ES6 Curry and Function Composition

Currying in ES6: Exercises.

Questions:

1. What is currying?
2. What is partial application?
3. What is the difference between curry and partial application?
4. What is point-free style?
5. What is function composition?
6. How does currying help with function composition?

add2 (curried)

add2(a) => b => Number

Question: What does it mean to curry a function?

Given two numbers, a and b in curried form, return a Number which is the sum of a and b.

Usage

add2(2)(3); // 5

add3 (partially applied / autocurried)

add3(a) => b => c => Number

Questions:

1. What is partial application?
2. What is the difference between curry and partial application?

Given 3 numbers, curried or partially applied, return the sum of all 3 numbers.

Lodash and Ramda both supply curry functions that create auto-curried functions. Here's a function you can use to create add3:

// Tiny, recursive autocurry
const curry = (
  f, arr = []
) => (...args) => (
  a => a.length === f.length ?
    f(...a) :
    curry(f, a)
)([...arr, ...args]);

This curry utility takes a function that takes any number of arguments and returns a function that will curry or partially apply as necessary depending on how many arguments you pass in to the returned function.

Usage

add3(1, 2, 3); // 6
add3(1, 2)(3); // 6
add3(1)(2, 3); // 6
add3(1)(2)(3); // 6

inc (from add2)

inc(n) => Number

Question: What is point-free style?

Use add2() to create a new function that adds 1 to any number.

Your function should not have a reference to its argument in the function definition. In other words, it should be written in point free style. Write the function without using any of the following: =>, function, Function, eval.

Usage

inc(3); // 4

trace

trace(label: s) => (value: v) => v, effects(log to console)

Given a label and a value in curried form, log a message to the console using template literal notation:

label: value

Usage:

trace('inc')(inc(3)); // inc: 4

compose2

compose(f: Function, g: Function) => Function

Question: What is function composition?

Given two functions, f and g, return a new function representing the composition: f ∘ g (f after g).

Hint: In math notation, the application of f ∘ g is equivalent to (f ∘ g)(x) which is equal to f(g(x)). Where does x come from?

Usage:

const g = n => n + 1;
const f = n => n * 2;

const meaning = compose2(f, g);

meaning(20); // 42

compose

compose(...fns: [...Functions]) => Function

Question: How does currying help with function composition?

Given any number of functions, fns, e.g., f, g, h, etc..., return a new function representing the composition of all given functions from right to left. In other words, compose(f, g, h) represents the composition f ∘ g ∘ h.

Usage

const composed = compose(
  trace('after f'),
  f,
  trace('after g'),
  g
);

composed(20); // 42

Hint: You can use a reducer function, but Array.prototype.reduce() probably won't give you what you need. Is there another form of reduce you can use?

pipe

Pipe is exactly like compose, but instead of working from right to left, it works left to right.

pipe(...fns: [...Function]) => Function

Given any number of functions, fns, e.g., f, g, h, etc..., return a new function representing the composition of all given functions from left to right. In other words, pipe(f, g, h) represents the composition h ∘ g ∘ f.

Usage

const piped = pipe(
  f,
  trace('after f'),
  g,
  trace('after g')
);

piped(20); // 41