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I have heard that C++ class member function templates can't be virtual. Is this true?
If they can be virtual, what is an example of a scenario in which one would use such a function?
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A virtual function is a member function that you expect to be redefined in derived classes. When you refer to a derived class object using a pointer or a reference to the base class, you can call a virtual function for that object and execute the derived class's version of the function.
A virtual function cannot be global or static because, by definition, a virtual function is a member function of a base class and relies on a specific object to determine which implementation of the function is called. You can declare a virtual function to be a friend of another class.
A non-template class can have template member functions, if required. Notice the syntax. Unlike a member function for a template class, a template member function is just like a free template function but scoped to its containing class.
Member functions can be function templates in several contexts. All functions of class templates are generic but are not referred to as member templates or member function templates. If these member functions take their own template arguments, they are considered to be member function templates.
Templates are all about the compiler generating code at compile-time. Virtual functions are all about the run-time system figuring out which function to call at run-time.
Once the run-time system figured out it would need to call a templatized virtual function, compilation is all done and the compiler cannot generate the appropriate instance anymore. Therefore you cannot have virtual member function templates.
However, there are a few powerful and interesting techniques stemming from combining polymorphism and templates, notably so-called type erasure.
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From C++ Templates The Complete Guide:
Member function templates cannot be declared virtual. This constraint is imposed because the usual implementation of the virtual function call mechanism uses a fixed-size table with one entry per virtual function. However, the number of instantiations of a member function template is not fixed until the entire program has been translated. Hence, supporting virtual member function templates would require support for a whole new kind of mechanism in C++ compilers and linkers. In contrast, the ordinary members of class templates can be virtual because their number is fixed when a class is instantiated
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