On Linux, we use the inotify subsystem to be informed every time you save a source file or switch branches. The hh_server process can then update its data structures immediately, without being explicitly asked.

I don't really get why this is the second paragraph on the page of a language though. It's like touting the jar command in an overview of Java.

Because this is tremendously important to the usability of the language.

One of the reasons that PHP has been such a success is that you can simply save a source file and reload a web page to see what's going on.

The server-based typechecker that runs instantaneously is what makes it possible for Hack to replicate this experience: you save a file and reload a web page, but you have the safety net of a typechecker that told you about your type errors as soon as you saved the file.

I can't overstate how important this instant feedback is: it's really the thing that distinguishes Hack from working in a more traditional compile-based static language.

Adding static typing to a dynamic language means that more work must be done at compile time than at run time.

One appeal of dynamic languages is you don't have a long compile time[1].

So I imagine they emphasize this to address the worry that this will get ruined and there will be a horrible workflow.

[1] However Turbo Pascal was a one-pass typed compiler in the early 80s that was blazingly fast with 1 MHz CPUs and 64 KB RAM. :)

The fact that we wanted the type system to be instantaneous drove some of our design decisions.

Was it debated whether this should be a tooling feature - thinking of an IDE plugin that parses and type-checks in the background rather than a dedicated service to watch text files on disk

In Hack's case, the language is the implementation anyway.