> This article isn't really about callbacks and it isn't even really about APIs.
Well then, perhaps you should have named the article something else...?
The essential problem is that any program which can incorporate arbitrary recursion is subject to the halting problem. The seemingly simple initial fixes, like a lock or asynchronous callback queue, can improve things. The author proposes third-party code analysis tools to help; I'm less sure of that. The Gödel dragon is not easily pushed back, and we often accidentally create Turing machines.
I think the title's fine. It's better than "Callbacks and the Halting Problem", since most of the essay covers, after all, "Pitfalls of Callback-Based APIs".
Yes, further automated analysis can find some of these problem. That's what the author of the essay proposes, and it's good to know that there are some solutions.
Let's go down the road further and expand the system so there are multiple loggers, and where subsystem logger configuration via an external configuration file occurs at run-time. Some configurations are acyclic, others are not.
This could be prohibited by edict - if a program cannot be analyzed then it's not valid. As the essay points out, there are also formal verification techniques - and that very few people use them. As I pointed out, it's surprisingly easy to make a Turing machine by accident. (See http://beza1e1.tuxen.de/articles/accidentally_turing_complet... and its HN comments https://news.ycombinator.com/item?id=6577671 .)
In practice then, it's very unlikely that most complex software will be able to use these tools, because it's hard to restrict the solution space to what those tools can analyze.
Here there be dragons.