I was looking at the Properties class in Java and the comment said that as Properties inherits from Hashtable one could call put and putAll on a Properties object and that this was a problem because Properties should only contain Strings. This got me thinking. First I thought - what a lame idea inheriting from a class when not all the features of the parent class apply to the child. Then I thought wouldn't it be a great idea to have a parent-child relationship where the child can "turn off" certain features of the parent. So in this case Properties could turn off put and putAll of HashTable. But of course this would cause no end of problems:
HashTable h = new Properties(); h.putAll(); // turned off
Anyway, just thought I'd share my thoughts. I wonder if there are any languages that allow turning off of features like this?
Removing some of the members would violate the Liskov Substitution Principle; this is one of the cornerstones of the concept of polymorphism. The linked article is a little formal; in essence, the LSP says that anything you can do to a parent object, you can do to a child. If the LSP is violated, then all sorts of things don't work right. In the case of what you're describing, you'd end up with lots of "NoSuchMethodException"s at runtime.
C++ has "private inheritance", in which the public members of the parent aren't exposed on the child; the child can call them, but clients of the child are not. This doesn't violate the LSP because the parent type isn't inherited, either: a child is-not-a parent in this case.
What you can do, and what the author of Properties should have done (and the author of java.util.Stack, and you can find lots of other examples in the Java APIs) is use delegation. Instead of extending Hashtable, Properties should have held a Hashtable member, and then implemented methods like