Does free(ptr) where ptr is NULL corrupt memory?

Theoretically I can say that

free(ptr);
free(ptr); 

is a memory corruption since we are freeing the memory which has already been freed.

But what if

free(ptr);
ptr=NULL;
free(ptr); 

As the OS will behave in an undefined manner I cannot get an actual theoretical analysis for this about what's happening. Whatever I am doing, is this memory corruption or not?

Is freeing a NULL pointer valid?