And Ugh... Monoids? 🙄 please 🙄
What a bunch of complicated gobbledygook. I mean first off, you have to have like, a PhD in mathematics just in order to get started with crap like that, and then if you do decide to put in the work, what's the payoff? Look, I just make webapps here. The only return I'd ever see on that type of investment is maaaayybe the dubious honor of hanging out with developer cliques that fetishize abstruse words like "Endofunctor" and "Isomorphism." They're so exclusive anyway, and that's not what I'm about. I build real things, and so this isn't for me.
Does any of that sound like an internal dialogue you may have had with yourself at some point in the last few years? I know it certainly captures the color of my thinking on the subject of formal functional programming during that time. Sure, I took half-hearted swipes at understanding things like Monads here and there, but it never really stuck. And more often than not, I was inclined to chalk it all up to sour grapes... That is, of course, until I realized something amazing. I realized that contrary to what I was brought up to believe, formal FP wasn't something that would forever lie just beyond my reach.
Imagine my surprise in realizing that not only was this not true, but in realizing that I had actually been an FP super hero all along; descended from a long line of FP super heroes. And do you know what the most amazing thing is? Whether you know it or not, you are too. Don't believe me? Just listen.
A Functor? Are you kidding me?
I know, I know. Even now just saying it still makes me want to giggle. But if you're still doubting your own powers, then Functor is where the journey begins. That's where it began for me. Because you know what? If you code for a living, then odds are you use Functors every coding minute of every coding day. You just haven't realized it yet.
So Functor is the name, and the concept it references is "mapping over a structure". There's nothing more to it than that. Functors are things that can be mapped. End of story. Arrays can be mapped: Arrays are Functors. Observables can be mapped: Obvservables are Functors. So guess what? Like it or not, if you are comfortable mapping Arrays, then you are also comfortable working with Functors.
Mapping an Array always returns an Array of the same length, but with different values at every index. Mapping an Observable always returns an Observable with the exact same sequence and timing of states, but with different values inhabiting each state. The general pattern is that mapping doesn't change the object's structure.
At its core, an Array is nothing but a sequence of indexed placeholders
that contain values. That is its structure, and that's exactly what
doesn't change when you map it. The structure of observables is the timing
and sequence of states coming through a stream, so it's the same
timing sequence that remains intact when you map it. So no matter the
Functor, when you map it, it returns a new Functor with the exact same
structure. In other words:
S -> S.
But you knew already that mapping an Array of the same length always returns an Array of the same length because you've been working with them for as long as you've been writing code.
So yeah. I know how to map Arrays. Big deal. How does assigning some new name to what I'm already doing actually help me in any tangible way? It seems an awful lot like some boring thing to remember.
Well, this is where the plot takes an unexpected turn. This is the part in the story where a chance encounter with a secret Functor plants the suspicion that perhaps you've been lied to your entire life by the ones that raised you. Sure, they meant well, and all they ever really wanted to do was to save you sweat and tears, but in the end the only thing they actually accomplished was to delay your inevitable confrontation with destiny.
Here's your first clue: Have you used and/or thought about Promises lately?
Promises don't have a
map method, and yet they are nevertheless
Functors. They're the functoriest of Functors that ever were, and
their functorality is as constant and sure as the sun rising in the
east and setting in the west. But how can this be if there isn't any
way to map them? The answer is of course that you can map them. You
just have to use the
then method to do it. It's this alternatively
named mapping function that makes Promise a secret Functor.
It makes sense when you think about how
then works. You start with a
Promise of some value that will resolve at some later time, and you
end up with another Promise that has the exact same structure as the
original in that it will also resolve at the exact same time as the
first. The only difference is that the value has been transformed by
the passed in function. Once you come to recognize it, you see that
it's a clear stamp out of the Functor pattern, and that the method
might as well have been called
map instead of
And that's when you begin to wonder "what if it had been named
then, and explicitly identified as a Functor from the
get-go?" Learning to work with Promises was tricky enough, but what if
you'd been able to leverage the fact that the greater part of working
with them was strongly analogous to working with Arrays? What if
you'd been able to apply everything you knew about mapping Arrays and
bring it to bear on Promises? How much time and mental exhaustion
would it have saved? Looking back at my own experience, it would have
been extraordinarily helpful to have sidestepped the process of trial
and error that happened as my brain settled around the semantics of
Here's the rub. The method name
then is a reference to the timing of
Promise resolution, which of course seems reasonable at first. After
all, it's a good thing for an API to be concrete and descriptive
right? The hidden tradeoff is that the name
then orients the
API around what makes Promise unique, instead of what makes Promise
literally like every other Functor. And there are thousands of
They inhabit so many of the programming structures that you use every single day, that once you're aware of them, they will begin to reveal themselves to you. As you start to perceive the common nature in things like Promise, Array, and Observable, you begin to re-perceive all of the objects in your world through this new prism. You ask yourself "Is this a Functor?" and you're shocked by how often the answer is yes. Plain JS Object? Yes. DOM Element? Yes. Express middleware? Yes. React Component? Also yes.
And then it hits you.
If you're using Ruby on Rails, and someone tells you about a
Controller, it doesn't matter if it's a controller for products, or
users, or blog posts. The mere fact that it's a
Controller gives you
most of what you need to know about its role and how you can set to
work with it to build the larger application. By the same token, if
someone tells you that some object is a Functor, it doesn't matter if
it's a list, or a tree, or a stream. The mere fact that it's a Functor
gives you most of what you need to know about its role and how you can
set to work with it to compose it into larger structures.
I use Ruby on Rails as an example to illustrate this point because the framework is synonymous with the concept of convention over configuration, and that's the fundamental dynamic at play here. But whereas Ruby on Rails is a framework for web applications, formal FP grounded in Category Theory is a framework for composable APIs.
Because Functor is just the beginning. Like a programmer
learning Ruby on Rails can start with
Controller first, and then
move on to
Middleware, so you can you move on
from Functor (at your very own pace) to using Applicatives, Monads, and
So go for it! I remember the first time I took a tree class I'd been working with and started thinking of it as a Functor. All of a sudden, the brain-hurty, recursive aspects of the tree were abstracted into the map method and I was able to relate entire trees to each other with nothing more than a simple function. I cannot describe the feeling other than it felt like flying. The ground below was all very familiar because I'd walked it back and forth many times over the years. The only difference was that now I had the perspective of ten thousand feet and the airspeed of a jetliner.
You know the ground too. You walk it every day, and if you're willing to learn the math framework, the same feeling is waiting for you.
I’m Charles Lowell, and I build UI for a living at Frontside. If you enjoyed this post, I’d love to hear from you. You can give me a shout on Twitter where I'm @cowboyd, or drop me a line at firstname.lastname@example.org