Nonsense. Most abstraction isn't about state at all (you won't find state anywhere in the definition of a group, say). You can of course abstract over the difference between having state and not having it (as OO does), but that's a virtually useless abstraction because it doesn't preserve any nontrivial rules/symmetries.

Perhaps a better way of saying is is that hidden data is a characteristic of abstraction. Which is certainly fair, and fits the analogy to algebra quite well.

But in any case, parent's comment that "OOP has no special claim" to hidden state/data (or abstraction) is sound; after all, ADTs already do that.

> Perhaps a better way of saying is is that hidden data is a characteristic of abstraction. Which is certainly fair, and fits the analogy to algebra quite well.

I'd disagree with even that much; I'd say abstraction is much more about parameterisation - factoring out the common structure from different constructions - than outright hiding anything.

> But in any case, parent's comment that "OOP has no special claim" to hidden state/data (or abstraction) is sound; after all, ADTs already do that.

ADTs don't hide mutable state. That much is something OO has a special claim to.

"hiding data" and "factoring out the common structure" are almost always intrinsically connected in software systems, because if you can poke at the data then you can violate contracts that give rise to the common structure.

This is particularly true of software, but I'd argue it's also true of basically every branch of mathematics outside of a few particular sub-fields of algebra (which are either extremely simple or extremely abstract, and often both).

> ADTs don't hide mutable state. That much is something OO has a special claim to.

How so? Abstract datatypes certainly hide mutable state. Just because a language doesn't have the "private" keyword doesn't mean that internal data can't be excluded from the interface... this was done all the time in e.g. C without the message passing semantics that characterize OO languages.

> if you can poke at the data then you can violate contracts that give rise to the common structure.

Maybe if you can mutate it, but having it be visible isn't an issue.

> Abstract datatypes certainly hide mutable state.

ADTs are normally understood to be values i.e. immutable. Hidden structure is not the same thing as hidden state.

> Most abstraction isn't about state at all (you won't find state anywhere in the definition of a group, say).

Sure, but you also wouldn't care that π is defined as an equivalence class of cauchy sequences if you're treating (R, +) as a group. In fact, one does not care at all about the particular details of a group being a set-- one treats groups up to isomorphism.

But of course, I was talking about abstraction in programming.

> Sure, but you also wouldn't care that π is defined as an equivalence class of cauchy sequences if you're treating (R, +) as a group. In fact, one does not care at all about the particular details of a group being a set-- one treats groups up to isomorphism.

You don't care at that point, but you don't destroy the information either. You know that (R, +) forms a group and you might use that group structure to, say, efficiently sum a list of reals - but you know that the answer is a real and not just a "group element", and you would go back to doing real-specific operations on your total. So it's more about parameterisation than about outright hiding information.

> But of course, I was talking about abstraction in programming.

What's the difference? If you don't mean the normal kind of abstraction then what's the definition of the thing that you're talking about?

> You don't care at that point, but you don't destroy the information either. You know that (R, +) forms a group and you might use that group structure to, say, efficiently sum a list of reals - but you know that the answer is a real and not just a "group element", and you would go back to doing real-specific operations on your total. So it's more about parameterisation than about outright hiding information.

When you reason about something as a group, that reasoning operates with the details hidden. When you apply that abstract reasoning to a concrete problem, of course that information is still there. Abstraction is a boundary that looks different on either side. In a similar vein of your example, the compiler knows all the information you're hiding through your program abstractions, but from the point of view of pieces of your code, that abstraction has hidden something.

> What's the difference? If you don't mean the normal kind of abstraction then what's the definition of the thing that you're talking about?

The word abstraction is so... abstract that it isn't actually a uniform concept applied in different areas but instead many similar concepts that look the same if you squint.

The concept I'm talking about is abstraction in the context of program structure. This is more related to mathematical abstraction than a mere metaphor but it's not exactly the same thing as the abstraction in a definition like groups, nor is it the same abstract as in abstract art.

> When you reason about something as a group, that reasoning operates with the details hidden. When you apply that abstract reasoning to a concrete problem, of course that information is still there. Abstraction is a boundary that looks different on either side. In a similar vein of your example, the compiler knows all the information you're hiding through your program abstractions, but from the point of view of pieces of your code, that abstraction has hidden something.

If I write a function like:

    f(x) = x + 2

would you say the value of x is "hidden" in the expression x + 2? I would say no: it's clear that there is a value of x at the point where we evaluate that expression. That's a different kind of thing from the OO style where we write o.f() and genuinely can't distinguish whether there is relevant internal state in o (and whether that state is mutated by the call to f()), or not.

There is a difference between a function `f` and the expression `x + 2` in your example. In fact, `f` as a function completely hides the expression from which it was defined. Usually functions are considered equal if they have the same values at every point. The upshot is, you can define a function from two different expressions and they can end up being the "same" function. This is indeed the hiding of some information.

In the composition of functions, f . g (x) = f(g(x)), that there is a result of g(x) is hidden by the composition, which only allows examination of the first input and the final output.

There is nothing special about OOP here.

> There is a difference between a function `f` and the expression `x + 2` in your example. In fact, `f` as a function completely hides the expression from which it was defined. Usually functions are considered equal if they have the same values at every point. The upshot is, you can define a function from two different expressions and they can end up being the "same" function. This is indeed the hiding of some information.

It's hiding the differing constructions, but at that point I don't see that as a true difference. (\x . x + 2) . (\x . x + 2) seems to me to be the same value as \x . x + 4 in exactly the same way that 2 + 2 is the same value as 4.

> In the composition of functions, f . g (x) = f(g(x)), that there is a result of g(x) is hidden by the composition, which only allows examination of the first input and the final output.

> There is nothing special about OOP here.

Having mutable state hidden/encapsulated with a bundle of functions that may be entangled with that state is unique to OOP; as I said in the side thread, hidden structure is not the same as hidden state.

So if all fields are public the object is still the object, not a data structure?