What is applicative functor:

the ability to apply functors to each other.

For example we have tow functors: Container(2), Container(3)

// We can't do this because the numbers are bottled up.
add(Container.of(), Container.of()); // NaN

We cannot just add two functors!

Instead we should do:

const map = (fn, m) => m.map(fn);
const containerOfAdd2 = map(add(), Container.of()); // Container(5)

or

Container.of().chain(two => Container.of().map(add(two)));

Previous solution should work. but there are better way to do it:

1. ap

Container.prototype.ap = function (otherContainer) {
return otherContainer.map(this.$value);
};

As you can see, 'ap' takes a fuctor then applya map to it.

We can see ap:

Container.of().map(add).ap(Container.of()); // Container(5)

Or, we add lift 'add(2)' into Container, then apply Container(3):

Container.of(add()).ap(Container.of()); // Container(5)

Because 'add' is partially  applied in add(2), when doing '.ap(Container.of(3))', we give the rest input '3' to it.

Now, we can define applicative functor in programming language:

An applicative functor is a pointed functor with an ap method

Note the dependence on pointed.

Laws behind:

F.of(x).map(f) === F.of(f).ap(F.of(x))

Main idea is: lift 'f' (function) into Functor, then 'ap' (apply) another Functor with the value (x).

Some example:

Maybe.of(add).ap(Maybe.of()).ap(Maybe.of()) // Just(5)
Task.of(add).ap(Task.of()).ap(Task.of()) // Task(5)

Equals:

Maybe.of(add()).ap(Maybe.of()) // Just(5)
Task.of(add()).ap(Task.of()) // Task(5)

More examples:

// Http.get :: String -> Task Error HTML

const renderPage = curry((destinations, events) => { /* render page */ });

Task.of(renderPage).ap(Http.get('/destinations')).ap(Http.get('/events'));
// Task("<div>some page with dest and events</div>")
// $ :: String -> IO DOM
const $ = selector => new IO(() => document.querySelector(selector)); // getVal :: String -> IO String
const getVal = compose(map(prop('value')), $); // signIn :: String -> String -> Bool -> User
const signIn = curry((username, password, rememberMe) => { /* signing in */ }); IO.of(signIn).ap(getVal('#email')).ap(getVal('#password')).ap(IO.of(false));
// IO({ id: 3, email: 'gg@allin.com' })

----

const R = require('ramda');

class Container {
static of(x) {
return new Container(x);
} constructor(x) {
this.$value = x;
} map (fn) {
return Container.of(fn(this.$value));
} ap (functor) {
return functor.map(this.$value);
} join() {
return this.$value;
} chain(fn) {
return this.map(fn).join();
} inspect() {
return `Container(${this.$value})`;
}
} class Maybe {
get isNothing() {
return this.$value === null || this.$value === undefined;
} get isJust() {
return !this.isNothing;
} constructor(x) {
this.$value = x;
} inspect() {
return this.isNothing ? 'Nothing' : `Just(${this.$value})`;
} // ----- Pointed Maybe
static of(x) {
return new Maybe(x);
} // ----- Functor Maybe
map(fn) {
return this.isNothing ? this : Maybe.of(fn(this.$value));
} // ----- Applicative Maybe
ap(f) {
return this.isNothing ? this : f.map(this.$value);
} // ----- Monad Maybe
chain(fn) {
return this.map(fn).join();
} join() {
return this.isNothing ? this : this.$value;
} // ----- Traversable Maybe
sequence(of) {
this.traverse(of, identity);
} traverse(of, fn) {
return this.isNothing ? of(this) : fn(this.$value).map(Maybe.of);
}
} const add = a => b => a + b;
const map = (fn, m) => m.map(fn);
const notWorking = add(Container.of(2), Container.of(3));
const containerOfAdd2 = map(add(3), Container.of(2));
console.log(containerOfAdd2); // Contianer(5) const works = Container.of(2).chain(v => Container.of(3).map(add(v)));
console.log(works); // Contianer(5) const ap = Container.of(2).map(add).ap(Container.of(3));
console.log(ap) const ap2 = Container.of(add(2)).ap(Container.of(3));
console.log(Maybe.of(add).ap(Maybe.of(2)).ap(Maybe.of(3)))
console.log(Maybe.of(add(2)).ap(Maybe.of(3)))

  

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