> The whole point of OOP is that each object is responsible for maintaining its own invariants.
I think there are a whole lot of people who might disagree with the assertion that this is "the whole point" of OOP. Including one Alan Curtis Kay.
OOP to me means only messaging, local retention and protection and
hiding of state-process, and extreme late-binding of all things. It
can be done in Smalltalk and in LISP. There are possibly other
systems in which this is possible, but I'm not aware of them.
http://userpage.fu-berlin.de/~ram/pub/pub_jf47ht81Ht/doc_kay...
> Open classes are useless without open methods
You seem to mix "class" and "object" rather freely. They are quite different things. Also, not sure what you mean with "open methods". I can add methods to something in a subclass. I can override methods in a subclass.
> letting your child classes mess up those invariants.
Who is the "you" of the "your" in this context? A class? But a class is not a really a thing, objects are. And it is the objects that are the units of encapsulation in OOP. Not classes. Classes are just convenient bundles of behaviour and templates for state that is attached to objects.
You might think this is silly nitpicking, but it's actually a really, really important distinction:
As a teacher of object-oriented programming, I know that I have succeeded when students anthropomorphise their objects, that is, when they turn to their partners and speak of one object asking another object to do something. I have found that this happens more often, and more quickly, when I teach with Smalltalk than when I teach with Java: Smalltalk programmers tend to talk about objects, while Java programmers tend to talk about classes. I suspect that this is because Smalltalk is the more dynamic language: the language and the programming environment are designed to help programmers interact with objects, as well as with code. Indeed, I am tempted to define a “Dynamic Programming Language” as one designed to help the programmer learn from the run-time behaviour of the program.
http://web.cecs.pdx.edu/~black/publications/O-JDahl.pdf
And the object in question is an instance of the subclass, and if you are going to involve classes, it is the subclass that is responsible for maintaining invariants. The superclass no longer has that responsibility for instances of the subclass. So nobody is messing with anyone's invariants.