"A monad is just a monoid in the category of endofunctors". Anyone who says that - or anything anywhere close to it - is gatekeeping, no matter how true the statement is.

And it's not just the statement. It seems to me (from my outside perspective) that category theory is often used in a gatekeeping way.

In contrast, take SQL. How much of the mathematical theory of relations do you need to know to be able to write SQL queries? Yes, it might help, but the SQL gurus don't try to drag you into it every time you get close to a database.

SQL is intrinsically tied to set theory and borrows a ton of terminology and logic from set theory. Whether you understand that it's from mathematics or not doesn't really matter. You are using set theory and it's terminology regardless.

I've only really ever seen monoids referred to in Haskell. If you actually read my comment, Haskell is not all FP (no PL is). It's not even a significant portion of FP. So just don't use Haskell, it's hardly the first FP language I would reach for and it's probably not the one you should either.

SQL was explicitly designed to appeal to business people, and uses strictly familiar words and phrases. It was very explicitly designed (though I would say it has mostly failed) to read like pseudo-natural language.

SQL DBs and the precise semantics of SQL are somewhat based on relational algebra, but SQL syntax is definitely not. It's also not using set theoretic terms in general, with the exception of UNION and INTERSECT.

SQL tables are not actually sets at all since you can insert duplicate rows! In practice they usually are though.

You can't actually insert a complete duplicate row because the ROWID (or whatever your particular RDBMS calls it) is a implicit, but unique property of each row (and corresponds to the offset in the file the row is located at). Further, while tables can be the identity element of all records they contain, they themselves aren't really a set. Usually when people associate set theory with SQL, it's with queries (and their results).

Nobody says that seriously.

It tells a lot how people go for common jokes to complain about a community. It's easy to fall for that if you never actually interacted with the people.

Nobody claims you have to understand category theory to write Haskell. In fact, most will tell you it's not needed.

The saying "a monad is just a monoid..." is a cliché and an in-joke, not gatekeeping. It's the community having a laugh at itself.

But why is it funny? Isn't it funny because the community knows it comes off that way, at least some of the time (and/or some of the people)?

> Nobody claims you have to understand category theory to write Haskell.

I've seem the claim that you can't really use Haskell without it, here on HN, more than once. (Or at least something that I interpreted as being that claim...)

It's funny because the community knows some people too deep in the rabbit hole come across that way, but because the community acknowledges this is a hilarious assertion that would alienate newcomers -- if said with a straight face -- then it cannot be gatekeeping.

Gatekeeping would be if the community said this with a straight face and everyone got impatient when you just "don't get it".

> I've seem the claim that you can't really use Haskell without [knowing category theory], here on HN, more than once

I've almost never come across this assertion; it's certainly not common in the community (or wasn't when I was learning Haskell). I can tell you it's certainly false: you can very well write Haskell without knowing or studying category theory.

Well, try understanding the Haskell docs around Applicative, Functor or Monad without understanding at least basic category theory - not to mention the heavy use of notation/operators in place of traditional programming idioms (named functions).

Here [0] is an example:

> This module describes a structure intermediate between a functor and a monad (technically, a strong lax monoidal functor). Compared with monads, this interface lacks the full power of the binding operation >>= [...]

[0] https://hackage.haskell.org/package/base-4.17.0.0/docs/Contr...

Counterpoint: I learned about Applicative, Functor and Monad by reading docs and tutorials, and I haven't the faintest idea about category theory.

These are the building blocks of Haskell. You learn them as you go, just as you learn what a "method" is when learning OOP. You don't need to know category theory.

Learning what Applicative, Functor and Monad are is category theory. It's like saying "you can learn how to do unions, intersections, and differences on collections of unique objects without understanding set theory".

That seems a little silly to me and I think we're splitting hairs with what it means to do category/set theory. I don't know category or set theory, so I hope you will forgive me for using yet another allegory.

Let's say I make a type class for Groups (in the abstract algebra sense). The rationale behind this is that there's an algorithm for exponentiation which is O(log(n)) versus the naive O(n) algorithm. So if you make an instance that's a Group, you get to use this fast exponentiation.

Sure, to understand and use this type class you have to understand what a Group is. However, I think it's a bit of a stretch to tell someone "in order to use Group you must first learn abstract algebra" because they'll think you're telling them to take a university level course. In actuality, they don't have to know much at all (they don't even need to understand _why_ the exponentiation algorithm works) - they just need to know what is a lawful Group.

The first day of the intro to abstract algebra course I took introduced much more information than you'd need to use this made up type class, and I expect the same of the others.

Like this is my understanding of Functors/Applicatives/Monads. I kind of know their shape and how to use them. If you asked me about any of the underlying math I would shrug and maybe draw a pig (https://bartoszmilewski.com/2014/10/28/category-theory-for-p...).

That's not really true. When some people claim you must learn category theory to use Haskell, they mean they have to learn the math-subject-capital-letter Category Theory, which goes way beyond programming and comes with a lot of baggage.

They never mean you have to learn Functor, Applicative, etc as used in Haskell and taught in every tutorial. If they did mean the latter, it would be a tautology, which is not very useful.

Compare "in order to do OOP you have to learn what an object truly is, its essence, and possibly take some courses on the philosophy of being" vs "you have to learn about methods and objects".

> It's like saying "you can learn how to do unions, intersections, and differences on collections of unique objects without understanding set theory".

You can totally do unions, intersections and differences without knowing set theory.

I've had someone do that on this very website. I was assured that affine types in Rust are too difficult to understand without a solid grounding in Category Theory.

The years have proven that ease of programming and the burden of knowledge are the two most important elements of a programming language. FP zealots simply won't accept that their chosen paradigm is opaque to most for benefits that can't seem to be written out in human language.

> I've had someone do that on this very website

On this website you will hear anyone say the wildest assertions. There's the whole human range of expression here. But what makes you think actual FP practitioners (and Haskelers) really believe this?

The proof wouldn't be what some random person here on HN tells you. The proof would be you getting involved in an actual FP community trying to write an actual FP project and being told that you just cannot do this unless you understand category theory. Which, as I said, is not something that happens... at least not in my (limited) experience.

Never confuse what people tell you here on HN, random forums or even throwaway StackOverflow comments with what actually happens in the actual communities when trying to achieve real goals and not just chat about stuff.

> "A monad is just a monoid in the category of endofunctors". Anyone who says that - or anything anywhere close to it - is gatekeeping, no matter how true the statement is.

You just tried to badmouth whole community of FP programmers by taking serious a running gag, wow.

> "A monad is just a monoid in the category of endofunctors". Anyone who says that - or anything anywhere close to it - is gatekeeping, no matter how true the statement is.

The original attribution of this line about monads comes from the (intentionally) comedic article "A Brief, Incomplete, and Mostly Wrong History of Programming Languages", published by James Iry in 2009: http://james-iry.blogspot.com/2009/05/brief-incomplete-and-m...

It is not a stance I have ever seen taken up in a serious manner by anybody in the FP community, and I work in PL academia (the region of the community from which I would expect to see the most snobbery). Please stop misrepresenting people based on a misunderstood joke.

There are people in the FP community who gatekeep and take on a snobbish tone — with that I do not disagree. However, their prevalence is generally overstated; it's a vocal minority situation. Most people I know or have talked to are very welcoming.

That article went round the Edinburgh mailing list when it was published, and Phil Wadler, who got monads into Haskell, replied saying something like "I didn't know this. Does anyone have the proof?"

The actual quote that monads are monoids in the category of endofunctors comes from MacLane, and is intended for mathematicians.

I'm honestly not sure the MacLane reference applies here.

Although the abstract phrasing can be traced to him, the particular use of "just" in the parent comment's quote tells me they're specifically thinking of the (deliberately condescending) version from the Iry post, especially since that's the version that gets memed throughout the FP community. After all, that particular phrasing is meant to convey a sense of "this is obvious and you are stupid if you don't understand it immediately", which is a far cry from the MacLane version (since that one is, as you said, intended for mathematicians).

But I probably ought to have included the full provenance regardless; thank you for bringing it up!

"an X is just a Y" is a common turn of phrase in mathematical writing. It means that Xs and Ys are the same thing, whereas "an X is a Y" may, depending on context, mean only that every X is a Y. A human is a mammal, but a human is not just a mammal.

The original quote (from Categories for the Working Mathematician) is:

> All told, a monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor.

> "A monad is just a monoid in the category of endofunctors". Anyone who says that - or anything anywhere close to it - is gatekeeping, no matter how true the statement is.

Quite frankly, if you don't understand that sentence then you are in no position to judge whether the concepts could be made more accessible. Sometimes the important question is not "could this be easier to learn?" but "is learning it worth the effort?".

Notions of Computation as Monoids https://www.fceia.unr.edu.ar/~mauro/pubs/Notions_of_Computat...