What is "point free" style (in Functional Programming)?

Point-free style means that the arguments of the function being defined are not explicitly mentioned, that the function is defined through function composition.

If you have two functions, like

square :: a -> a
square x = x*x

inc :: a -> a
inc x = x+1

and if you want to combine these two functions to one that calculates x*x+1, you can define it "point-full" like this:

f :: a -> a
f x = inc (square x)

The point-free alternative would be not to talk about the argument x:

f :: a -> a
f = inc . square

A JavaScript sample:

//not pointfree cause we receive args
var initials = function(name) {
  return name.split(' ').map(compose(toUpperCase, head)).join('. ');
};

const compose = (...fns) => (...args) => fns.reduceRight((res, fn) => [fn.call(null, ...res)], args)[0];
const join = m => m.join();

//pointfree
var initials = compose(join('. '), map(compose(toUpperCase, head)), split(' '));

initials("hunter stockton thompson");
// 'H. S. T'

Reference

Point free style means that the code doesn't explicitly mention it's arguments, even though they exist and are being used.

This works in Haskell because of the way functions work.

For instance:

myTake = take

returns a function that takes one argument, therefore there is no reason to explicit type the argument unless you just want too.

The best explanation for this is in Haskell wiki (excerpt below), pointed out by Petr in a comment.

In the declaration

f x = x + 1

we define the function f in terms of its action on an arbitrary point x. Contrast this with the points-free version:

f = (+ 1)

where there is no mention of the value on which the function is acting.

The point is a mathematical point (x above), hence "points-free" notation. The link gives more detail, if you need.

I can't make the javascript sample provided Brunno work, although the code illustrate pointfree idea (i.e. no arguments) clearly. So I use ramda.js to provide another example.

Say I need to find out the longest word in a sentence, given a string "Lorem ipsum dolor sit amet consectetur adipiscing elit" I need output something like { word: 'consectetur', length: 11 }

If I use plain JS style code I will code like this, using a map and a reduce function

let str = 'Lorem ipsum dolor sit amet consectetur adipiscing elit'
let strArray = str.split(' ').map((item) => ({ word: item, length: item.length }))
let longest = strArray.reduce(
    (max, cur) => (cur.length > max.length ? cur : max), 
    strArray[0])
console.log(longest)

With ramda I still use a map & a reduce but I will code like this

const R = require('ramda')
let longest = R.pipe(
  R.split(' '),
  R.map((item) => ({ word: item, length: item.length })),
  R.reduce((max, cur) => (max.length > cur.length ? max : cur), { length: 0 })
)
let tmp = longest(str)
console.log(tmp)

I will argue that the gist of my ramda code is the pipe that chains my functions together and it makes my purpose more clearly. No need to create a temporary variable strArray is a bonus (if I have more than 3 steps in the pipe then it will become a real bonus).

Here is one example in TypeScript without any other library:

interface Transaction {
  amount: number;
}

class Test {
  public getPositiveNumbers(transactions: Transaction[]) {
    return transactions.filter(this.isPositive);

    //return transactions.filter((transaction: {amount: number} => transaction.amount > 0));
  }

  public getBigNumbers(transactions: Transaction[]) {
    // point-free
    return transactions.filter(this.moreThan(10));

    // not point-free
    // return transactions.filter((transaction: any) => transaction.amount > 10);
  }

  private isPositive(transaction: Transaction) {
    return transactions.amount > 0;
  }

  private moreThan(amount: number) {
    return (transaction: Transaction) => {
      return transactions.amount > amount;
    }
  }
}

You can see point-free style is more "fluent" and easier to read.