This question arised in the context of this answer.
As I would expect, this translation unit does not compile:
template int getNum()
Both, explicit specialization and explicit instantiation definition will violate ODR based on the context they are used and the meaning of the entities they generate.
The following explain the first and the third case and why they does violate ODR with NDR [temp.spec]/5
For a given template and a given set of template-arguments,
(5.1) an explicit instantiation definition shall appear at most once in a program,
(5.2) an explicit specialization shall be defined at most once in a program (according to 6.2), [...]
function templates may have different points of instantiation in both the same translation unit where they are defined and in others translation units, these specialization are guaranteed not to violate ODR when the meaning of these specialization is the same in all the points of instantiation.
since by [temp.point]/6
An explicit instantiation definition is an instantiation point for the specialization or specializations specified by the explicit instantiation.
and [temp.point]/8
[...] If two different points of instantiation give a template specialization different meanings according to the one-definition rule (6.2), the program is ill-formed, no diagnostic required.
the second case does not violate ODR, because the meaning of the instantiations in these TU is the same.
// decl.h
template int getNum() { return Num; }
// a.cc
#include
template int getNum<0>();
// b.cc
#include
template int getNum<0>();
int main() { getNum<0>(); return 0; }
But the last is certainly not a valid one (violate ODR NDR), because even the function templates have the same signatures the instantiations from them will have different meanings. You can't relay in the result you got, the standard don't guarantee the behavior when these violation happens.
// a.cc
template int getNum() { return Num + 1; }
template int getNum<0>();
// b.cc
#include
template int getNum() { return Num; }
template int getNum<0>();
int main() { std::cout << getNum<0>() << std::endl; return 0; }