Comment by ivanjermakov
6 hours ago
People think category theory is weird and confusing, but really it just managed to name things (classes) that before were just "things". One might not know what monad or functor is, but they surely used it and have intuition on how it works.
Right. I don't know how many times I've been exasperated by how monads are perceived as difficult.
Do you understand "flatmap"? Good, that's literally all a monad is: a flatmappable.
Technically it's also an applicative functor, but at the end of the day, that gives us a few trivial things:
- a constructor (i.e., a way to put something inside your monad, exactly how `[1]` constructs a list out of a natural number)
- map (everyone understands this bc we use them with lists constantly)
- ap, which is basically just "map for things with more than one parameter"
Monads are easy. But when you tell someone "well it's a box and you can unwrap it and modify things with a function that also returns a box, and you unwrap that box take the thing out and put it inside the original box—
No. It is a flatmappable. That's it. Can you flatmap a list? Good. Then you already can use the entirety of monad-specific properties.
When you start talking about Maybe, Either, etc. then you've moved from explaining monads to explaining something else.
It's like saying "classes are easy" and then someone says "yeah well what about InterfaceOrienterMethodContainerArrangeableFilterableClass::filter" that's not a class! That's one method in a specific class. Not knowing it doesn't mean you don't understand classes. It just means you don't have the standard library memorized!
People have different "aha" moments with monads. For me, it was realizing that something being a monad has to do with the type/class fitting the monad laws. If the monad laws hold for the type/class then you've got a monad, otherwise not.
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!"
Yes, I 100% agree. But I want to mention something that isn't a disagreement, just a further nuance:
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.
Forget programming, everyday business and physics is monadic in function.
And if-then statements are functorial.
These are very general thought patterns.
> everyday business and physics is monadic in function.
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.
These are vacuous statements.
It's also important to note that in Haskell and other functional programming languages, there is no implied order of operations. You need a Monad type in order to express that certain things are supposed to happen after other things. Monads can also express that certain things happen "in between" two operations, which is why we have different kinds of Monads and mathematical axioms of what they're all supposed to do.
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.
> Maybe/Either get talked about because they're the simplest Monads you can make, but it makes Monads sound like a spicy container type.
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).
There is an implied order of operations in Haskell. Haskell always reduces to weak head normal form. This implies an ordering.
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).
> You need a Monad type in order to express that certain things are supposed to happen after other things
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.
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> Do you understand "flatmap"? Good, that's literally all a monad is: a flatmappable.
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?
But words like "incapsulation" or "polymorphism" or even "autoincrement" also sound unfamiliar and scary to a young kid who encounters them the first time. But the kid learns their meaning along the way, in a desire to build their own a game, or something. The feeling that one already knows a lot, sort of enough, and it'd be painful and boring to learn another abstract thing is a grown-up problem :-\
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I mean people need to be familiar with mathematics. In mathematics things form things without having to understand them.
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.
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