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Redux Selectors are Applicative Functors

What that means and why it matters.

March 11, 2019
javascriptreduxfunctorapplicativefunctional programming

Redux selector functions are applicative functors. Why does this matter? If we can express our selectors as an applicative functor in a standardized way (wrt the static-land standard), we can leverage a whole suite of reusable code for free (from the fp-ts library), replacing some of the specialized code from reselect!

Prerequisites: typescript, generics, and higher order functions.

The shape of a selector

Redux selectors are functions from state to some other value. This can be expressed in a type like:

type Selector<State, A> = (state: State) => A;

Where State is the type of our app state and A is the type of value we're selecting out of the state. So, for example, a Selector<AppState, User> would represent a function that takes AppState as it's parameter, and returns a User. A Selector<AppState, Post[]> represents a function that takes in AppState and returns a list of Posts.

For example:

type AppState = { currentUser: User; posts: Post[] };

const selectCurrentUser: Selector<AppState, User> = state => state.currentUser;

// selectCurrentUser returns a 'User'
const currentUser: User = selectCurrentUser(currentAppState);

const selectPosts: Selector<AppState, Post[]> = state => state.posts;

// selectPosts returns an array of Posts
const posts: Post[] = selectPosts(currentAppState);

We can think of Selector<AppState, A> as a kind of "wrapper" around the A value, where in order to get that value, we need to pass in an object with type AppState.

Selectors are Functors

All functors are generic (which means they have a type parameter), and have a function called map which takes a function that takes that generic value and returns a different value, thus changing or "mapping" the type of the generic value.

So, in order for Selector<State, A> to be a functor, it must have a map method which takes a function from A to something else (B), and returns a Selector<State, B>. We can define this function as a free-standing static function, instead of defining it on the Selector type itself; this just means we'll invoke it like map(selectPosts, posts => ...) instead of => ...):

function map<State, A, B>(
  selector: Selector<State, A>,
  mapper: (a: A) => B
): Selector<B> {

This function takes a selector (State => A) and a function from A => B (a to b), and returns a selector (State => B). This function must work for any type of state, any type of A and any type of B. Take some time to try and implement this function (You'll likely learn something in the process)! If you get stuck, come back and look at an example usage for some inspiration. Hint: start with what you have to return, and work backwards from there.

The key is to remember that mapping over a selector just applies the passed callback on the result of the selector.

Side track:
Why did we define map as a plain static method? why not have a Selector class where each instance has a .map method?

Functionally, there is no difference between:

map(postsSelector, posts => posts.length);

and => posts.length);

Both of these are viable ways of expressing a 'functor'. In fact, the second example is how fantasy-land specifies how a functor should behave.

static-land is an alternative standard to fantasy-land which prefers the first form. One benefit to this approach is that you can define functors for types that you don't own.

Where would this map function be useful in practice? Consider if we had a selector that selects the recent posts out of the app state:

const postSelector: Selector<AppState, Posts[]> = state => state.posts;

Suppose that we wanted a new selector, which only selected the count of all posts. We could create a new selector:

const postCountSelector: Selector<number> = state => state.posts.length;

This would duplicate the logic for getting the posts out of state (a trivial example, for simplicity). Instead, we could reuse the postsSelector, and map over the result of that selector, returning just the size of the posts array:

const postCountSelector = map(postsSelector, posts => posts.length);

See the second parameter to map? That's the callback function that takes the result of the postsSelector and returns something else, thus 'mapping' the value inside. We had a Selector<..., Post[]> and we mapped that into a Selector<.., number>.

Selectors are Applicatives

The term 'applicative functor' is often shorthanded to 'applicative.' Both mean the same thing.

All applicatives are also functors.

An Applicative has a method called ap which takes a wrapped value A and a wrapped function A => B, and returns a B. It's very similar to map, except that the callback function you pass is itself wrapped in the wrapper type. For our Selector type, this looks like:

function ap<State, A, B>(
  aSelector: Selector<State, A>,
  abSelector: Selector<State, (a: A) => B>
): Selector<B> {

Think on this for a little bit: It takes two wrappers, Selector<..., A> and Selector<..., A => B> but yet only returns one Selector<..., B>. So this ap function must include a way to compose selectors! With that information, try to implement this ap function which combines two selectors. Remember, start with the return type and work backwards from there.

How are applicatives useful? Using the ap and map methods, we can derive another method that maps over two wrappers of anything simultaneously, For example, given a wrapper type (Wrapper), we can make a method combine2 which takes two wrappers, Wrapper<A> and Wrapper<B>, and composes them into a Wrapper<[A, B]> ("Wrapper" here, just refers to any applicative type, it could be Option, List, or even our Selector).

For selectors, this would look like:

function combine2<State, A, B>(
  aSelector: Selector<State, A>,
  bSelector: Selector<State, B>
): Selector<State, [A, B]> {

Try to implement combine2 using only our ap and map functions we built above.

This same strategy can be used to implement combine3, combine4, etc, all the way to combineN. The fp-ts library provides this combineN function for us for free (we just need to implement ap and map)! This function is called sequenceT, and you'd use it like:

import { sequenceT } from "fp-ts/lib/Apply";

const abcSelector: Selector<State, [A, B, C]> =
  sequenceT(...)(aSelector, bSelector, cSelector)

aSelector, bSelector and cSelector are all composed into abcSelector (I'll explain the ... further down)!

It turns out this pattern is incredibly powerful, and you have undoubtedly already used this without knowing it. Consider Promise.all; what does it's signature look like? It takes a unbound list of promises, and returns promise of a list, thus "composing" all the promises in the list:

const abcPromise = Promise.all([aPromise, bPromise, cPromise]);

can you see the resemblance to our selector example?

const abcSelector = sequenceT(...)(aSelector, bSelector, cSelector)

The main difference is that Promise.all is specialized for promises, but sequenceT works for all applicatives!


In fp-ts, a type is considered an applicative if a static instance of the Applicative interface exists for that type. Instead of having a class implement an interface, fp-ts makes you implement all of the methods on a separate object. For our Selector type we need map, ap, and of (of just takes a static value and puts it into our wrapper type).

Our selector typeclass would look like:

type Selector<State, A> = (s: State) => A;
export const URI = "Selector";

export const selector: Applicative2<URI> = {
  of<State, A>(a: A) {
    return () => a;
  map<State, A, B>(aSelector: Selector<State, A>, ab: (a: A) => B) {
    return (state: State) => {
      const a = aSelector(state);
      const b = ab(a);
      return b;
  ap<State, A, B>(
    abSelector: Selector<State, (a: A) => B>,
    aSelector: Selector<State, A>
  ): Selector<State, B> {
    return (state: State) => {
      const ab = abSelector(state);
      const a = aSelector(state);
      return ab(a);

The selector constant is an instance of the Applicative typeclass, but it's completely divorced from our Selector type itself; this makes it a "typeclass." While this is a bit more clumsy/verbose than the dot notation you're probably used to (i.e., it has one major benefit; you can define a typeclass for any type, even types that come from a completely different package, including the standard library types (looking at you, promises)! This means that if a library doesn't specify the functor or applicative behavior for their type, you can simply define it on a typeclass that you make yourself, instead of having to wrap the type in another class that you make.

Since we have access to this selector typeclass, this means we can consider our Selector class as an applicative. Whenever a function needs to work for any applicative they simply take an instance of an applicative typeclass. sequenceT is an example of such a function, and so if we want to use it with our Selector type, we just supply the selector typeclass value (filling in the "..." from before):

const abcSelector = sequenceT(selector)(aSelector, bSelector, cSelector);

This works for any applicative; consider the need to compose many optional values into one optional value. We can just use the option typeclass provided by fp-ts:

import { option } from "fp-ts/lib/Option";

const abcOption = sequenceT(option)(aOption, bOption, cOption);

createSelector from reselect is just map + sequenceT

Consider the shape of the createSelector method that reselect provides:

  (a, b, c) => {

It takes n selectors and allows you to compose them, finally providing you with a function to map the selected values into the value returned from a new selector.

This pattern can be emulated using the sequenceT method from fp-ts and the map function we implemented above:

const mapped =
  ([a, b, c]) => {

Remember: selector is an instance of our typeclass, not an actual instance of a selector. Also note that in the fp-ts example, a, b, and c's types are properly inferred.

The reselect version is less characters, but it's implemented specifically for selectors. In the fp-ts example, it was provided for us for free! We just needed to describe how two selectors are combined, and the library takes care of the rest for us.

Why go through all this trouble?

It can be hard at first to see these patterns in code you're using and writing. The only advice I can give is to learn as many examples of functors, applicatives, and monads that you can. Don't just read materials, bust out an editor, where you can quickly try out these concepts and verify what you're reading. I'm sure you'd be surprised how quickly you can gain an intuition.

One of the biggest benefits that comes from recognizing these patterns is that you'll find new ways to use your types. For example, if you were only exposed to the reselect library, you might not realize that you can turn an array of selectors into a selector of array. If you had an intuition around applicatives, this becomes easier to recognize, and in turn you'll be rewarded with a bunch of reusable code.