Asynchrony is not concurrency

"Asynchrony" is a very bad word for this and we already have a very well-defined mathematical one: commutativity. Some operations are commutative (order does not matter: addition, multiplication, etc.), while others are non-commutative (order does matter: subtraction, division, etc.).

    try io.asyncConcurrent(Server.accept, .{server, io});
    io.async(Cient.connect, .{client, io});

Usually, ordering of operations in code is indicated by the line number (first line happens before the second line, and so on), but I understand that this might fly out the window in async code. So, my gut tells me this would be better achieved with the (shudder) `.then(...)` paradigm. It sucks, but better the devil you know than the devil you don't.

As written, `asyncConcurrent(...)` is confusing as shit, and unless you memorize this blog post, you'll have no idea what this code means. I get that Zig (like Rust, which I really like fwiw) is trying all kinds of new hipster things, but half the time they just end up being unintuitive and confusing. Either implement (async-based) commutativity/operation ordering somehow (like Rust's lifetimes maybe?) or just use what people are already used to.

Strictly speaking commutativity is defined over (binary) operations - so if one were to say that two async statements (e.g. connect/accept) are commutative, I would have to ask, "under what operation?"

Currently my best answer for this is the bind (>>=) operator (including, incidentally, one of its instances, `.then(...)`), but this is just fuzzy intuition if anything at all.

Commutative operations (all of them I think?) are trivially generalized to n-ary operations (in fact, we do this via ∑ and ∏, in the case of addition and multiplication, respectively). You're right that the question of what "operation" we're dealing with here is a bit hazy; but I'd wager that it's probably in the family of the increment operation (N++ === N + 1 = 1 + N) since we're constantly evaluating the next line of code, like the head of a Turing machine.

Edit: maybe it's actually implication? Since the previous line(s) logically imply the next. L_0 → L_1 → L_2 → L_n? Though this is non-commutative. Not sure, it's been a few years since my last metalogic class :P

Generalizing an associative binary op to an n-ary op just requires an identity element Id (which isn't always obvious, e.g. Id_AND=true but Id_OR=false).