• will focus on undefined when it doesn't find an item to focus on.

For example:

> L.deleteAll(L.findWith("a"), [{x: 1}, {a: 2}, {a: 3, y: 4}, {z: 5}])
[{x: 1}, {y: 4}, {z: 5}]

Lenses

In alphabetical order.

L.append

L.append is a special lens that operates on arrays. The view of L.append is always undefined. Setting L.append to undefined has no effect by itself. Setting L.append to a defined value appends the value to the end of the focused array.

L.augment({prop: obj => val, ...props})

L.augment({prop: obj => val, ...props}) is given a template of functions to compute new properties. When viewing or setting undefined, the result is undefined. When viewing a defined object, the object is extended with the computed properties. When set with a defined object, the extended properties are removed.

L.choose(maybeValue => PLens)

L.choose(maybeValue => PLens) creates a lens whose operation is determined by the given function that maps the underlying view, which can be undefined, to a lens. The lens returned by the given function will be lifted.

L.filter(predicate)

L.filter(predicate) operates on arrays. When viewed, only elements matching the given predicate will be returned. When set, the resulting array will be formed by concatenating the set array and the complement of the filtered context. If the resulting array would be empty, the whole result will be undefined.

Note: An alternative design for filter could implement a smarter algorithm to combine arrays when set. For example, an algorithm based on edit distance could be used to maintain relative order of elements. While this would not be difficult to implement, it doesn't seem to make sense, because in most cases use of normalize would be preferable.

L.find(value => boolean)

L.find(value => boolean) operates on arrays like L.index, but the index to be viewed is determined by finding the first element from the input array that matches the given predicate. When no matching element is found the effect is same as with L.append.

L.findWith(l, ...ls)

L.findWith(l, ...ls) is defined as

L.findWith = (l, ...ls) => {
  const lls = L(l, ...ls)
  return L(L.find(x => L.view(lls, x) !== undefined), lls)
}

and basically chooses an index from an array through which the given lens, L(l, ...ls), focuses on a defined item and then returns a lens that focuses on that item.

L.firstOf(l, ...ls)

L.firstOf(l, ...ls) returns a partial lens that acts like the first of the given lenses, l, ...ls, whose view is not undefined on the given target. When the views of all of the given lenses are undefined, the returned lens acts like l.

Note that L.firstOf is an associative operation, but there is no identity element.

L.identity

L.identity is equivalent to R.lens(R.identity, R.identity) and is the identity element of lenses: both L(L.identity, l) and L(l, L.identity) are equivalent to l.

L.index(integer)

L.index(integer) or L(integer) is similar to R.lensIndex(integer) (see lensIndex), but acts as a partial lens:

• When viewing an undefined array index or an undefined array, the result is undefined.
• When setting an array index to undefined, the element is removed from the resulting array, shifting all higher indices down by one. If the result would be an array without indices (ignoring length), the whole result will be undefined.

L.normalize(value => value)

L.normalize(value => value) maps the value with same given transform when viewed and set and implicitly maps undefined to undefined. More specifically, L.normalize(transform) is equivalent to R.lens(toPartial(transform), toPartial(transform)) where

const toPartial = transform => x => undefined === x ? x : transform(x)

The main use case for normalize is to make it easy to determine whether, after a change, the data has actually changed. By keeping the data normalized, a simple R.equals comparison will do.

L.pick({p1: l1, ...pls})

L.pick({p1: l1, ...pls}) creates a lens out of the given object template of lenses. When viewed, 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. undefined is treated as the equivalent of empty or non-existent in both directions.

Note that, when set, L.pick simply ignores any properties that the given template doesn't mention. Note that the underlying data structure need not be an object.

L.prop(string)

L.prop(string) or L(string) is similar to R.lensProp(string) (see lensProp), but acts as a partial lens:

• When viewing an undefined property or an undefined object, the result is undefined.
• When setting property to undefined, the property is removed from the result. If the result would be an empty object, the whole result will be undefined.

L.replace(inn, out)

L.replace(inn, out), when viewed, replaces the value inn with out and vice versa when set. Values are compared using R.equals (see equals).

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 default and required:

L.default(out)

L.default(out) is the same as L.replace(undefined, out).

L.define(value)

L.define(value) is the same as L(L.required(value), L.default(value)).

L.required(inn)

L.required(inn) is the same as L.replace(inn, undefined).

Background

Motivation

Consider the following REPL session using Ramda 0.19.1:

> R.set(R.lensPath(["x", "y"]), 1, {})
{ x: { y: 1 } }
> R.set(R.compose(R.lensProp("x"), R.lensProp("y")), 1, {})
TypeError: Cannot read property 'y' of undefined
> R.view(R.lensPath(["x", "y"]), {})
undefined
> R.view(R.compose(R.lensProp("x"), R.lensProp("y")), {})
TypeError: Cannot read property 'y' of undefined
> R.set(R.lensPath(["x", "y"]), undefined, {x: {y: 1}})
{ x: { y: undefined } }
> R.set(R.compose(R.lensProp("x"), R.lensProp("y")), undefined, {x: {y: 1}})
{ x: { y: undefined } }

One might assume that R.lensPath([p0, ...ps]) is equivalent to R.compose(R.lensProp(p0), ...ps.map(R.lensProp)), but that is not the case.

With partial lenses you can robustly compose a path lens from prop lenses R.compose(L.prop(p0), ...ps.map(L.prop)) or just use the shorthand notation L(p0, ...ps).

Types

To illustrate the idea we could give lenses the naive type definition

type Lens s a = (s -> a, a -> s -> s)

defining a lens as a pair of a getter and a setter. The type of a partial lens would then be

type PLens s a = (Maybe s -> Maybe a, Maybe a -> Maybe s -> Maybe s)

which we can simplify to

type PLens s a = Lens (Maybe s) (Maybe a)

This means that partial lenses can be composed, viewed, mapped over and set using the same operations as with ordinary lenses. However, primitive partial lenses (e.g. L.prop) are not necessarily the same as primitive ordinary lenses (e.g. Ramda's lensProp).