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If I skip the back story and any thoughts I have on this topic, there's really only one question left to ask:
How can I find out if I have a "good grasp" on OOP?
(I am specifically using PHP, but it probably won't matter...)
Right now I kind of think of classes as a collection of functions with some global-ish variables accessible by all those functions. This helps to reuse code, keep files short and the namespace clean.
Some of you mentioned inheritance: To me that again just means that I can extend an existing class with more functions and more global-ish variables. It's like an add on to my existing class. And the same benefits come into place: reuse code, keep files short.
I have a ominous feeling that I'll be disillusioned here in a minute...