The Fundamentals of Functional Programming are Fun!
funcadelic
takes the simple idea that a single function can operate on many
different data structures (typeclass oriented programming) and brings
it to JavaScript. Sure, there are a lot of FP libraries out there, but
this one is geared towards unlocking the magical powers of functional
programming while always maintaining a tangible and accessible
experience for JavaScript developers. Because if you're a JavaScript
developer today, you're already using most of the structures in funcadelic!
Quick example:
import { map } from 'funcadelic';
function double(i) { return i * 2; }
map(double, [1,2]); //=> [2,4]
map(double, {one: 1, two: 2}) //=> {one: 2, two: 4}
Notice how we used a single function map
to operate on both an
Array
and an Object
? That's because they're both instances of
the Functor
typeclass which has a single operation called
map
. Look familiar? It should because map
is something you
probably do with Arrays all the time. Funcadelic just takes
this concept and lets you make it available to any data type for
which it makes sense, not just Array. And as it turns out there are
tons of them out there!
And just remember: Don't be afraid of weird names like Semigroup, Functor, Monad, Monoid and the like! They're just arbitrary names that describe really useful concepts. Kinda like this one.
Taskulamppu
Looks pretty weird right? Exotic, even. It's hard to parse, so it must be a hard concept.
Turns out it's the Finnish word for flashlight; A strange name at first (to non-finnish ears) for a very useful and easily understood tool.
These typeclasses are currently contained within funcadelic.
A semi group is fancy name isn't it? It's just a data structure that
can be "mashed" together with itself. Instead of Semigroup
, you
could call it MashableTogetherableWithItselfable
, but that's a lot
to say every time. You mash two items in a Semigroup
together with
the append
function.
Combine two members of a semigroup into a single value of the same semigroup.
Arrays are classic example of Semigroup
. What do you get when you
mash two arrays together? Well another array of course! Array + Array => Array
import { append } from 'funcadelic';
append([1,2], [3,4]) //=> [1,2,3,4]
But arrays aren't the only things that can be mashed together. Objects can too!
append({name: 'Charles'}, {occupation: 'Developer'}) //=> {name: 'Charles', occupation: 'Developer'}
When you smush two members of a semigroup together, you always get the
same type back. In that example above: Object + Object => Object
Monoids take the concept of Semigroup
and extend it just teeeeeny
weeeny bit further so that you can use the append
operation to fold
any list of monoids really easily into a single value.
Fold a list of monoids into a single value by smushing them together, starting with an empty value.
For example, a thing you see often is merging a list of objects together to produce a single object with all of the keys and values.
let name = {name: 'Charles'}
let occupation = {occupation: 'Developer'}
let height = {height: {unit: 'cm', amount: 200}}
In order to produce this single merged value you might use
Array.prototype.reduce
[name, occupation, height].reduce((accumulator, object) => append(accumulator, object), {})
Here we start with an initial value of our accumulator (an empty
object) and successively append
each object to it to produce the
final object.
But if you know for certain what your start state is ({}
), and how to
combine any two objects (append
), then you don't actually need to bother
with writing your reduce, you can just use a monoidal reduction where
those operations are implicit:
reduce(Object, [name, occupation, height])
//=> {name: 'Charles', occupation: 'Developer', height: {unit: 'cm', amount: 200}}
Of course, you may have recognized this as something akin to using
Object.assign
,
with an empty object:
Object.assign({}, name, occupation, height);
The only difference is that it's not treating it as a unique, snowflake of an interface, but instead acknowledging it for what it is: the same fundamental operation as array concatenation and string concatenation (to name just a few)
Oh, and surprise, suprise! Arrays are Monoids as well....
reduce(Array, [[1,2], [3,4]]) //=> [1,2,3,4]
Some types, like numbers have many ways that they could be
reduced. You could add them or multiply them just to name two. For these cases,
funcadelic provides you a helper Monoid.create
const Sum = Monoid.create(class {
empty() { return 0; }
append(a, b) { return a + b; }
})
Sum.reduce([1,2,3,4]) //=> 10
const Multiplication = Monoid.create(class {
empty() { return 1; }
append(a, b) { return a * b; }
})
Multiplication.reduce([1,2,3,4]) //=> 24
I used to think that Functor was some strange amalgamation of the words "Function" and "Constructor". I don't think that any more because it isn't true, although I still have yet to find a satisfying origin for that word.
Nowadays, it's enough for me to reflect upon the fact that if George Clinton were running an empire, instead of calling the provincial governors "Satraps", he would have probably called them "Functors".
Once you give up hope on trying to understand the etymology of the
word "Functor", you can focus on the idea that it represents some
kind of "container" or "context" with its own intrinsic structure
separate from the things that it contains. Using the map
function,
you can swap out the values in a container without changing the
structure of the container itself.
Create a new Functor by appplying the function
fn
to the content offunctor
. The structure of the output Functor exactly matches that of the input.
Arrays are once again a classic example of Functors. You can use map
to change the values in an array without changing the structure of the
array itself:
import { map } from 'funcadelic';
map(i => i * 2, [1,2]); //=> [2,4]
The key here is that structure of the Array doesn't change. The input
to map
is an array of two elements, therefore the output of map
must be an array of two elements. The content of that two element
array has changed, but the structure has not.
And guess what? Objects, are also Functors! you can map over them too. When you map over an object, you change the value associated with each key, but the keys present remain the same.
map(i => i * 2, {one: 1, two: 2}); //=> {one: 2, two: 4}
Again, notice how map
preserves the structure of the object, even
though the values change. Both the input and the output are objects of
two keys "one" and "two"
Functors let you map a function with a single argument across a single Functor. But what do you do if you have a function with multiple arguments? Applicatives to the rescue.
Given
list
of functors each of which holds a value, callfn
using the values held inlist
as the arguments.
Let's say for example that I have a function greet
that
takes three arguments:
function greet(say, to, excited) {
return `${say}, ${to}${excited ? '!!' : '.'}`;
}
greet('Hello', 'Charles', false); //=> "Hello, Charles."
greet('Hello', 'Friend', true); //=> "Hello, Friend!!"
That's great if we are using literal values, but what if we're fetching them over the network?
let say = $.get('/greeting'); //=> Promise([pending])
let to = $.get('/entity'); //=> Promise([pending])
let isExcited = $.get('/excitement-level'); //=> Promise([pending])
We could do this manually:
Promise.all([say, to, isExcited])
.then(([sayResult, toResult, isExcitedResult]) => greet(sayResult, toResult, isExcitedResult))
Of course, this obfuscates our original intent to call greet
with the
values in the promises. Instead, the actual greeting happens as
the very last thing in a rightward drift! It's ugly, and I don't
appreciate it.
What if we could just apply the greet
function almost like using the
builtin Function.apply
? like:
greet.apply(null, [say, to, isExcited]);
That would be awesome right? Well with instances of Applicative
like
Promise
, you totally can!
import { apply } from 'funcadelic';
apply(Promise, greet, [say, to, isExcited]);
This says: take these three promises, use the values that
they contain as the three arguments to greet
, and then return a
promise containing the result. Nifty!
Take
value
and place it into the minimum possible context of applicativeApplicative
Are you tired of hearing about Functors? Well too bad! Because we're going to talk about them some more.
So anyway, what is a Functor really? 🤔
One way to think about it is that it represents a context. It could
be the context of being in a sequence like an array. Or it could be
the context of something that will happen in the future like a
Promise
. Whatever the context, how do you get a value into it?
Let's look at a couple of contexts that we know like Array
and
Promise
. How would we get the value "Hello My Friend-o"
into each
of these contexts? Well, what does "Hello My Friend-o"
look like as
an Array. How about ["Hello My Friend-o"]
? That works. We did the
smallest thing we could possibly to take the value and put it into the
context of an array.
What's the smallest amount of work that we could do and put that value
into a Promise
? The answer is.............
Promise.resolve("Hello My Friend-o");
And in fact, both of these techniques, though seemingly different really just the same thing: taking a value and putting into the smallest possible or "purest" context that you can. That's what pure is all about:
pure(Array, "Hello My Friend-o") //=> ["Hello My Friend-o"]
pure(Promise, "Hello My Friend-o") //=> Promise {<resolved>: "Hello My Friend-o"}
By contrast, the Array
["Hello My Friend-o", "Hey what's this!!! How the heck did this get in here?"]
is an example of something that is not the purest array context for
"Hello My Friend-o"
.
Monads are a tad controversial, yes? I think that this might well be because we try to come at them without a full appreciation and understanding of Functors first, and it turns out that that's just silly! So if you don't feel completely comfortable with Functors, I recommend you go read up on them first, then work with them a little bit and then come back here when you've got your head fully inside and around them. Because the simple fact is that Monad's just aren't going to make much sense unless you understand Functor first.
So if you need to go back and learn Functor's first, go for it! Monad's will still be waiting for you right here when you get back. It might take 2 hours, two weeks, or two years.
Ok.
The basic Functor
method map
lets you transform values, but not
the enclosing context. In many ways that's the power of
mapping. You're freed from thinking of the context because it remains
constant. If you map an Array of 10 elements the result will also have
10 elements. If you map a Promise that resolves at 5:15pm and 3
seconds, the result will also resolve at 5:15pm and 3 seconds.
But sometimes that's not enough. Sometimes you want to change the
structure of the Array, or change the timing of the Promise. To unlock
this power, you need Monad
.
Unlike map
, the flatMap
method of the Monad
type class
lets you actually modify the context. So you can do things like
generate an Array of a different length than the original, or generate
a Promise that resolves at a different time than the original.
Whereas map
takes a function that converts a value into another
value, flatMap
takes a function that converts a value into a new
value _in a new context. It then takes that new context and combines
it in some way with the existing context. Of course what "combine"
means is up to the specific Monad.
Create a new Monad by applying the function
fn
to the content ofmonad
.fn
is expected to return a new monadic context which is then "flattened" into the original context.
What does this look like? Well, here's a monad that you use all the time, but might not know it: Promise.
Have you ever returned a new Promise from within a Promise#then
?
Well if you have, then you're already well versed in monadic
operations because that's exactly the kind of thing you would do with
a flatMap
.
let user = $.get('/');
flatMap(user => $.get(`/wingdings/`${user.wingdingId}`))
.then(wingding => console.log(wingding));
Notice how the flat mapping function takes the value contained within
the Promise, but then returns a completely new promise. That's how
flatMap
allows you to actually change the context.
Functors are all about changing the values contained within a structure while at the same time preserving the shape of the structure itself. When we map an array of 10 items, you get an array of 10 items.
Foldable structures are ones where you can consider all of the values it contains and use them to compute a single value. You may have heard of this before if you're familiar with OO design patterns as "visiting". You have a visitor that is passed each value in the collection, and then updates an accumulated value it maintains. Once the visitor has visited every value, the final accumulated value is your result.
Foldable is the same way, Starting with an initial value, you "visit"
each piece of data inside of a structure, and then incorporate it into
the final value. For many Foldables
there is a
difference between folding from "left" and folding
from the "right", although much of the time you don't need to consider
this.
Compute a single value, starting with
initial
from all of the values contained withinfoldable
by applyingfn
to each element it contains starting with the "left most" value. For a discussion of "left most" see Right vs Left
For each element in foldable
, fn
is called with an accumulator
value (memo) and the element. The result of this call becomes the new
value for the memo. After all elements have been been folded in this way,
the final value of the memo is the return value of the fold.
Let's turn to our workhorse friend the Array for a great example of
Foldable
that's worth a thousand words.
import { foldl } from 'funcadelic';
foldl((sum, i) => sum + i, 0, [1,2,3,4]) //=> 10
foldl((sum, i) => sum - i, 0, [1,2,3,4]) //=> -10
If this looks familiar, it is. Folding is exactly what happens when
you use
Array.prototype.reduce
Compute a single value, starting with
initial
from all of the values contained withinfoldable
by applyingfn
to each element it contains starting with the "right most" value. For a discussion of "right most" see Right vs Left
For each element in foldable
, fn
is called with an accumulator
value (memo) and the element. The result of this call becomes the new
value for the memo. After all elements have been been folded in this way,
the final value of the memo is the return value of the fold.
Like our friend foldl
, Array gives a great demonstration of foldr
.
import { foldr } from 'funcadelic';
foldr((sum, i) => sum + i, 0, [1,2,3,4]) //=> 10
foldr((sum, i) => sum - i, 0, [1,2,3,4]) //=> -10
In this case, foldr
is roughly equivalent to
Array.prototype.reduceRight
What "right" and "left" means is a bit mushy and varies from Foldable to Foldable. In an array it means starting from the first value and ending with the last and vice-versa.
In a tree structure, it might be the difference between starting with the leaf nodes instead of starting with the root and moving downward.
For the most part, you can ignore the difference in a language like
JavaScript with eager evaluation. It's a pretty advanced topic, and if
you find yourself coming up against problems and wondering which to
use and this documentation doesn't help. Shoot me a line and we can
talk it over about how to improve it. When in doubt, foldl
.
$ yarn
$ yarn test