Why does an overridden function in the derived class hide other overloads of the base class?

Judging by the wording of your question (you used the word “hide”), you already know what is going on here. The phenomenon is called “name hiding”. For some reason, every time someone asks a question about why name hiding happens, people who respond either say that this called “name hiding” and explain how it works (which you probably already know), or explain how to override it (which you never asked about), but nobody seems to care to address the actual “why” question.

The decision, the rationale behind the name hiding, i.e. why it actually was designed into C++, is to avoid certain counter-intuitive, unforeseen and potentially dangerous behavior that might take place if the inherited set of overloaded functions were allowed to mix with the current set of overloads in the given class. You probably know that in C++ overload resolution works by choosing the best function from the set of candidates. This is done by matching the types of arguments to the types of parameters. The matching rules could be complicated at times, and often lead to results that might be perceived as illogical by an unprepared user. Adding new functions to a set of previously existing ones might result in a rather drastic shift in overload resolution results.

For example, let’s say the base class B has a member function foo that takes a parameter of type void *, and all calls to foo(NULL) are resolved to B::foo(void *). Let’s say there’s no name hiding and this B::foo(void *) is visible in many different classes descending from B. However, let’s say in some [indirect, remote] descendant D of class B a function foo(int) is defined. Now, without name hiding D has both foo(void *) and foo(int) visible and participating in overload resolution. Which function will the calls to foo(NULL) resolve to, if made through an object of type D? They will resolve to D::foo(int), since int is a better match for integral zero (i.e. NULL) than any pointer type. So, throughout the hierarchy calls to foo(NULL) resolve to one function, while in D (and under) they suddenly resolve to another.

Another example is given in The Design and Evolution of C++, page 77:

class Base {
    int x;
    virtual void copy(Base* p) { x = p-> x; }

class Derived : public Base{
    int xx;
    virtual void copy(Derived* p) { xx = p->xx; Base::copy(p); }

void f(Base a, Derived b)
    a.copy(&b); // ok: copy Base part of b
    b.copy(&a); // error: copy(Base*) is hidden by copy(Derived*)

Without this rule, b’s state would be partially updated, leading to slicing.

This behavior was deemed undesirable when the language was designed. As a better approach, it was decided to follow the “name hiding” specification, meaning that each class starts with a “clean sheet” with respect to each method name it declares. In order to override this behavior, an explicit action is required from the user: originally a redeclaration of inherited method(s) (currently deprecated), now an explicit use of using-declaration.

As you correctly observed in your original post (I’m referring to the “Not polymorphic” remark), this behavior might be seen as a violation of IS-A relationship between the classes. This is true, but apparently back then it was decided that in the end name hiding would prove to be a lesser evil.

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