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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Top comments (7)
If you don't care for readability, you can write it as a tiny on-liner :
It nice to have such power in one line.
I believe that this concept is called "Currying" : en.wikipedia.org/wiki/Currying
FP 101 - Currying vs. Partial application
Currying is converting one function of arity
nintonfunctions of arity one.There is no requirement that partial application be bound to a particular arity (one, in the case of currying), it simply states that if you call a function with only some of the arguments - you get back another function "binds" or "fixes" the arguments that you passed in, as demonstrated by the author here. It's a very prevalent concept in FP languages like Haskell.
Thanks for clarifying this! I did do my research before deciding what keyword to use. I also thought curry is the same as partial function application. It's great someone could verify my word choice! :D
If nothing else, it forces you to think in ways you wouldn't otherwise. I believe Larry Wall (creator of Perl) recommends Haskell as an "academic" language for this reason :)
It can be useful if you design a library and you are thinking on the proper api. It can be combined for example with fluent interface:
x(a).y(b)(c)etc. So it is good only for sugar syntax.I used partial function with elm-lang.
Thanks for sharing !!