There is nothing in the standard or definition of C++ that states that undefined behavior renders a program invalid.
On the contrary the actual C++ standard explicitly states that permissible undefined behavior includes, and I quote "behaving during translation or program execution in a documented manner characteristic of the environment".
It's also worth noting that numerous well known and used C++ libraries explicitly make use of undefined behavior, including boost, Folly, Qt. Furthermore, as weird and ironic as this sounds, implementing cryptographic libraries is not possible without undefined behavior.
"valid program" is not really a term that is used in the standard (I only count one normative usage). What the standard does say is:
"A conforming implementation executing a well-formed program shall produce the same observable behavior as
one of the possible executions of the corresponding instance of the abstract machine with the same program
and the same input. However, if any such execution contains an undefined operation, this document places
no requirement on the implementation executing that program with that input (not even with regard to
operations preceding the first undefined operation)."
I.e. a program the contains UB is undefined.
Of course, as you observer, an implementation can go beyond the standard and extend the abstract machine to give defined semantics to those undefined operations.
That's still different from implementation defined behaviour, where a conforming implementation must give defined semantics.
On the contrary the actual C++ standard explicitly states that permissible undefined behavior includes, and I quote "behaving during translation or program execution in a documented manner characteristic of the environment".
It's also worth noting that numerous well known and used C++ libraries explicitly make use of undefined behavior, including boost, Folly, Qt. Furthermore, as weird and ironic as this sounds, implementing cryptographic libraries is not possible without undefined behavior.