Building Expressive Monads in Javascript: Introduction

The monad is a powerful design pattern that, when used correctly, can completely change how you think about handling values in Javascript (JS). This introductory tutorial is for any level of JS familiarity, even (and perhaps, especially) beginners.

For those already familiar with monads, this introduction only covers the essentials for using monads effectively, and will only touch upon the origins and more technical language when necessary to give context. No attempts will be made to explain category theory or deep concepts of functional programming.

What does "monad" mean?

For the purposes of this introduction, I'd like to refer to the dictionary definition, which pre-dates its use in mathematics and programming: a single unit.

This definition is akin to dyad and triad - meaning two, or three units respectively.

The term "monad" is used differently in mathematics, and in category theory. For programming, the monad was made popular by Haskell, and has been transposed into various languages, including JS. It is used as a way of containing values and controlling mutations.

I think though that the definition of "a single unit" is good to keep in mind. It helps me, at least.

What problems do monads solve?

Any time you've had to deal with trying to keep track of value mutation, any compatible type of monad would have helped wrangle how the values are changing.

If you've struggled with null and undefined causing havoc in functions that can't handle them, a Maybe monad would solve that problem.

For myself, it helps break down value-altering processes into small steps, allowing me to think about one piece at a time, not worrying about values mutating in unexpected ways. One can focus better on individual functions more easily. The results are so much more predictable, and the steps in the process more testable.

Monads can even handle processes that are asyncronous, but for the purposes of this introduction, we're only going to focus on syncronous cases.

How is it used in Javascript?

A monad is best thought of as a container of a value: much like how the container-like types Array and Object can hold a collection of values, a monad does the same.

Each monad you build is like building a new kind of container-like type. As Array has methods like forEach, and as Object has methods like keys, a monad will have standard methods, and methods you can add on a case-by-case basis.

If you've used Array and Object, you've already got some experience that will be useful with monads.

The most basic monad: Identity

We'll start our first example with the most basic possible monad, an Identity monad.

First though, a quick note on monad naming and style conventions...

Before we begin to build an Identity monad, I'd like to make clear the naming and styles you'll see in this introduction. When first learning monads, I was quickly hung up on the names and styles. It was enough to slow me down quite a bit.

You'll see monads named with capital letters, often with rather abstract names.

Do not get too concerned with the naming; if an abstract name is confusing you, remember that it is said that "naming things is one of the hardest things in computer science". Often these names point to a particular established design pattern that may have multiple possible awkward-sounding names.

The monad names will be capitalized -- this is an established convention, my assumption is this is to demonstrate they are a special type, much like a class name.

The same will go with monad method names, the most common ones have many established names. When one is introduced, I'll mention other names you may find being used for the same method. I will aim to focus on whichever method name I feel is most expressive for someone new to monads, though opinions will likely differ.

Second, a quick note on the term "identity"...

One more brief side-note: the monad name Identity is based on a term "identity" used for a function which simply returns the value given to it. The Identity monad will effectively do the same. This may seem like a near-useless function (it doesn't do anything!) but it is great for giving the most basic example, and there are some actual use cases in functional programming.

For instance, if you are required pass a function as an argument to potentially alter a value, but wanted to ensure that function didn't actually alter the value in certain circumstances, an identity is a great way to do that.

Identity: the code

const Identity = x => ({
    emit: () => x,
    chain: f => f(x),
    map: f => Identity(f(x))
});

// example use:
const one = Identity(1);

Yes, that is all. Write something like the above, and you have written a monad. These are the three required methods.

Many tutorials will hand you a library and just show how to use monads, but I feel a hands-on approach is going to actually make it easier to understand the concept.

That all stated, this Identity monad, at 5 lines, has a lot going on. Let's break that down.

const Identity = x => ({ ... });

The simplest part: we'll be using const as we don't want our defintion to ever change. You might know or have heard that const isn't perfect at locking down mutations: if you use const to define an Array or Object, and those can subsequenly mutate.

Thankfully, we're assigning a function expression to our const, which I like to refer to as a Constant Function Expression (CFE). I prefer these over the standard function defintion as they prevent anyone ever meddling with the function prototypes.

If you look up monad libraries in JS often you will find them based upon function or class, which makes them susceptible to meddling.

Our value we're going to pass into the Identity monad is x, and the beauty of a CFE is that the arguments passed into it cannot ever be altered or changed: it is absolutely immutable without having to use any special APIs.

This is why I love this pattern for monads: in just a few lines with no advanced syntaxes it creates an absolutely immutible value!

Once we pass 1 as a value in, nothing can ever change that 1 was the value passed in. If we had used a class and stored the value in an accessor, without some special API usage we'd be able to something like myIdentity.__value = 2 and just change the value.

And while I have not tested this hypothesis, I would think this is the JS monad pattern with the least-possible memory footprint.

Let's start looking at the core methods.

Method: emit

Alternative names: join, value, valueOf

Code

emit: () => x,

Example use

console.log(one.emit());
// > 1

This is the simplest method, that just returns the value contained within. Most commonly known as join, however I find that quite unexpressive when it comes to learning in Javascript. I like emit for explaining what it does as a verb: emit the value contained within.

A quick note of warning though, emit isn't something you should necessarily depend on in anything but debugging. In fact, you won't see me use it at all in the primary examples.

Method: chain

Alternative names: flatMap, bind

Code

chain: f => f(x),

Example use

console.log(one.chain(a => a + 1));
// > 2

The next simplest method is chain, which is intended to chain various monads together, but can operate as demonstrated above.

f => f(x) indicates a function f is taken, and value x is passed to said function. In this example, a => a + 1 takes the value, returns it plus one.

A more typical usage may be:

one.chain(a => SomeMonad(a + 1));

Where SomeMonad is a monad. In this chain, we transform Identity(1) into SomeMonad(2). When you are using chain, typically you're indicating that the function you are passing in either will itself return a monad (preventing recursive monad-inside-monad-inside-monad...) or that you intend for the result to be non-monadic.

Don't worry too much about why right now, as this I find is less commonly useful as compared to the next method, map. But it is important to understand first before we look at map.

Method: map

Alternative name: fmap ("functional map")

Code

map: f => Identity(f(x))

Example use

console.log(one.map(a => a + 1));
// > [not pretty: outputs monad defintion... at least until we implement .inspect() below]

map is the most important method. This is what makes monads so useful: we can take an established monad Identity(1) and through a function, generate Identity(2) without any mutation of our example constant one.

Put simply, it is the chain function with a built-in rewrapping of the resulting value into a new Identity, which itself can be subject to map, chain, and emit on and on for as many functions you'd like to apply to it.

This is the method I most use in a monad.

I sometimes like to think of it like a bank account ledger. All values must be accounted for: where they started (.of), and how they changed over time (map & chain methods). The initial value of a monad is like a new bank account being opened with an initial deposit, each map or chain is a transaction atop it. Nothing will ever change the value of the initial deposit, but we have methods to figure out how much remains in the account today.

One more method: inspect

You may have noticed doing a console output of the value after a map isn't going to look pretty. While not strictly required to make a monad work correctly, inspect can help inform us via the console what exactly is in the monad, and what type of monad it is.

const Identity = (x) => ({
    chain: f => f(x),
    emit: () => x,
    map: f => Identity(f(x)),
    inspect: () => `Identity(${x})`
});

const one = Identity(1);
const two = one.map(a => a + 1);

console.log(two.inspect());
// > Identity(2)

This method is important in debugging as a simple emit would not give you the type Identity; just the contained value 2. This is very important when working with multiple monad types.

Lastly, adding a constructor

In all the examples above I have been calling directly Identity. Typically, however, there is a constructor method. In JS, the convention is to add an of constructor. This looks like:

const one = Identity.of(1);

This helps in a couple ways. One, of() is a very strong hint we're dealing with a monad, as there's probably nowhere else you'll see it.

Secondly, it'll allow you to do type-checking behaviour, should your monad have restrictions on what is passed into it.

Typically I handle this using import/export, as such:

const Identity = x => ({
    emit: () => x,
    chain: f => f(x),
    map: f => IdentityOf(f(x)),
    inspect: () => `Identity(${x})`
});

// you might do type-checking here
const IdentityOf = x => Identity(x);

const exportIdentity = {
    of: IdentityOf
}

// or module.exports
export {
    exportIdentity as Identity
}

// or require()
import { Identity } from './Identity.js`;

Enough examples from me, though. Time for you to give it a try.

Try it out: Identity Monad Example REPL

Let's make another monad: List

List is the typical name of an Array-like monad.

We'll start with our Identity, but rename it.

const List = x => ({
    emit: () => x,
    chain: f => f(x),
    map: f => List.of(f(x)),
    inspect: () => `List(${x})`
});

For the purposes of this example, we'll assume of constructor has been added to this. When actually making one, we'd also type-check in the of constructor to ensure the passed value is an Array.

Adding more methods

As you can see with the addition of inspect, adding new methods is very easy. And if you write your own monad, why not add methods if you have a particular function you use with map or chain a lot?

In my experience, there are two kinds of methods you might add:

1. map-like: methods that return back the same type of Monad
2. chain-like: methods that either return a different kind of monad, or a non-monadic value; it may or may not "exit" the monad pattern, which I like to refer to as "unwrapping" the monad value

Method: concat

Concatenation is a fairly simple concept from Array: take one array, and add it onto the end of another. This seems like a method that would be very useful to have available.

concat: a => List.of(x.concat(a)),

// e.g.

const myNumbers = List.of([1, 3, 4, 7, 10]);

myNumbers.concat([12]).inspect();
// > List(1,3,4,7,10,12);

The function is simple: make a new List from using Array.concat on the contained value and the incoming value.

Note that this is map-like; it returns a new List.

Method: head

Let's say we wanted to just know what the first item in the List is. It's not an Array so using an index accessor like [0] isn't going to work.

head: () => x[0],

// e.g.

const myNumbers = List.of([1, 3, 4, 7, 10]);

myNumbers.head()
// > 1

This method is chain-like, as it returns a non-monadic value -- in this case, unwrapping part of the value. This one exits the monad pattern, so be aware when using these kinds of methods that continuing to chain map, emit, inspect, etc will not work.

const myNumbers = List.of([1, 3, 4, 7, 10]);

myNumbers.head().inspect();
// > ERROR! We unwrapped from the monad at `.head()`!

More methods

If you know Array well, you know it has an awful lot of methods. You can build a List with all kinds of things.

So here's a good excercise -- take this basic List monad and write some methods of your own!

Try it out: List Monad Example REPL

Maybe: the most powerful monad

It's possible you've heard of Maybe (also known as Option): the oddly named, but incredibly useful and powerful monad pattern.

The name "maybe" refers to the idea of "maybe there is a value... but maybe there is not".

In JS, having values that are undefined and null can cause havoc in the wrong place. What if, in every case where we currently have to place an awkward if (x === undefined || x === null) statement, we just could handle those cases right inside the value's container and never expose those unsightly and troublesome null values?

The code

Here comes a lot of code. Don't worry, we'll go through it all.

const Just = (x) => ({
  chain: f => f(x),
  emit: () => x,
  map: f => MaybeOf(f(x)),
  fork: (_, g) => g(x),
  isJust: true,
  isNothing: false,
  inspect: () => `Just(${x})`,
});

const Nothing = (x) => ({
  chain: _ => Nothing(),
  emit: () => Nothing(),
  map: _ => Nothing(),
  fork: (f, _) => f(),
  isJust: false,
  isNothing: true,
  inspect: () => `Nothing`,
});

const MaybeOf = x => x === null || x === undefined || x.isNothing ? Nothing() : Just(x);

const exportMaybe = {
  of: MaybeOf
};

export { 
    exportMaybe as Maybe
}

Use case

To give an example where this would be useful, let's have system that reads a temperature in Fahrenheit and gives it out in Celsius.

const fahrenheitToCelsius = a => (a - 32) * 0.5556;

const reading1 = 15;
const reading2 = null;

const temp1C = Maybe.of(reading1)
                    .map(fahrenheitToCelsius);

console.log(temp1C.inspect());
// > Just(-9.4444)

const temp2C = Maybe.of(reading2)
                    .map(fahrenheitToCelsius);

console.log(temp2C.inspect());
// > Nothing()

Right away we have a problem: for function fahrenheitToCelsius to work, we need a to be a number. Since reading2 is null (maybe a dead thermometer?), Javascript will cast null to 0, giving a constant false reading of -17.7792.

However, since we have encapsulated in a Maybe monad we only have two possibilities: a real number (Just, as in "just a value"), and no value at all (Nothing).

Explanation

How did this happen?

Our Maybe.of constructor did it:

const MaybeOf = x =>
    x === null ||
    x === undefined ||
    x.isNothing ? Nothing() : Just(x);

If the value being encapsulated in the monad was not undefined, null, or already a Nothing, then it is kept in Just. While the name Just may look new to you, its concept is almost identical with Identity! So you pretty much know already how Just works.

Nothing is a rather different monad than most: it doesn't take a value, and every method you use will result in Nothing(). After a Maybe has cast a value to Nothing there's no going back -- all attempts to map or chain just result in Nothing, so you need not worry about functions having unexpected behaviours since they never actually run.

Even emit here returns Nothing(), not null or undefined. This is because I lied slightly earlier, our emit method sometimes can't actually emit a value, especially if it has Nothing()!

But we need to handle what we do with Nothing, eventually...

Method: fork

Here enters the prized method of the Maybe monad given above: fork.

One quick side note: not all Maybe monad implementations will have a fork, but handle Nothing in other ways. For this tutorial however, we'll be using it, because we can!

fork is a method in two places here: in Just and Nothing

// Just
fork: (_, g) => g(x),

// Nothing
fork: (f, _) => f(x),

Right away you might see something odd. _ is a style choice often used in functional programming to indicate where we know there will be a value passed, but we plan not to use it. It is like the opposite of a placeholder.

Now let's use it for temperature display:

// assume a `display` function to display the temperature reading, and act like console.log

const fahrenheitToCelsius = a => (a - 32) * 0.5556;

const reading1 = 15;
const reading2 = null;

Maybe.of(reading1)
    .map(fahrenheitToCelsius)
    .fork(
        _ => display('ERR!'),
        t => display(`${t}°C`) // will read `-9.4452°C`
    );

Maybe.of(reading2)
    .map(fahrenheitToCelsius)
    .fork(
        _ => display('ERR!'), // will read `ERR!`
        t => display(`${t}°C`)
    );

Note in this use case we're not even assigning the results of the Maybe into a const value, as in this example we just need to display it.

But if we did need that string value to do something else...

const display = a => {
    console.log(a);
    return a;
};

const fahrenheitToCelsius = a => (a - 32) * 0.5556;

const reading1 = 15;

const temp3C = Maybe.of(reading1)
    .map(fahrenheitToCelsius)
    .fork(
        _ => display('ERR!'),
        t => display(`${t}°C`)
    );

console.log(temp3C)
// > "-9.4452°C"

This should be enough to get you started on using Maybe. It's a very different way of thinking about values than one is usually taught in JS, and will likely take some time to fully grasp.

What helps a lot with understanding the use of monads is practice! On your next small project, try adding in a Maybe module (suggestion below), or write your own. Given enough time, you might not be able to imagine writing code in JS without it!

For now, you can give Maybe a spin in the following REPL.

Try it out: Maybe Monad Example REPL

A note about emit

You may have noticed there's not really any examples of using emit (aka join) here. This is because "unwrapping" a monad is something you should actually completely avoid if possible, except when removing multiple layers of container monads.

It's great for debugging, but when you emit you'll need to realize you're leaving the safe world of monads, and into side-effects and mutability again.

There are many monad libraries that don't even have this method, as it isn't technically necessary -- after all, chain can achieve the same effect if it's fed a simple identity function.

The best thing you can do, if possible, rather than using a monad to compute a value to return, is build the monad and pass it all the functions it needs to do what it needs to do.

Don't worry if you can't figure out how to do that for every situation right now though. Just starting to use monads at all can be an exciting learning experience.

Quick review

What has helped me the most over the years is to think of monads as a container. That may help you, or to fall back to the dictionary defintion of single unit may also be of help.

Much like a bank ledger, monads keep their values immutible but allow methods to apply functions atop them to generate new monads, and thus new values.

But do be aware, doing a web search to find solutions on monad problems you might encounter may be a bit challenging. A lot of documentation out there is deeply saturated with technical language you might not be familiar with. A lot of it even I'm not familiar with. Hopefully that will change as this powerful pattern is adopted more widely.

Monad modules you can use right now

My own module, which is not very different from what has been demonstrated in this introduction is available as simple-maybe on npm.

What next?

Once you have grasped completely the concepts outlined in this introduction, other monads will mostly be just slight variations on the types of monad shown here.

In the near future I'll be posting about some other monad modules I've been building, and how they are used, and constructed.

I hope this article's approach has been accessible, even to those new to Javascript, and the code sufficiently expressive to not be a barrier to learning. Please feel free to leave suggestions for improvements or to share some other methods that have helped you better understand the use of monads.

Comments

[Eric Brisco]

Happy to see your interest in Monad. However, there are numerous errors throughout this tutorial beginning from a wrong definition of Monad.

I hope you continue to study what a Monad is. In the interim, for the sake of other learners, this tutorial should be taken offline until it can be corrected.

Give me a shout and I'll provide what information and answers I can to help you fix this tutorial.

[Rob Porter]

If you can find code not working correctly, please post it here. I would love to know what you have found wrong in the code if so.

It was stated at the beginning of the article that is more of an expressive, practical approach in JS, and not a lesson in category theory or mathematics.

I'm more or less following the principal of not overloading the reader with information that isn't required in order to make use of the pattern in day to day programming. This approach is used often in many forms of education, where certain things are glossed over in order to serve the broader goal of transferring knowledge. One doesn't learn how a car's engine works when learning to drive, just how to operate it, as an example. But if you want to be a car mechanic: yes, you learn more than how to accelerate and break to get to know a lot more and know that everything is not so simple.

[Eric Brisco]

Explaining concepts clearly and simply is a laudable task. However, several parts, while perhaps being digestible, are factually wrong.

An example: emit is not part of monads. Also, emit and join are not the same thing.

If the goal is just to present some technique for writing JS programs then I have no qualms. If the technique is ascribed to monads, however, then I have to object.

[Rob Porter]

emit as I described, is a made up term. I borrowed it from CouchDB because I do find it far more expressive. join was also made-up when monads were adapted to Haskell, as a term to remove an abstraction layer. This is why I mention about expressivity in the article, to someone unfamiliar the term join (and Haskell, etc) doesn't make a lot of sense and it's just another weird thing to learn that I feel could be made easier. In my opinion as long as the functionality of a join exists, the name doesn't matter. But I do know others do not share that opinion and that is fine.

Like I say above, naming things is hard. Expressivity helps people immensely overcome barriers to using new techniques. Some monad libraries for JS use value for a join, but to me value is not being used as a verb, so I prefer emit. When teaching folks how to use it, many pause and ask for why it's called join, which interrupts the flow in learning just to satisfy some historical reason that has nothing to do with Javascript.

When I do write a monad I always make sure that join is there, and emit is just added as an alias. Same with map and fmap and so on. I always make sure the Monad Laws pass (I didn't even mention those here because that would be a whole other explanation). But for an "introduction" that can get someone doing something that is so different and almost counter to how JS works, I think a lot of the historical names and advanced conventions can be postponed for another day.

[Eric Brisco]

I have no problems with the names you have chosen.

When I say emit is not the same as join, what I mean is that emit (as you have defined it) is not equivalent to join (as Haskell defines it — if you wish to use that as a point of reference).

Emit is in fact equivalent to extract, which is part of Comonad but not part of Monad. There is no way to do what emit does with a Monad.

You can define join from Monad, or join can be used in the definition of Monad — there are different equivalent ways to formulate Monad.

This is not a naming problem. This is a problem with the definition of Monad.

[Rob Porter]

Well, at this point I'd have to say you'll need to also take it up with various other existing monad implementations that have been created in Javascript. These are all from folks who know way more than me and could answer better your concerns.

It's done in Professor Frisby's guide here and in his videos:

mostly-adequate.gitbooks.io/mostly...

And in the Composing Software book (this is a part of it):

medium.com/javascript-scene/javasc...

(He also points out rightly that one can just omit join altogether and use a chained identity for this kind of thing. That might actually be easier from an educational perspective, I'm not sure.)

As does the monet.js monad library which aliases join to be like .chain(a => a) which might as well be () => x in the end, it's just a semantic difference.

And this last one on Maybe by James Sinclair is another, just using a class-style monad.

jrsinclair.com/articles/2016/marve...

[Eric Brisco]

For Monad to make sense, types cannot be ignored. That is why join is being misunderstood.

I have not watched Professor Frisby's explanation so I have no comment there.

Eric Elliot misunderstands join in his article you linked. I'll try and get in touch.

monet.js does it right. Read carefully what the type of join is.

James Sinclair describes join accurately and then, following that, explains why emit cannot be defined for Maybe. I recommend rereading his work carefully.

[Giovanni Ravalico]

TS Identity interfaces

interface IdentityMonad<A> {
  /**
   * method that just returns the value contained within.
   */
  emit: () => A

  /**
   * method which is intended to chain various monads together
   */
  chain: <B>(f: (x: A) => B) => B
  /**
   * `map` it is the chain function with a built-in rewrapping of the resulting value into a
   * new Identity, which itself can be subject to map, chain, and emit on and on for as many
   * functions you'd like to apply to it.
   */
  map: <B>(f: (x: A) => B) => IdentityMonad<B>

  inspect: () => string
}

interface IdentityFactory {
  <A>(x: A): IdentityMonad<A>
}

[Rob Porter]

This is great! 👍

[joe cool]

@rgeraldporter Are you using the Monad pattern in all your codebases on an everyday basis ? For instance, have you replaced all of your try/catch block with some Monads ?
I'm an experienced dev, but I've never used it, I'm trying to understand this pattern, and your article is a fresh air among a lot of not very practical explanations on the web.
With javascript, an app can easily crash with a null/undefined error, so I'm a bit surprised that the Monad pattern is not more widespread if it's really a safe wrapper.

[artydev]

It is a radically another way of thinking, and changing minds is very very difficult.
It takes very long time to convince your colleagues in a team .
Once the brain is wired in some way, changing minds is like 'digging' and 'rewiring' new ways of thinking in this brain, and it can be a pain, especially if you have reached a certain age...(I am 61 years old :-))

[artydev]

Thanks for this introduction.
Regards

[potbunker]

Nice way to ease into Monad! Appreciated.

[Rob Porter]

Thank you!

[Sean G. Wright]

Great explanations. I liked how you started with Identity and slowly build up to Maybe.

Thanks!

[Rob Porter]

Thanks!

[joe cool]

instead of exporting the monads with an intermediate "of" construct, we could add the "of" method as a property of the monad, eg:

List.of = x => List(x)