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I tried learning Haskell for a decent chunk of time and could make some stuff, but despite trying to learn, I still could not tell you what a monad actually is. All the explanations for it seemed to make no sense.
Monads are a generalization of Promises. Each type in Monad defines their own `.then` in a different way. For promises, `.then` is defined as "run this function once you have this deferred value from the last promise". For optionals (`Maybe`), `.then` is defined as "run this function if the last optional had an actual value". For Either, `.then` is defined as "run this function if the last Either returned Right, otherwise early-return with the value from Left" (this is functional early-return, basically).
This is the first explanation of monads I've heard that makes intuitive sense to me and feels like it sufficiently captures the point. Unless I come back in a few hours to see a bunch of replies from uber-haskellers saying "no that's not what a monad is at all," then I'll consider my search for a good monad explanation to finally be over.
No I believe he's basically formally correct.

You need to be able to "wrap" values and then also "wrap" functions in the way you expect. That's literally it.

Btw, the list monad example is stupid imo and borderline misleading. The promise/nullable/Either examples are better. you "wrap" a function by putting it as the only value in a list, and "map" pretty much acts as your function wrapper, but technically this you need to jump through a couple hoops to make it monadic, and I'm just not sure the metaphor is helpful here

This is misleading IMO because Promise is a particular kind of monad but in general monads don’t necessarily have anything to do with asynchrony. It is a useful example though because some people are more familiar with the API of promises.

I might have some inaccuracies in how I state this since I’m not from a functional programming background, but I think of monads as an abstraction of chaining functions over a value such that each returned value can specify what further transformations it supports, and particularly in such a way that generic transformations (like sequence reversal) can easily be applied, and errors or empty values can be accounted for within the control flow.

I think sometimes people call this a “fluent API”, but I would never call it “a generalization of callbacks” or of promises.

Anyway there’s a much more mathematically precise way of stating it but this is my intuitive caveman way of thinking about it.

Promises? Even more generally, Monads are a generalization of Chaining.

(I'm trying very hard not to fall into the trying-to-explain-monads trap!)

The important thing to know first is that a monad is not a single thing like "Optional". "monad" is a pattern or "interface" (called a "typeclass" in Haskell), that has many implementations, (Optional, Either, List, State Transormer, IO (Input/Output), Logger, Continuation, etc). Sort of how "Visitor" pattern in C++/Java is not a single thing.

https://hackage.haskell.org/package/base-4.21.0.0/docs/Contr...

https://book.realworldhaskell.org/read/monads.html

A common metaphor for monad is "executable semicolons". They are effectively a way to add (structured) hook computations (that always returns a specific type of value) to run every time a "main" computation (akin to a "statement" in other languages) occurs "in" the monad.

It's sort of like a decorator in Python, but more structured. It lets you write a series of simple computational steps (transforming values), and then "dress them up" / "clean them up" by adding a specific computation to run after each step.

This makes SchemaLoad's comment perfectly clear.

(but do I appreciate the effort you put into your reply - reading that monad's are more like interfaces is new information to me, and might help down the road)

Somehow I hear this all the time, but the haskell people have to realize that code patterns are absolutely a thing in all languages, ever? A lack of syntactic sugar doesn't mean monads don't exist in other languages.

Typeclasses are a distraction, the point is computation ignoring annoying contexty stuff (file not found errors, null on failure, etc) and there's dozens of examples in literally every language ever.

Not all problems are solved with a technical definition.

Monad is a pattern for constructing container types so that their instances can be used in chain operations safely. Given a value type, you can build a monad type wrapping the value type with a set of prescribed monadic functions. Instances of the monad type are called monadic values.

Example is best for illustration. I'll use a made-up syntax.

  // 'Maybe' is a monad wrapping any value type T that can be null.
  class Maybe<T> {
    // The value wrapped by the monadic value
    value: T;

    // A constructor to make a Maybe monadic value from a plain value T.
    // This is called 'unit' or 'return' in Haskell, or 'lift' in other languages.
    // It's really a constructor.
    static wrap(v: T) Maybe<T> {
        return new Maybe { value = v } 
    }

    // then() applies fn on the unwrapped value. fn returns a Maybe<T>.
    // This is called 'bind' in Haskell, or 'flatMap' in other languages.
    then(fn: (T) => Maybe<T>) Maybe<T> {
        return this.value == null ? Maybe.wrap(null) : fn(this.value);
    }
  }
That's it! That's all to to monad. You can use the same pattern to build other monadic types, like List<T>, Promise<T>, IO<T>, as long as the wrap() and then() functions are built accordingly. Back to this example, to use it,

  let a = Maybe<int>.wrap(4)                   // construct a monadic value
  let b = a.then(x => Maybe<int>.wrap(x + 1))  // add 1 to it
  let c = Maybe<int>.wrap(null)                // construct a null monadic value
  let d = c.then(x => Maybe<int>.wrap(x + 1))  // safely handle null; d is null

  let e = Maybe<int>.wrap(5)
    .then(x => Maybe<int>.wrap(x + 1))
    .then(x => Maybe<int>.wrap(x * 2))    // chain the calls

  let f = Maybe<float>.wrap(5.0)          // The same Maybe on a different type
    .then(x => Maybe<float>.wrap(null))
    .then(x => Maybe<float>.wrap(x * 2))  // chain the calls; safely handle null
Why does it sound so complicated when it is just a wrapper type that conforms to an interface?
A monad is just a monoid in the category of endofunctors
It's like an enchilada, right?
Unfortunately no one can tell you what a monad is. You have to experience it for yourself. - Haskell Morpheus
I’m convinced that this kind of talk is cope dreamed up by people who don’t understand monads but are expected to in their professional or student setting.
Forget all the academic definitions, at it's core a monad is a container or wrapper that adds additional functionality to a type.
Yes, this is the only definition I get, but then I don't get all the rage about monads, because containers and standardized interfaces are nothing new, so surely that definition must be wrong?
It's an implementation of the typeclass Monad, which happens to come with a special "do" keyword.
The largest problem I found when I was going through the same thing was that every explanation that's trying to provide a non-abstract answer will always suffer the flaw of not being universally true. Because they're an abstract concept.
Just think of it as a design pattern, but a bit more strict than the Gang of Four patterns. Fundamentally it's a relationship between types and other types such that certain operations make sense and follow well-understood rules (the monadic laws). Study the monadic laws, and try playing with the State, IO, and List monads to get a better sense of what those operations are and why they're useful for sequencing in a pure-functional context.
Nan-in received a university professor who came to inquire about Monads

Nan-in served tea. He poured his visitor’s cup full, and then kept on pouring.

The professor watched the overflow until he no longer could restrain himself. “It is overfull. No more will go in!”

“Like this cup,” Nan-in said, “you are full of your own opinions and speculations. How can I show you a Monad unless you first empty your cup?”

This is as good an explanation of monads as any. Which is to say, bad.
Someone may correct me but - in three levels of conciseness...

A monad is a function that can be combined with other functions.

It's a closure (or functor to the cool kids) that can be bound and arranged into a more complex composite closure without a specification of any actual value to operate on.

It's a lazy operation declaration that can operate over a class of types rather than a specific type (though a type is a class of types with just a single type so this is more a note on potential rather than necessary utility) that can be composed and manipulated in languages like Haskell to easily create large declarative blocks of code that are very easy to understand and lend themselves easily to abstract proofs about execution.

You've probably used them or a pattern like them in your code without realizing it.

So it's a function pointer, right? /s
beats me. I spent so much time learning what a fundamental group is and I still cannot tell ppl what a fundamental group is convincingly.

I can’t even make stuff with fundamental groups.

You should first understand what a typeclass and a Functor is.
no, you do not.
Yes monads in general are too expressive but the answer isn't to limit the typeclass to something between applicative and monad but rather to limit what monads are allowed. The problem is that there should only be one monad: an effect monad loaded with various effects depending on the side effect needed. Instead of defining this or that monad, there should only be the capability to define the effect you need.

In that case, everything runs within the effect monad and then no one would ever really need to learn what a monad is, just that some calls are effectful (like reading a file or throwing an exception).

I'd argue the exact opposite. Compared to what you can do if you can write compilers anything that involves composing functions is weak beer and most monad examples cover computational pipelines as opposed to computational graphs. It's like that Graham book On Lisp, it's a really fun book but then you realize that screwing around with functions and macros doesn't hold a candle to what you learn from the Dragon Book.
> screwing around with functions and macros doesn't hold a candle to what you learn from the Dragon Book

This depends a lot on what you mean. My first take is that the more you know about macros the more you realize what they can do.

I don’t know what your takeaway from the Dragon Book was, but writing DSLs using macros feels very usefully powerful to me.

I think you are undervaluing modern macros.

I maintain that the big advantage of the On Lisp approach is that all of that is available without having to write a new compiler.

Granted, I also don't have as heavy an attachment to pure functional as most people seem to build. Don't get me wrong, wanton nonsense is nonsensical. But that is just as true in immutable contexts.

What I found remarkable about that book is that 80% of what is in it can be done with functions and no macros, mostly you can rewrite the examples in Python except for the coroutines but Python already has coroutines. It also irks me that the I don’t think the explanation of coroutines in Scheme is very clear but it’s become the dominant one you find in the net and I can’t find a better one.

As for ‘compiler’ you also don’t need to go all the way to bare metal, some runtime like WASM or the JVM which is more civilized is a good target these days.

But lisp programs are compilers. That's the whole point of lisp and macros. Your functions can happily emit assembly direction.
> if you can write compilers anything that involves composing functions is weak beer

> screwing around with functions and macros doesn't hold a candle to what you learn from the Dragon Book.

---

So, what is it that you learn from that book that's a revelation for you compared to the weak beer of composable effect systems?

It'd be nice to have a process like the following:

1. I free solo a bunch of junk in vanilla javascript with state flowing hither and thither until I'm out of coffee

2. I test the exact behaviors(s) I wanted to make possible in the GUI I just wrote.

3. The framework whitelists only the event chains from my test.

4. For any blacklisted event chains, the user gets a Youtube video screencast of the whitelisted test so they can learn the correct usage of my GUI.

If someone paired this with a code-lite GUI designer, the world would be a brighter place indeed
Interesting, but it seems like he kind of proved himself wrong? Monads are the only option he presented that are sufficiently powerful for normal programs.
I don't think you're being fair to Chris Penner. He ends his blog post with: "It may take me another 5 years to finally finish it, but at some point we'll continue this journey and explore how we can sequence effects using the hierarchy of Category classes instead." Emphasis by me.

So while it is true, that what he has described so far is not sufficiently powerful for normal programs, he has clearly stated that there are more abstractions between Applicative and Monad to explore than what he has presented so far.

took a bit less than five years :) https://chrispenner.ca/posts/arrow-effects
And here I thought it was a pedantic word for “data box”
Yes. For the same reason that the Yoneda lemma and the Cayley theorem are almost meaningless tautologies once you fully understand what they're saying. "Every small thing (of a certain type) is able to be expressed as a subcase of a bigger thing that contains every single possible subcase in existence." Well no shit.
Haskell looks a heck lot like F#, even more than Ocaml if you ask me
I'd say the family resemblance is the other way around. F# was influenced by Haskell, both in syntax and semantics. Just as Haskell was influenced by early ML.

Haskell and ML make up one of the major language families. They are more like each other than they are like other languages. Inspired by the lambda calculus. Strong static typing with type inference. A succinct math-like syntax that emphasizes pattern matching.

Haskell goes further with syntactic sugar and tries to be almost equation-like:

    a = 5
    f = \x -> x + 1
    g x = x + 2
    f $ g a
SML:

    val a = 5
    val f = fn x => x + 1
    fun g x = x + 2
    f (g a)
But F# like Haskell makes no distinction between values and functions:

    let a = 5
    let f = fun x -> x + 1
    let g x = x + 2
    f (g a)
The use of indent-based blocks is another Haskell-ish influence on F#. But now we're awfully close to bikeshedding.
Paging John Harrop...

https://news.ycombinator.com/item?id=1396763