The reason the compiler doesn't accept this is that the standard tells it not to.
The reason the standard tells it not to, is that the committee did not what to introduce a rule that const MyTemplate<Derived*> is a related type to const MyTemplate<Base*> even though the non-const types are not related. And they certainly didn't want a special rule for std::set, since in general the language does not make special cases for library classes.
The reason the standards committee didn't want to make those types related, is that MyTemplate might not have the semantics of a container. Consider:
template <typename T>
struct MyTemplate {
T *ptr;
};
template<>
struct MyTemplate<Derived*> {
int a;
void foo();
};
template<>
struct MyTemplate<Base*> {
std::set<double> b;
void bar();
};
Then what does it even mean to pass a const MyTemplate<Derived*> as a const MyTemplate<Base*>? The two classes have no member functions in common, and aren't layout-compatible. You'd need a conversion operator between the two, or the compiler would have no idea what to do whether they're const or not. But the way templates are defined in the standard, the compiler has no idea what to do even without the template specializations.
std::set itself could provide a conversion operator, but that would just have to make a copy(*), which you can do yourself easily enough. If there were such a thing as a std::immutable_set, then I think it would be possible to implement that such that a std::immutable_set<Base*> could be constructed from a std::immutable_set<Derived*> just by pointing to the same pImpl. Even so, strange things would happen if you had non-virtual operators overloaded in the derived class - the base container would call the base version, so the conversion might de-order the set if it had a non-default comparator that did anything with the objects themselves instead of their addresses. So the conversion would come with heavy caveats. But anyway, there isn't an immutable_set, and const is not the same thing as immutable.
Also, suppose that Derived is related to Base by virtual or multiple inheritance. Then you can't just reinterpret the address of a Derived as the address of a Base: in most implementations the implicit conversion changes the address. It follows that you can't just batch-convert a structure containing Derived* as a structure containing Base* without copying the structure. But the C++ standard actually allows this to happen for any non-POD class, not just with multiple inheritance. And Derived is non-POD, since it has a base class. So in order to support this change to std::set, the fundamentals of inheritance and struct layout would have to be altered. It's a basic limitation of the C++ language that standard containers cannot be re-interpreted in the way you want, and I'm not aware of any tricks that could make them so without reducing efficiency or portability or both. It's frustrating, but this stuff is difficult.
Since your code is passing a set by value anyway, you could just make that copy:
std::set<Derived*> objs;
register_objects(std::set<Base*>(objs.begin(), objs.end());
[Edit: you've changed your code sample not to pass by value. My code still works, and afaik is the best you can do other than refactoring the calling code to use a std::set<Base*> in the first place.]
Writing a wrapper for std::set<Base*> that ensures all elements are Derived*, the way Java generics work, is easier than arranging for the conversion you want to be efficient. So you could do something like:
template<typename T, typename U>
struct MySetWrapper {
// Requirement: std::less is consistent. The default probably is,
// but for all we know there are specializations which aren't.
// User beware.
std::set<T> content;
void insert(U value) { content.insert(value); }
// might need a lot more methods, and for the above to return the right
// type, depending how else objs is used.
};
MySetWrapper<Base*,Derived*> objs;
// insert lots of values
register_objects(objs.content);
(*) Actually, I guess it could copy-on-write, which in the case of a const parameter used in the typical way would mean it never needs to do the copy. But copy-on-write is a bit discredited within STL implementations, and even if it wasn't I doubt the committee would want to mandate such a heavyweight implementation detail.