Update: Learn how to type PartiallyApplicable in TypeScript

TL; DR

const enablePartialApplication = (fn) => (...args) => {
    if (args.length >= fn.length) return fn(...args);
    return enablePartialApplication(fn.bind(null, ...args));
};

What is partial function application?

Partial function application describes the ability to partially apply some arguments to a function. Sounds abstract? Let's look at some example.

Let's say we have a function add which simply adds two numbers:

const add = (x, y) => x + y;
add(3, 5); // 8

If we only supply one argument, the result yields to NaN.

add(3) // basically equivalent to: add(3, undefined)
// -> 3 + undefined
// -> NaN

Pretty straightforward?

Some functional programming languages would handles this differently however. For example, if Haskell were to handle add(3), instead of executing the function body x + y, it will do something like the following:

// let's pretend haskell is running the following JavaScript
const addThreeTo = add(3);
// addThreeTo is basically the function: (y) => 2 + y
addThreeTo(5); // 8
// or simply
add(3)(5); // 8

// but we could still do
add(3, 5); // 8

Notice how we supply the second argument 5 by doing addThreeTo(5).

Haskell detects the number of arguments supplied. When it is less than what is expected in the function definition, instead of executing the function body, it returns another function that accepts the remaining arguments. This is called partial function application.

Okay. That's quite cool. But why do we need this? Well you don't. But it is something very convenient to have.

Imagine having a list of numbers and we wish to add 5 to each of them, without partial function application, we have to wrap an arrow function around add.

const add = (x, y) => x + y;
[1, 2, 3, 4, 5, 6].map(i => add(5, i));

However, with partial function application, we could do something like:

// let's pretend haskell is running the following JavaScript
const add = (x, y) => x + y;
[1, 2, 3, 4, 5, 6].map(add(5));

Arguments fixing

Partial function application can also be thought of as fixing arguments.

// let's pretend haskell is running the following JavaScript
const fn = (x, y, z) => (x * y) / z;
const fnFixedX = fn(3); // fixes x to 3: (y, z) => (3 * y) / z
fnFixedX(2, 1); // (3 * 2) / 1 -> 6

Or we could also fix x and y altogether.

// let's pretend haskell is running the following JavaScript
const fn = (x, y, z) => (x * y) / z;
const fnFixedXY = fn(3, 2); // fixes x to 3: (z) => (3 * 2) / z
fnFixedXY(1); // (3 * 2) / 1 -> 6

I hope you have understood what partial function application is by now. If not, read again before continuing.

Implementation

In the previous examples, we pretend that haskell is running the JavaScript in order to illustrate what partial function application is. Now can we actually implement something to enable partial function application in JavaScript? Yes we could!

Let's define a function enablePartialApplication(fn) which would return a function that we could use partial function application.

What we want to achieve:

const sum = enablePartialApplication((x, y) => x + y);
const sum3 = sum(3);
sum3(10); // 13
sum(3, 5); // 8
sum(3)(4); // 7

Another example:

const fn = enablePartialApplication((x, y, z) => (x * y) / z);
fn(3, 2, 1); // (3 * 2) / 1 -> 6
fn(3, 2)(1); // 6
fn(3)(2, 1); // 6
fn(3)(2)(1); // 6

Skeleton

The function input and output are obvious, so we could sketch the skeleton of our function:

const enablePartialApplication = (fn) => {
    return () => {

    };
};

Looking at the arguments

As I mention earlier, Haskell look at 1) the number of arguments passed in and 2) the number of arguments expected by the definition of the function to decide whether partial application is needed.

The first one is simple, we can just use the rest operator and take in the arguments as a list, then do .length() on it.

const enablePartialApplication = (fn) => {
    return (...args) => { // use rest operator to take arguments as a list
        args.length // number of arguments passed in
    };
};

The second one is also not that hard, we could use Function.length. See here for the documentation.

const enablePartialApplication = (fn) => {
    return (...args) => {
        args.length // number of arguments passed in
        fn.length // number of arguments expected by fn
    };
};

We know that it is a partial function application if args.length < fn.length, otherwise, i.e. args.length >= fn.length, it would just be a simple function invocation. So let's put this into our function:

const enablePartialApplication = (fn) => {
    return (...args) => {
        if (args.length >= fn.length) return fn(...args); // function invocation
        // partial function application here
    };
};

Fixing arguments with `Function.prototype.bind`

Recall the argument fixing analogy, does it remind you of some functions in JavaScript? Yes! Function.prototype.bind! We could fix arguments of a function with it!

const add = (x, y) => x + y;
const add3 = add.bind(null, 3); // the first argument is the thisArg
add3(5); // 8
add3.length; // 1

We could simply bind the input args to fn so that the bound function would expect the remaining arguments.

const enablePartialApplication = (fn) => {
    return (...args) => {
        if (args.length >= fn.length) return fn(...args);
        return fn.bind(null, ...args); // use Function.prototype.bind to fix arguments
    };
};

This implementation would allow us to do the following:

const sum = enablePartialApplication((x, y) => x + y);
const sum3 = sum(3);
sum3(10); // 13
sum(3, 5); // 8
sum(3)(4); // 7

const fn = enablePartialApplication((x, y, z) => (x * y) / z);
fn(3, 2, 1); // (3 * 2) / 1 -> 6
fn(3, 2)(1); // 6
fn(3)(2, 1); // 6

Awesome! However, the returned bound function do not support partial application. So the following would not work

const fn = enablePartialApplication((x, y, z) => (x * y) / z);
fn(3)(2)(1); // Trying to partially apply the function: fn(3)
// -> ((y, z) => (3 * y) / z)(2)(1)
// -> ((3 * 2) / undefined)(1)
// -> (NaN)(1)
// -> ERROR: NaN is not a function

Recursion

Now all we have to do, is make the bound function partially applicable. Easy! Recursivly call enablePartialApplication on it!

const enablePartialApplication = (fn) => {
    return (...args) => {
        if (args.length >= fn.length) return fn(...args);
        return enablePartialApplication(fn.bind(null, ...args)); // make the bound function partially applicable
    };
};

With this implementation, we could chain as much as we want!

const g = enablePartialApplication((a, b, c, d, e, f) => a + b - c * d / e ** f);
g(1, 2, 3, 4, 5, 6); // 2.999232
g(1, 2)(3, 4, 5)(6); // 2.999232
g(1)(2)(3)(4)(5)(6); // 2.999232
// ...

AWESOME!

Clean up

Notice our function enablePartialApplication returns another function immediately. We can therefore simplify this with:

const enablePartialApplication = (fn) => (...args) => {
    if (args.length >= fn.length) return fn(...args);
    return enablePartialApplication(fn.bind(null, ...args));
};

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How to make functions partially applicable in JavaScript