It's not about what a monad can do, it's about a property of the language: referential transparency. Haskell has referential transparency, Python doesn't. That's a technical condition but here's a simple consequence: effect typing. In Haskell you can know what possible effects an operation has from its type. Here's an example from my effect system, Bluefin:
foo ::
_ =>
Exception String e1 ->
State Int e2 ->
Eff es Bool
foo = ...
We know that `foo` produces a `Bool` and the only effects it can do are to throw a `String` exception and mutate an `Int` state. That's it. It can't yield anything to a stream, it can't make network connections, it can't read from disk. In order to compose these operations together, `Eff` has to be an instance of `Monad`. That's the only way `Monad` turns up in this thing at all.
So, that's what you get in Haskell that Python doesn't give you.
Those annotations create a compile-time enforced typological relationship between the input and output values of the function. Python doesn't have mandatory type-checking so it can't do that. But parent wasn't referring to type-checking. They claimed monads have expressive power unavailable in other languages.
> Those annotations create a compile-time enforced typological relationship between the input and output values of the function. Python doesn't have mandatory type-checking so it can't do that
Python doesn't have (mandatory) compile time type checking, no, but in principle a dynamically typed language could still be referentially transparent, and then it would (or at least could) still be the case that the only effects that a particular operation can perform are those arguments that are passed into it.
> But parent wasn't referring to type-checking. They claimed monads have expressive power unavailable in other languages.
That's true. But think of other syntax sugar like async/await. That comes for free in Haskell with monads and do notation.
Monad is a weird type that a lot of languages can't properly represent in their type system. However, if you do what dynamically-typed scripting languages do, you can do any fancy thing that Haskell does, because it is weakly typed in this sense. (The sense in which Python is "strongly typed" is a different one.)
What you can't do is not do the things that Haskell blocks you from doing because it's type-unsafe, like, making sure that calling "bind" on a list returns a list and not a QT Window or an integer or something.
> Monad is a weird type that a lot of languages can't properly represent in their type system.
While true, a lot of FP-inspired libraries in the majority of languages that don't have HKT will just implement one or several specific monads as well as the common operations on them. This creates some redundancy and slight inconsistency, but often the shared vocabulary is still strong enough to carry around expectations more or less, even if it's not explicitly enforced by the type system. That's how you can have sequence(): List<Either<L,R>> -> Either<L, List<R>> in e.g. Kotlin, for example.
Even in Scala, where you actually can define a monad typeclass (trait), there are very popular libraries like ZIO that effectively give you a monad without actually adhering to any Monad trait. I believe they do this for type inference reasons.
Haskell monads have been described as "programmable semicolons" because they specify ways to interpret "do" blocks.
In some sense they are a little bit similar to Python classes. A Python class is a block of code, which runs in a normal Python way, and then the variables put in scope by that code are passed to a metaclass constructor which creates some kind of object based on them. Monads are nothing like that, but they are similar in that user code is interleaved with framework code to produce an effect similar to a DSL. Monads run one statement at a time, interleaving one statement execution with one monad join operation.
This may be a dissenting opinion, but... Haskell tried to avoid mutable state. "Local state manipulation" was not really a thing you could do in Haskell, deliberately. Then someone figured out that you could (ab)use a monad to do that. And because that was the only way, whenever they needed to manipulate state, Haskell programmers reached for a monad.
So it's not "what can a Haskell monad do that a Python class cannot". It's "what can a Python class do in a straightforward way that Haskell has to use a monad for, because Haskell put the programmer in a straightjacket where they couldn't do it without a monad". It's basically a pattern to get around the limitations of a language (at least when it's used for state).
This is not historically how Haskell was developed. Haskell didn't try to "avoid mutable state". Haskell tried to be (and indeed succeeded in being) referentially transparent. Now, it turns out that you can't uphold referential transparency whilst having access to mutable state in the "traditional" way, but you can access mutable state if you introduce monads as a means of structuring your computation.
So, they're certainly not a means of getting around a limitation of the language. If it was just a limitation that limitation would have been lifted a long time ago! It's a means of preserving a desirable property of the language (referential transparency) whilst also preserving access to mutable state, exceptions, I/O, and all sorts of other things one expects in a normal language.
But historically, wasn't there a fair period of time between Haskell insisting on referential transparency (and therefore not allowing traditional mutable state) and monads being introduced as a way to deal with it? That was my understanding of the history.
And if so, then it seems fair to say at least that monads were a way to get around the limitations imposed by a desirable feature of the language...
> But historically, wasn't there a fair period of time between Haskell insisting on referential transparency (and therefore not allowing traditional mutable state) and monads being introduced as a way to deal with it? That was my understanding of the history.
Yes, although there were solutions in the meantime. I/O was performed in the original version of Haskell through input-output streams and continuation passing style. It turns out that both approaches could have been given monad interfaces if "monad" as an abstraction had been understood at the time, but it wasn't, so they had ad hoc interfaces instead.
> And if so, then it seems fair to say at least that monads were a way to get around the limitations imposed by a desirable feature of the language...
I mean, sort of, but that seems more of a judgement than a fact. Would you say that function calls in C were a way to "get around the limitations imposed by not allowing global jumps"?
In both cases I'd just say they're a useful abstraction that lets you achieve a well-specified goal whilst preserving some desirable language property.
