I can't quite figure out what I have seen referred to as an Objective-C "class continuation". Is this / are these…
A continuation class is what Apple calls a class extension. I have seen clang call them "continuation class" and gcc uses "class continuation".
Compile this in clang or gcc:
@interface Foo : NSObject @property int a; @end @interface Foo() @property float a; @end
... and you will get errors with the funny names.
To answer the rest of your question:
- What is the scope, lifetime, and usage case for such a thing?
Extensions are used to declare the private interface for a class. You can also use it to redeclare (refine) public property declarations.
- Is this an ARC-specific "feature"?
- Are there specific runtime, or other requirements for their use?
Class Extensions are a compile time concept and do not require a special runtime. Of course they do require a compiler that supports them (both clang and gcc do in current versions).
- Is this an appropriate place to create an @property, as well? And why would this be a better place for setting ivars or properties than, say, the @interface file / declaration?
YES. Because you might want to have private properties.
- Why do people complicate discussions by using such specific terminology - that seems NOT to exist in any official documentation (that I could find)?
Well, you know... I'd also prefer if the whole world spoke English, but for the time being I'm happy with the fact that I had to learn it in school.