[Compose] 15. Applicative Functors for multiple arguments

Working our way backwards from solution to problem, we define an applicative functor, then use it to apply a function of multiple arguments.

For example we have this line of code:

const res = Box(x => x +).ap(Box())// Box(3);

We want to use a funciton 'ap' (apply) on Box. And x will be 2.

To define 'ap' function.

const Box = x =>
({
  chain: f => f(x),
  ap: other => other.map(x),
  map: f => Box(f(x)),
  fold: f => f(x),
  inspect: () => `Box(${x})`
})

So '

Box(x => x +1).ap(Box(2))

'

Can be translated to:

Box() => Box().map(x => x + );

This can be useful when apply curry function:

const res = Box(x => y => x + y).ap(Box()).ap(Box());
console.log(res.inspect()); //Box(3)

after apply .ap(Box(1)), it becomes to:

Box(y => 1 +y).ap(Box(2))

after apply .ap(Box(2)), it becomes to:

Box( + )

It ends up, we have a function and continue to using 'ap':

const add = x => y => x + y;
const res = Box(add).ap(Box()).ap(Box());

This partten is called click-functor!

The rule is:

F(val).map(fn) === F(fn).ap(F(val))

For example now we have:

const liftA2 = (fn, Fx, Fy) =>
  F(fn).ap(Fx).ap(Fy);

The problem is we don't know what 'F' it is here...

So what we can do is transform accorind to the rule we have:

const liftA2 = (fn, Fx, Fy) =>
  Fx.map(fn).ap(Fy)

Therefore we don't need to memtion any Functor.

Example:

const res2 = liftA2(add, Box(), Box());
console.log(res2.inspect()); //Box(3)

Applicate Functor is really good to work with Async functor, because async by natural, data arrives different time:

const add = x => y => z=> x + y + z;
const addAsyncNumbers = liftA3(add);
const res = addAsyncNumbers(
    Async.of(),
    Async((_, res) => {
        setTimeout(() => {
            console.log('resolve 2');
            res()
        }, )
}), Async((_, res) => {
    setTimeout(() => {
        console.log('resolve 3');
        res()
    }, )
}));
res.fork(e => console.error(e), x => console.log('async', x)) //