Map, filter, and reduce are useful tools that facilitate a coding ethos known as Functional Programming.

Functional programming is a paradigm in which we create programs using expressions and declarations rather than statements.

const cats=[ //expression
  { name: 'fluffy', age:10 },
  { name: 'charles', age:14 },
  { name: 'earl', age:1 },
  { name: 'antoinette', age:3 }
];
//declaration
let catsAfterFiveYears = cats.map(cat=>Object.assign({}, cat, {age:cat.age+5}));

Writing this code using a statement would iterate through with a for loop like this:

//statement
function insteadOfUsingMap() {
  var nextCats=[];
  for (var i=0;i<cats.length;i++) {
    let thisCat=cats[i];
    thisCat.age+=5;
    nextCats.push(thisCat);
  }
  return nextCats;
}

let catsAfterFiveYears = insteadOfUsingMap();

Both pieces of code work. But imagine what would happen if we wanted to tweak the code slightly. The FP approach is more maintainable, and it’s easy to see at a glance what is going on. Also, it is not prone to typos (what if you accidentally mutate your for loop variable, for instance).

So what does it look like?

map, filter, and reduce enable programming in an FP style. A good way to understand what a function is doing is to see how it is invoked and then try to mimic its behavior by coding it yourself. That’s what we’ll do, as well as provide a few examples of how the built-in functions can be used.

Map and filter both take a callback function that is passed these parameters:

  • the current element (required)
  • the index of the element in the array (optional)
  • the array that is being mapped over (optional)
  • a value to use as this when executing the function (optional)

Map

Map applies a function to every element of an array and returns an array containing the results of these applications. In FP, it is often called “apply-to-all”.

Here are some examples.

[1,2,3,4,5].map(num=>num*2);
//[2, 4, 6, 8, 10]
multiply every element by two
[1,2,3,4,5].map((num,idx)=>idx%2!==0 ? num*2 : num);
//[1, 4, 3, 8, 5]
multiply every odd-indexed element by two
[1,2,3,4,5].map((num,idx,arr)=>(idx!==0&&idx<arr.length-1) ? num*2 : num);
//[1, 4, 6, 8, 5]
multiply every element (except the first and last) by two

We can also apply the array’s map to other types, like strings.

'fluffykins'.map(e=>e) gives us a TypeError, because strings do not have a map function. But we can apply array map’s function to strings, like this:

Array.prototype.map.call('fluffykins', (letter)=>{
  return String.fromCharCode(letter.charCodeAt()+1);
}).join("");
//"gmvggzljot"
shift every letter of a string one to the “right” in the alphabet

Map can also be chained: for example, to operate on nested arrays.

[[1,2],[3,4],[5]].map(subArray=>{
  return subArray.map((e, idx, arr)=>arr.length>1 ? e*2 : e)
});
//[[2,4],[6,8],[5]]
multiply each element of every nested array by two if it contains more than one element

Let’s write our own map.

function myOwnMap(array, callback, thisArg) {
    thisArg = thisArg || null;
    let results=[];
    for (var idx=0;idx<array.length;idx++) {
      results.push(callback.apply(thisArg,[array[idx],idx,array]));
    }
    return results;
}

Note what map’s doing: it’s taking this iteration over the elements and wrapping it up into a function that we only have to write once. We can then re-use that function with more complex logic (checking indices, comparing elements) or more complex data types (arrays of objects with many interrelated keys) without worrying about the low-level implementation.

myOwnMap([1,2,3,4,5], (num,idx,arr)=>(idx!==0&&idx<arr.length-1) ? num*2 : num);
//[1, 4, 6, 8, 5]

Nice!

Filter

Filter tests every element of an array against a callback function, returning all elements that pass the test. In FP, it is often called “remove-if”.

Filter passes its callback functions the same parameter as map. The only difference is that instead of returning a result array with the callback’s return value, it returns a result array with the elements for which the callback’s return value is true.

Here are some examples.

const firstFibs=[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233];
const fibsUnder100 = firstFibs.filter(fNum=>fNum<100);
//[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
Fibonacci numbers under 100 from a larger list
const numbers=[1,2,3,4,5,6,7,8,9,10];
const middle8 = numbers.filter((num,idx,arr)=>(idx!==0&&idx<arr.length-1));
//[2, 3, 4, 5, 6, 7, 8, 9]
filter out the first and last numbers from an array
const mixedTypes=[1,'3',{obj:'a'},77,'cats','cute cats','misc text'];
const onlyStrings = mixedTypes.filter(e=>typeof e==='string')
//["3", "cats", "cute cats", "misc text"]
extract strings from an array

Filter can also be chained.

const mixedTypes=[1,'3',{obj:'a'},77,'cats','cute cats','misc text'];
const onlySingleWordStrings = mixedTypes
.filter(e=>typeof e==='string')
.filter(e=>e.split(" ").length===1)
//["3", "cats"]
extract strings from an array that only have a single word (no spaces)

Let’s write our own filter.

function myOwnFilter(array, callback, thisArg) {
    thisArg = thisArg || null;
    let results=[];
    for (var idx=0;idx<array.length;idx++) {
      let result = callback.apply(thisArg,[array[idx],idx,array]);
      if (result) { // if element meets conditions
        results.push(array[idx]);
      }
    }
    return results;
}

It works!

myOwnFilter([1,2,3,4,5], e=>e>2)
//[3,4,5]

Reduce

Reduce takes an array of elements and reduces them to a single element, following the rule given by the callback function supplied. Reduce also takes an optional initialValue, the value of the accumulator before any operations are performed. It is often used to sum/multiply/subtract/divide.

In FP, reduce is known as fold.

Reduce passes its callback different parameters than map and filter.

  • accumulator -> holds result of all previous reduce calls, or initialValue, if provided (required)
  • currentValue -> the current value being processed (required)
  • currentIndex -> the index of currentValue (optional)
  • the array that reduce is being called upon (optional)

It is also passed the optional parameter initialValue.

Here are some examples.

[1,2,3,4,5].reduce((acc,ele)=>acc+=ele, 0);
//15
sum all the numbers in an array

Note the use of the initialValue. This is important. Imagine we try to reduce an empty array.

[].reduce((acc,ele)=>acc+=ele);

If we do not supply an initial value, we’ll get this error:

VM70:1 Uncaught TypeError: Reduce of empty array with no initial value
    at Array.reduce (<anonymous>)
    at <anonymous>:1:4

Reduce is trying to add nothing to nothing.

  • acc is undefined, since at the beginning, it is equal to intialValue
  • ele is undefined, since the array contains no elements. What’s undefined+undefined?
[1,2,3,4,5].reduce((acc,ele,idx)=>idx%2!==0 ? acc+=ele : acc, 0);
// 6
sum every odd-indexed element
[1,2,3,4,5].reduce((acc,ele,idx,arr)=>(idx!==0&&idx<arr.length-1) ? acc+=ele : acc,0)
// 9
sum all but the first and last element

Unlike map and filter, there is not an application for chaining reduce, since its end product is a single value from many values: a mapping from many-to-one.

Let’s write our own reduce.

function myOwnReduce(array, callback, initialValue) {
  let acc=initialValue;
  for (var idx=0;idx<array.length;idx++) {
    acc=callback.apply(null,[acc, array[idx], idx, array]);
  }
  return acc;
}

It works the same way.

myOwnReduce([1,2,3,4,5],(acc,ele,idx)=>idx%2!==0 ? acc+=ele : acc, 0);
// 6

What about dot notation?

Our methods can be chained by functional composition, but not with dot notation.

If you wanted to write your own dot-chainable methods, see this. The reason that we are able to chain the native .map is because it is a prototype method of the Array object.

You can but should not “monkey patch” built-in JS methods in this way:

Array.prototype.myOwnMap = function(callback, thisArg) {
    thisArg = thisArg || null;
    let results=[];
    for (var idx=0;idx<this.length;idx++) {
      results.push(callback.apply(thisArg,[this[idx],idx,this]));
    }
    return results;
}

Note that this is identical to our myOwnMap function, except instead of taking an array argument, it uses this to refer to the array it is operating on (itself).

Then we could do this:

[1,2,3,4,5].myOwnMap(e=>e*10).myOwnMap(e=>e/5)
//[2,4,6,8,10]

However, monkey-patching is almost never a good idea, nor is it a good idea to define a “special” map behavior for your own objects. If you need a special behavior that uses map, write a function that describes the behavior and use map inside of it. It would be an especially bad idea to modify Array.prototype.map directly, since every other instance in your code that uses map will be effected, almost certainly for the worse.

These are tenets of functional programming: create functions that do not create side-effects. Create small and maintainable functions that can be composed to create larger functions.

Bring it all together: Calculating Standard Deviation

Standard deviation is a common tool used to measure variance from a mean, assuming a normally distributed set of data. We’ll write a function using map, reduce, and filter to calculate the standard deviation of a set of data, excluding data that lies outside the bounds passed to the function.

function standardDeviation(data, lowerBound, upperBound) {
    lowerBound = lowerBound || Math.min(...data);
    upperBound = upperBound || Math.max(...data);
    let filteredData=data.filter(e=>(e>=lowerBound&&e<=upperBound));
    let average=filteredData.reduce((acc,ele)=>acc+=ele,0)/filteredData.length;
    let numerator=filteredData.map(e=>{
      return Math.pow((e-average),2);
    }).reduce((acc,ele)=>acc+=ele,0);
    //don't divide by zero
    let denominator=filteredData.length-1;
    if (denominator<=0) { return 0; }
    let division=numerator/denominator;
    return Math.sqrt(division);
}

We can use the ES6 spread operator with Math.min() and Math.max() to cleanly set default lower and upper bounds to the extent of the dataset, if no bounds are provided. Then, we just compose our previous functions to calculate the sample standard deviation using this formula:

Formula for sample standard deviation from Wikipedia

TIL

Today we learned about map, filter, and reduce, higher-order functions that facilitate FP.

One goal of functional programming is to create code that can be reused. This means coding small, functional units that can be composed in different ways to produce different results. This makes code easier to reason about, test, and debug.

Try to identify places in your code where you can utilize a functional approach. If you’re interested more, try playing with Haskell…see Learn You a Haskell For Great Good for a fun starting point.