Multiple non-identical definitions the One Definition Rule

If a class, enum, inline function, template, or member of a template has external linkage and is defined in multiple translation units, all definitions must be identical or the behavior is undefined according to the One Definition Rule (ODR).

foo.h:

class Foo {
  public:
    double x;
  private:
    int y;
};

Foo get_foo();

foo.cpp:

#include "foo.h"
Foo get_foo() { /* implementation */ }

main.cpp:

// I want access to the private member, so I am going to replace Foo with my own type
class Foo {
  public:
    double x;
    int y;
};
Foo get_foo(); // declare this function ourselves since we aren't including foo.h
int main() {
    Foo foo = get_foo();
    // do something with foo.y
}

The above program exhibits undefined behavior because it contains two definitions of the class ::Foo, which has external linkage, in different translation units, but the two definitions are not identical. Unlike redefinition of a class within the same translation unit, this problem is not required to be diagnosed by the compiler.