Comparing to another activity is useful if it helps you formulate questions, it's dangerous when you use it to justify answers.
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You're replying to a comment by fulano.
The way I see it is that there are two orthogonal axes here: polymorphism kind (ad-hoc vs parametric), and mechanism kind (dynamic vs static).
In parametric polymorphism the code works with an unlimited set of (variable, parametrized) types, and the behaviour is essentially identical for all of those types.
Contrast this with ad-hoc polymorphism, where there is a limited, enumerated set of types which are usable in the context, and the behaviour of the code varies as those types change.
On the other axis, dynamic vs static refers to whether the mechanisms which implement the polymorphism are run-time or compile-times ones.
In C++ this leads us to the following classifications:
Subclassing: dynamic, ad-hoc (NB it's only dynamic in the case of virtual functions)
Templates: static, parametric
Overloading: static, ad-hoc
(Can't think of a built-in, dynamic, parametric polymorphism in C++.)
Introduce template specialization, and you start mixing in ad-hoc features into the parametric polymorphism.
I don't really think that it is meaningful to think of casting as a kind of polymorphism.
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