So then when you look at List, Maybe, Either, et al. it's interesting to see how their conforming to the laws "unpacks" differently with respect to what they each do differently (what's happening to the data in your program), but the laws are just the same.
The reason this was an aha moment for me is that I struggled with wanting to understand a monad as another kind of thing — "I understand what a function is, I understand what objects and primitive values are, but I don't get that List and Maybe and Either are the same kind of thing, they seem like totally different things!"
1. my explanation of monad is sufficient for people who need to use them
2. your explanation of monad is necessary for people who might want to invent new ones
What I mean by this is that if you want to invent a new monad, you need to make sure your idea conforms to the monad laws. But if you're just going to consume existing monads, you don't need to know this. You only need to know the functions to work with a monad: flatmap (or map + flatten), ap(ply), bind/of/just. Everything else is specific to a given monad. Like an either's toOptional is not monadic. It's just turning Left _ into None and Right an into Some a.
And needing to know these properties "work" is unnecessary, as their very existence in the library is pretty solid evidence that you can use them, haha.
And if-then statements are functorial.
These are very general thought patterns.
So?
> And if-then statements are functorial.
So?
All the "this is hard" stuff around these ideas seems to focus on managing to explain what these things are but I found that to progress at the speed of reading (so, about as easy as anything can be) once it occurred to me to find explanations that used examples in languages I was familiar with, instead of Haskell or Haskell-inspired pseudocode.
What I came out the other side of this with was: OK, I see what these are (that's incredibly simple, it turns out) and I even see how these ideas would be useful in Haskell and some similar languages, because they solve problems with and help one communicate about problems particular to those languages. I do not see why it matters for... anything else, unless I were to go out of my way to find reasons to apply these ideas (and why would I do that? And no, I don't find "to make your code more purely-functional" a compelling reason, I'm entirely fine with code I touch only selectively, sometimes engaging with or in any of that sort of thing).
The "so?" is the part I found (and find) hard.
Outside of FP however, this seems really stupid. We're used to operations that happen in the order you wrote them in and function applications that just so happen to also print things to the screen or send bits across the network. If you live in this world, like most people do, then "flatmap" is a good metaphor for Monads because that's basically all they do in an imperative language[1].
Well, that, and async code. JavaScript decided to standardize on a Monad-shaped "thenable" specification for representing asynchronous processes, where most other programming languages would have gone with green threads or some other software-transparent async mechanism. To be clear, it's better than the callback soup you'd normally have[0], but working with bare Thenables is still painful. Just like working with bare Monads - which is why Haskell and JavaScript both have syntax to work around them (await/async, do, etc).
Maybe/Either get talked about because they're the simplest Monads you can make, but it makes Monads sound like a spicy container type.
[0] The FP people call this "continuation-passing style"
[1] To be clear, Monads don't have to be list-shaped and most Monads aren't.
Actually "spicy container type" is maybe a better definition of Monad than you may think. There's a weird sort of learning curve for Monads where the initial reaction is "it's just a spicy container type", you learn a bit and get to "it is not just a spicy container type", then eventually you learn a lot more and get to "sure fine, it's just a spicy container type, but I was wrong about what 'container' even means" and then settle back down to "it's a spicy container type, lol".
"It's a spicy container type" and "it's anything that is flatmappable" are two very related simplifications, if "container" is a good word for "a thing that is flatmappable". It's a terrible tautological definition, but it's actually not as bad of a definition as it sounds. (Naming things is hard, especially when you get way out into mathematical abstractions land.)
There are flatmappable things that don't have anything to do with ordering or sequencing. Maybe is a decent example: you only have a current state, you have no idea what the past states were or what order they were in.
Flatmappable things are generally (but not always) non-commutative: if you flatmap A into B you get a different thing than if you flatmap B into A. That can represent sequencing. With a Promise `A.then(() => B)` is different sequence than `B.then(() => A)`. But that's as much "domain specific" to the Promise Monad and what its flatmap operation is (which we commonly call `then` to make it a bit more obvious what its flatmap operation does, it sequences; A then B) than anything fundamental to a Monad. The fundamental part is that it has a flatmap operator (or bind or then or SelectMany or many other language or domain-specific names), not anything to do with what that flatmap operator does (how it is implemented).
Monads have nothing to do with order (they follow the same ordering as Haskell's normalization guarantees).
> JavaScript decided to standardize on a Monad-shaped "thenable" specification for representing asynchronous processes,
Its impossible for something to be monad shaped. All asynchronous interfaces form a monad whether you decide to follow the Haskell monad type class or decide to do something else. They're all isomorphic and form a monad. Any model of computation forms a monad.
Assembly language quite literally forms a category over the monoid of endo functors.
Jacquard loom programming also forms a category over the monoid of endo functors because all processes that sequence things with state form such a thing, whether you know that or not.
It's like claiming the Indians invented numbers to fit the addition algorithm. Putting the cart before the horse, because all formations of the natural numbers form a natural group/ring with addition and multiplication formed the standard way (they also all form separate groups and rings, that we barely ever use).
This is the kind of explanation that drives me absolutely batshit crazy because it is fundamentally at odds with:
> Do you understand "flatmap"? Good, that's literally all a monad is: a flatmappable.
So, I think I understand flatmap, assuming that this is what you mean:
https://www.w3schools.com/Jsref/jsref_array_flatmap.asp
But this has absolutely nothing to do with "certain things are supposed to happen after other things", and CANNOT POSSIBLY have anything to do with that. Flatmap is a purely functional concept, and in the context of things that are purely functional, nothing ever actually happens. That's the whole point of "functional" as a concept. It cleanly separates the result of a computation from the process used to produce that result.
So one of your "simple" explanations must be wrong.
And you are correct. Monads have nothing to do with sequencing (I mean any more than any other non commutative operator -- remember x^2 is not the same as 2^x)
Haskell handles sequencing by reducing to weak head normal form which is controlled by case matching. There is no connection to monads in general. The IO monad uses case matching in its implementation of flatmap to achieve a sensible ordering.
As for JavaScript flat map, a.flatMap(b).flatMap(c) is the same as a.flatMap(function (x) { return b(x).flatMap(c);}).
This is the same as promises: a.then(b).then(c) is the same as a.then(function (x) { return b(x).then(c)}).
Literally everything for which this is true forms a monad and the monad laws apply.
Awesome! Now I understand.
> Technically it's also an applicative functor
Aaaand you've lost me. This is probably why people think monads are difficult. The explanations keep involving these unfamiliar terms and act like we need to already know them to understand monads. You say it's just a flatmappable, but then it's also this other thing that gives you more?
Casual attempts at defining Monads often just sweep a pile of confusion around a room for a while, until everything gets hidden behind whatever odd piece of furniture that is familiar to the person generating the definition. They then imagine they have cleared up the confusion, but it is still there.
A monad is a generalization of all them. It's a structure that covers values of type T, some "payload" (maybe one, like Promise, maybe many, like List, maybe even none, like List or Optional sometimes). You can ask it to do some operations on these values "inside", it's the map() operation. You can ask it to do similar thing when operation on each value produces a nested structure of the same kind, and flatten them into one level again: this is flatMap(). This is how Promises are chained. The result is again a structure of the same kind, maybe with "payload" of a different type.
This is a really simple abstraction, simpler than most GoF patterns, to my mind, and more fundamental and useful.
For example, The natural numbers form a ring and field over normal addition and multiplication , but you don't need to know ring theory to add numbers..
People need to stop worrying about not understanding things. No one understands everything.
I'm not worried, but it's amusing to see this person say it's so simple, and then immediately trample on it.