What the f*ck is a monad

A monad is just a monoid in the category of endofunctors. Everyone knows that!

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Of course!

In other words though, for those just starting their monad journey:

An endofunctor is a box. If you have a box of soup, and a function to turn soup into nuts, you can probably turn the box of soup into a box of nuts. You don’t have to write a new function for this, if the box can take your existing function and “apply” it to its contents.

Arrays are endofunctors, because they hold things, and you can use Array.map to turn an array of X into an array of Y.

Monoids are things you can add together. Integer plus integer equals integer, so ints are monoids. String plus string (concatenation) equals a longer string, so strings are monoids. Grocery lists are monoids.

Arrays are monoids!

Arrays are both endofunctors and monoids, so for everyone except category theory purists, they are monads.

Javascript promises hold things, and you can transform their contents with .then - so they are endofunctors. You can “add them together” with Promise.all (returning a new promise), so they are monoids. They are both monoids and endofunctors, so they are monads.

I’ve just upset all the category theorists, but in the context of programming, that’s all it is. It’s surprisingly simple once you get it, it’s just complicated names for simple features.

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- "Complicated names for simple features" seems to describe Haskell crowd pretty well.
  
  Thank you for a straightforward explanation!
  
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- JavaScript promises are not monads: https://stackoverflow.com/questions/45712106/why-are-promises-monads
  
  They're close, but not quite. then can shift semantics from under you depending on what's supplied.
  
  It should also be added that monoids require the type to have an identity or "empty" value (which is the empty array for arrays).
  
  The explanation is pretty off in general, since it implies that any type that's both a functor and a monoid is a monad, which is simply not true. A good example is a ZipList (like lists, but with an applicative instance based on zipping). It's a functor and a monoid, but definitely not a monad.
  
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- IIRC monoid also requires you to have zero, so that an initial value is known for any repetitive operation. In case of an array that'd be an empty one, in case of promise that'd be doing nothing, I guess.
  
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Endodunctors? Now I have to know Minecraft too?

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Duh!

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Man. I recall watching the Computerphile video on monads and the first thing the presenter did was choose Haskell for example language.

Worst video of all of them, just some haskell masturbation. "Oooo, we can do infinite liiiists". Bitch that's called a generator.

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Unfortunately, no one can be told what a monad is. You have to see it for yourself (then you won’t be able to explain it to anyone)

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(for anyone wondering, a monad is just a monoid in the category of endofunctors)

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- I haven’t seen it for myself yet, so I can’t even read your comment. All the words look blurred out
  
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A monad isn't "a thing", it's a common interface shared by several different types that have a common mathematical structure that happens to be useful for structuring programs around. I think that's why it's so confusing to people, other programming languages tend to not have as abstract abstractions front and center.

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In my experience they're only really in your face when you're doing things with side-effects, and at that point it's just a lobster trap that collects your non-functional code until you pass it to main. Maybe I'm just a lame Haskeller though.

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- I use Either (for error handling) and State (for shared state in the program) fairly often, sometimes both at once with IO in a monad transformer stack. Having pure code is of course the best but error handling at least tends to sneak in through the program
  
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- I mean, List is a monad. It just happens that the mathematical pattern works well for encapsulating side effects too.
  
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I'm glad there is at least one serious answer on this thread.

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Functional programming is so much fun. Sadly people usually give it complicated concepts to a point that it scares beginners away.

I understand that by giving something a name, we have control and can communicate effectively with others about it (like design patterns). But still...

11

It's a pretty natural consequence of other languages simply not having a concept or word for the thing that we're trying to abstract over, so better names simply don't exist. I've yet to see anyone come up with a better name than "monad" for the concept. Same for monoids. We may as well use the names that come from math and are already used extensively rather than trying to invent some new name that would invariably be misleading anyway.

Every single programming language is chock full of jargon that is basically meaningless to anyone unfamiliar with it. It's really no different. The only difference is that monads are fundamentally an unfamiliar concept to many imperative programmers, particularly because programming in that style pretty much upends a basic assumption imperative programmers tend to have (namely, that the semantics of sequencing operations is a global, immutable property of programs).

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Give me both and wash it down with some Prolog goddammit

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In the mirror universe Morpheus is holding Go and Erlang

3

I mean, technically, Options are monads, so…

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Maybe I'm not understanding it correctly, but Monads are data-structure objects whose methods return an data-structure object of the same type.

Like, (using Typescript):


interface IdentityMonad<T> {
  map: ((fn: (v: T)) => T) => IdentityMonad<T>;
  value: T
}

const Identity = <T>(value: T) => {
  const map = (fn) => Identity(fn(initialValue));
  return {
    map, value
  }
}

const square = (x) => x * x;

const twoId = Identity<number>(2);
console.log(twoId.value) //=> 2;
const sixtyFourId = twoId.map(square).map(square).map(square).map(square).map(square);
console.log(sixtyFourId.value) // => 64;

2

The way I understood monads is they're a way to abstract the "executor" of a function. I/O monads run step-by-step based on stdin, List runs a function on every element, and the function is unaware of this, Option runs the function if the value exists (again the function's not aware of this)

That being said, I'm coming at this from a Rust view, and I've only scanned through one guide to monads so I may be wrong

0

That's not a monad, that's just typeclasses (also known as traits/interfaces/etc.).

If you're familiar with flat_map or and_then in Rust, you already get the basic idea of monads. Just imagine that instead of the ad-hoc implementations that Rust has to do (since it doesn't support higher-kinded data types), you could express it in a single trait. Then you can write code that generically works with any types that support flat_mapoperations (along with a couple of other requirements, like needing a From<T> impl, as well as abiding by some laws that are really only a concern for library authors).

If that sounds simple, it's because it is. It's mostly just that it just so happens that being able to write code in this fashion has some pretty significant implications. It essentially allows you to very strictly control the semantics of sequencing operations, while still giving you enough flexibility to enable many of the things you typically do in imperative programs. In a language like Haskell which is built on monads, it's a very powerful reasoning tool, much in the same way that purity in functions is a powerful reasoning tool. It allows us to do things like, say, represent async code blocks as first-class concepts requiring no special syntax (no async/await, etc.), because the monad interface allows us to dictate what it means to sequence async actions together (if you're curious to see what this looks like, here's a link to Haskell's Async type from the async library: https://hackage.haskell.org/package/async-2.2.4/docs/Control-Concurrent-Async.html#t:Async).

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- Ah, so is it right to say it's an abstraction of how functions are sequenced? I could kinda see that idea in action for I/O and Async (I assume it evaluates functions when their corresponding async input is ready?)
  
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