Functional JS with ES6 — Recursive Patterns

What’s the deal here?

Functional programming has been on the rise and is a topic that is very exciting to me. It allows me to write terse, declarative code that is easy to test and reason about. What is functional programming? I’ll defer that answer to someone with more knowledge on the subject, Eric Elliot:

Functional programming (often abbreviated FP) is the process of building software by composing pure functions , avoiding shared state, mutable data ,and side-effects. Functional programming is declarative rather than imperative , and application state flows through pure functions. Contrast with object oriented programming, where application state is usually shared and colocated with methods in objects.

ES6 brings many features that allow us to easily write pure functions, rest/spread being one of the most powerful. Using rest params, we’re able to “loop without loops” with recursion. In this article, we’re going to rewrite many commonly used JavaScript methods/functions that allow for functional patterns.

Preface

The following functions are for demonstration and learning purposes. Many functions below are tail-recursive and should be optimized further. Fixing tail-recursion is not the subject of this article. ES6 brings tail-call optimization, but must be used in conjunction with 'use strict' .

Head

Return the first item in an array. Is useful when you need to separate the first item from the rest of the array items. To do this, we make use of destructuring assignment.

const head = ([x]) => x

Example usage:

const array = [1,2,3,4,5]
head(array) // 1

Tail

Return all but the first item in an array.

const tail = ([, ...xs]) => xs

Which is essentially the same as writing:

const tail = ([x, ...xs]) => xs

Since we don’t need to use x in the returned output, we can drop it, but keep the comma to get the rest of the items in the array.

Example usage:

const array = [1,2,3,4,5]
tail(array) // [2,3,4,5]

Def

Return if argument supplied is defined.

const def = x => typeof x !== 'undefined'

Example usage:

const defined = 'this is defined'
def(defined) // true
def(doesntExist) // false

Undef

Return if argument supplied is undefined.

const undef = x => !def(x)

Example usage:

const defined = 'this is defined'
undef(defined) // false
undef(doesntExist) // true

Copy

Returns a copy of an array without using Array.slice(). Makes use of spread.

const copy = array => [...array]

Example usage:

let array = [1,2,3,4,5]
let copied = copy(array)
copied.push(6)

array // [1,2,3,4,5]
copied // [1,2,3,4,5,6]

Length

Return the length of an array. This is a very simple form of looping through an array with recursion, even though the values of the array don’t matter in this case (increments up starting at 1 for every item in array). We include the len param to avoid tail recursion.

const length = ([x, ...xs], len = 0) => def(x) ? length(xs, len + 1) : len

If we don’t care about tail recursion, we can write it as:

const length = ([x, ...xs]) => def(x) ? 1 + length(xs) : 0

This would add a stack frame for each item in the array, whereas the version that avoids tail recursion, replaces a single stack frame. If the array passed in is large enough, it will throw “Maximum call stack size exceeded”.

Example usage:

const array = [1,2,3,4,5]
length(array) // 5

Reverse

Return a reversed array.

const reverse = ([x, ...xs]) => def(x) ? [...reverse(xs), x] : []

Example usage:

const array = [1,2,3,4,5]
reverse(array) // [5,4,3,2,1]

Array.reverse() is okay, but it modifies the value in place which is a side-effect. Consider the following:

const array = [1,2,3,4,5]

const newArray = array.reverse() // [5,4,3,2,1]
array // [5,4,3,2,1]

// using the reverse method we just created
const array2 = [1,2,3,4,5]

const newArray2 = reverse(array2) // [5,4,3,2,1]
array2 // [1,2,3,4,5]

First

Returns a new array that contains the first n items of the given array.

const first = ([x, ...xs], n = 1) => def(x) && n ? [x, ...first(xs, n - 1)] : []

Example usage:

const array = [1,2,3,4,5]
first(array, 3) // [1,2,3]

Last

Returns a new array that contains the last n items of the given array.

const last = (xs, n = 1) => reverse(first(reverse(xs), n))

Example usage:

const array = [1,2,3,4,5]
last(array, 3) // [3,4,5]

Slice

Returns a new array with value inserted at given index.

const slice = ([x, ...xs], i, y, curr = 0) => def(x)
  ? curr === i
    ? [y, x, ...slice(xs, i, y, curr + 1)]
    : [x, ...slice(xs, i, y, curr + 1)]
  : []

Example usage:

const slice = ([x, ...xs], i, y, curr = 0) => def(x)
  ? curr === i
    ? [y, x, ...slice(xs, i, y, curr + 1)]
    : [x, ...slice(xs, i, y, curr + 1)]
  : []

isArray

Returns if the value supplied is an array. Allows us to write Array.isArray() in a more functional manner.

const isArray = x => Array.isArray(x)

Example usage:

const array = [1,2,3,4,5]
isArray(array) // true

Flatten

Combines nested arrays into a single array.

const flatten = ([x, ...xs]) => def(x)
    ? isArray(x) ? [...flatten(x), ...flatten(xs)] : [x, ...flatten(xs)]
    : []

Example usage:

const array1 = [1,2,3]
const array2 = [4,[5,[6]]]
flatten([array1, array2]) // [1,2,3,4,5,6]

Swap

Return a new array with 2 items swapped based on their index.

const swap = (a, i, j) => (
  map(a, (x,y) => {
    if(y === i) return a[j]
    if(y === j) return a[i]
    return x
  })
)

Example usage:

const array = [1,2,3,4,5]
swap(array, 0, 4) // [5,2,3,4,1]

Map

From MDN: “…creates a new array with the results of calling a provided function on every element in this array.”

const map = ([x, ...xs], fn) => {
  if (undef(x)) return []
  return [fn(x), ...map(xs, fn)]
}

Which can be simplified as:

const map = ([x, ...xs], fn) => def(x) ? [fn(x), ...map(xs, fn)] : []

Example usage:

const double = x => x * 2
map([1,2,3], double) // [2,4,6]

Filter

From MDN: “…creates a new array with all elements that pass the test implemented by the provided function.”

const filter = ([x, ...xs], fn) => {
  if (undef(x)) return []
  if (fn(x)) {
    return [x, ...filter(xs, fn)]
  } else {
    return [...filter(xs, fn)]
  }
}

Which can be simplified as:

const filter = ([x, ...xs], fn) => def(x) 
    ? fn(x)
        ? [x, ...filter(xs, fn)] : [...filter(xs, fn)]
    : []

Example usage:

const even = x => x % 2 === 0
const odd = x = !even(x)
const array = [1,2,3,4,5]

filter(array, even) // [2,4]
filter(array, odd) // [1,3,5]

Reject

The opposite of filter, returns an array that does not pass the filter function.

const reject = ([x, ...xs], fn) => {
  if (undef(x)) return []
  if (!fn(x)) {
    return [x, ...reject(xs, fn)]
  } else {
    return [...reject(xs, fn)]
  }
}

Example usage:

const even = x => x % 2 === 0
const array = [1,2,3,4,5]

reject(array, even) // [1,3,5]

Partition

Splits an array into two arrays. One whose items pass a filter function and one whose items fail.

const partition = (xs, fn) => [filter(xs, fn), reject(xs, fn)]

Example usage:

const even = x => x % 2 === 0
const array = [0,1,2,3,4,5]

partition(array, even) // [[0,2,4], [1,3,5]]

Reduce

From MDN: “…applies a function against an accumulator and each element in the array (from left to right) to reduce it to a single value.”

const reduce = ([x, ...xs], fn, memo, i) => {
  if (undef(x)) return memo
  return reduce(xs, fn, fn(memo, x, i), i + 1)
}

Which can be simplified as:

const reduce = ([x, ...xs], fn, memo, i = 0) => def(x)
    ? reduce(xs, fn, fn(memo, x, i), i + 1) : memo

Example usage:

const sum = (memo, x) => memo + x
reduce([1,2,3], sum, 0) // 6

const flatten = (memo, x) => memo.concat(x)
reduce([4,5,6], flatten, [1,2,3]) // [1,2,3,4,5,6]

ReduceRight

Similar to reduce, but applies the function from right-to-left.

const reduceRight = (xs, fn, memo) => reduce(reverse(xs), fn, memo)

Example usage:

const flatten = (memo, x) => memo.concat(x)

reduceRight([[0,1], [2,3], [4,5]], flatten, []) // [4, 5, 2, 3, 0, 1]

Partial

Partially apply a function by filling in any number of its arguments.

const partial = (fn, ...args) => (...newArgs) => fn(...args, ...newArgs)

Example usage:

const add = (x,y) => x + y
const add5to = partial(add, 5)

add5to(10) // 15

SpreadArg

Convert function that takes an array to one that takes multiple arguments. This is useful when partially applying.

const spreadArg = (fn) => (...args) => fn(args)

Example usage:

const add = ([x, ...xs]) => def(x) ? parseInt(x + add(xs)) : []
add([1,2,3,4,5]) // 15

const spreadAdd = spreadArg(add)
spreadAdd(1,2,3,4,5) // 15

If you only want to define a single function you can write it as:

const add = spreadArg(([x, ...xs]) => def(x) ? parseInt(x + add(...xs)) : [])
add(1,2,3,4,5) // 15

In the above, you need to remember to spread the array you are sending into the function recursively, since you are spreading the argument.

ReverseArgs

Reverse function argument order.

const reverseArgs = (fn) => (...args) => fn(...reverse(args))

Example usage:

const divide = (x,y) => x / y
divide(100,10) // 10

const reverseDivide = reverseArgs(divide)
reverseDivide(100,10) // 0.1

Reversing arguments can be useful when partially applying arguments. Sometimes you want to partially apply arguments at the end of the list, not those at the beginning. Reversing the arguments allows us to do that.

const percentToDec = partial(reverseDivide, 100)
percentToDec(25) // 0.25

Pluck

Extract property value from array. Useful when combined with the map function.

const pluck = (key, object) => object[key]

Example usage:

const product = {price: 15}
pluck('price', product) // 15

const getPrices = partial(pluck, 'price')
const products = [
  {price: 10},
  {price: 5},
  {price: 1}
]
map(products, getPrices) // [10,5,1]

Flow

Each function consumes the return value of the function that came before.

const flow = (...args) => init => reduce(args, (memo, fn) => fn(memo), init)

Example usage:

const getPrice = partial(pluck, 'price')
const discount = x => x * 0.9
const tax = x => x + (x * 0.075)
const getFinalPrice = flow(getPrice, discount, tax)

// looks like: tax(discount(getPrice(x)))
// -> get price
// -> apply discount
// -> apply taxes to discounted price

const products = [
  {price: 10},
  {price: 5},
  {price: 1}
]

map(products, getFinalPrice) // [9.675, 4.8375, 0.9675]

Compose

The same as flow, but arguments are applied in the reverse order. Compose matches up more naturally with how functions are written. Using the same data as defined for the flow function:

const compose = (...args) => flow(...reverse(args))

Example usage:

const getFinalPrice = compose(tax, discount, getPrice)

// looks like: tax(discount(getPrice(x)))

map(products, getFinalPrice) // [9.675, 4.8375, 0.9675]

Min

Return the smallest number in an array. Returns Infinity if array supplied is empty.

const min = ([x, ...xs], result = Infinity) => def(x)
    ? x < result
        ? min(xs, x)
        : result
    : result

Example usage:

const array = [0,1,2,3,4,5]

min(array) // 0

Max

Return the largest number in an array. Returns -Infinity if array supplied is empty.

const max = ([x, ...xs], result = -Infinity) => def(x)
    ? x > result
        ? max(xs, x)
        : max(xs, result)
    : result

Example usage:

const array = [0,1,2,3,4,5]

max(array) // 5

Factorial

Returns the factorial of a number. Uses an accumulator to allow replacing of stack frames to allow larger factorials to be returned.

const factorial = (x, acum = 1) => x ? factorial(x - 1, x * acum) : acum

Example usage:

factorial(5) // 120

Fibonacci

Returns the Fibonacci number at the given place.

const fib = x => x > 2 ? fib(x - 1) + fib(x - 2) : 1

Example usage:

fib(15) // 610

Quicksort

Sort an array from smallest to largest. This is done by re-ordering the array so that it contains two sub-arrays, one with smaller values, the other with larger values. The above steps are recursively applied to each sub-array until there are no arrays left, which is flatten to return a sorted array.

const quicksort = (xs) => length(xs)
  ? flatten([
    quicksort(filter(tail(xs), x => x <= head(xs))),
    head(xs),
    quicksort(filter(tail(xs), x => x > head(xs)))
  ])
  : []

This can also be implemented using partition , but requires variable assignment.

const quicksort = (array) => {
  if (!length(array)) return []
  const [less, more] = partition(tail(array), x => x < head(array))
  return flatten([quicksort(less), head(array), quicksort(more)])
}

Example usage:

const array = [8,2,6,4,1]

quicksort(array) // [1,2,4,6,8]

Everything as a Reduction

Many of the functions above can be converted into reductions, which should increase performance in most, if not all cases. This also shows the flexibility of the reduce function.

const reduce = ([x, ...xs], f, memo, i = 0) => def(x)
    ? reduce(xs, f, f(memo, x, i), i + 1) : memo

const reverse = xs => reduce(xs, (memo, x) => [x, ...memo], [])

const length = xs => reduce(xs, (memo, x) => memo + 1, 0)

const map = (xs, fn) => reduce(xs, (memo, x) => [...memo, fn(x)], [])

const filter = (xs, fn) => reduce(xs, (memo, x) => fn(x)
    ? [...memo, x] : [...memo], [])

const reject = (xs, fn) => reduce(xs, (memo, x) => fn(x)
    ? [...memo] : [...memo, x], [])

const first = (xs, n) => reduce(xs, (memo, x, i) => i < n
    ? [...memo, x] : [...memo], [])

const last = (xs, n) => reduce(xs, (memo, x, i) => i >= (length(xs) - n)
    ? [...memo, x] : [...memo], [])

const merge = spreadArg(xs => reduce(xs, (memo, x) => [...memo, ...x], []))

const flatten = xs => reduce(xs, (memo, x) => x
    ? isArray(x) ? [...memo, ...flatten(x)] : [...memo, x] : [], [])

const add = spreadArg(([x, ...xs]) => reduce(xs, (memo, y) => memo + y, x))

const divide = spreadArg(([x, ...xs]) => reduce(xs, (memo, y) => memo / y, x))

const multiply = spreadArg(([x, ...xs]) => reduce(xs, (memo, y) => memo * y, x))

Example usage:

reverse([1,2,3]) // [3,2,1]
length([1,2,3]) // 3
map([1,2,3], double) // [2,3,4]
filter([1,2,3,4], even) // [2,4]
reject([1,2,3,4], even) // [1,3]
first([1,2,3,4], 3) // [1,2,3]
last([1,2,3,4], 2) // [3,4]
merge([1,2,3],[4,5,6]) // [1,2,3,4,5,6]
flatten([1,[2,3,[4,[5,[[6]]]]]]) // [1,2,3,4,5,6]
add(1,2,3,4,5) // 15
multiply(2,5,10) // 100
divide(100,2,5) // 10

Wrapping Up

I hope this article helps shed insight on some of the patterns made available with JavaScript and ES6. Many problems that can be solved with iteration/loops, can also be solved functionally through recursion. I hope this article was also able to show you the flexibility of the reduce function.

If you like this post and need help with an issue or are looking to hire a freelancer, I am available for React, Redux, and JavaScript work!