# Currying reimagined

··

## What is currying? #

Currying is the process of transforming a function that takes multiple arguments in a tuple as its argument, into a function that takes just a single argument and returns another function which accepts further arguments, one by one

E.g. it’s process of converting funtion like that:

const func = (x, y, z) => [x, y, z];
func(1, 2, 3) === [1, 2, 3];

to

const func = (x) => (y) => (z) => [x, y, z];
func(1)(2)(3) === [1, 2, 3];

Other way to see it is those two representation are equivalent. As well as those:

const func = (x, y) => (z) => [x, y, z];
const func = (x) => (y, z) => [x, y, z];

Which brings us to “auto-currying” or partial application. Imagine if you provided not enough arguments for a function call, like this

const func = (x, y, z) => [x, y, z];
func(1, 2);

The system can automatically transform function to equivalent function, which takes the required number of arguments and call it with given arguments

// original function transformed to (x, y) => (z) => [x, y, z];
// where x = 1 and y = 2
// so the final version is (z) => [1, 2, z];
func(1, 2)(3) === [1, 2, 3];
// the same as
func(1)(2, 3) === [1, 2, 3];

Historical note: Currying and curried functions are named after Haskell B. Curry. While Curry attributed the concept to Schönfinkel, it had already been used by Frege (citation needed).

## Practical usage #

From practical point of view partial application requires less boilerplate (less closures). For example, if we have following code:

// Let's assume we have a sort function similar to this
const sort = (comparator, arr) => arr.sort(comparator);
// but we can't change implementation, for example,
// imagine it works with a linked list instead of JS array
const sortIncrementaly = (arr) => sort((x, y) => x - y, arr);

With partial application this code requires less boilerplate:

const sortIncrementaly = sort((x, y) => x - y);

## Discomfort points #

Currying and partial application have the following discomfort points:

1. It relies on positional arguments e.g. (1, 2, 3) instead of named arguments (x: 1, y: 2, z: 3)
2. It needs the “subject” argument to be the last one in the list of arguments

Positional arguments are hard to remember (especially if there are more than 2 of them). For example, without looking into the manual, can you tell what the second argument stands for:

JSON.stringify(value, null, 2);

It is easier to work with named params:

JSON.stringifyNamedParams({ value, replacer: null, space: 2 });

Functions with the “subject” argument, in the end, works better for currying. For example, lodash’es and underscore’s map function:

_.map(arr, func);

doesn’t work with _.curry out of the box. There is _.curryRight and _.curry with placeholders. It would work better if arguments would be another way around (_.map(func, arr)).

## Reimagine #

Currying, as idea, came from math, which has rigid idea of function. In programming we have more “free” definition. We can have:

• optional arguments: (x, y = 2) => ...
• varied length of arguments: (x, ...y) => ...
• named arguments: ({ x, y }) => ...

How would currying work for named params?

const func = ({ x, y, z }) => [x, y, z];
const curriedFunc = curry(func);
curriedFunc({ x: 1 })({ y: 2 })({ z: 3 }); // [1, 2, 3]
curriedFunc({ z: 3 })({ y: 2 })({ x: 1 }); // [1, 2, 3]
curriedFunc({ z: 3, y: 2 })({ x: 1 }); // [1, 2, 3]
// ...

There are no problems to remember the order of arguments. Arguments can be partially applied in any order.

Just for fun I implemented this function in JavaScript: source code

## Feedback? #

Would you use the partial application more if it would be natively supported in your programming language?