Undefined behavior causing time travel

There is a flow in the reasoning.

When a compiler writer says: we use Undefined Behavior to optimize a program, there are two different interpretations:

• most people hear: we identify Undefined Behavior and decide we can do whatever we want (*)
• the compiler writer meant: we assume Undefined Behavior does not occur

Thus, in your case:

• dereferencing a nullptr is Undefined Behavior
• thus executing value_or_fallback(nullptr) is Undefined Behavior
• thus executing the else branch is Undefined Behavior
• thus door_is_open being false is Undefined Behavior

And since Undefined Behavior does not occur (the programmer swears she will follow the terms of use), door_is_open is necessarily true and the compiler can elide the else branch.

(*) I am slightly annoyed that Raymond Chen actually formulated it this way...

It's true that undefined behaviour may happen only at runtime (e.g. dereferencing a pointer which happens to be null). Other times, a program may statically be "ill-formed, no diagnostic required" (e.g. if you add an explicit specialization for a template after it has already been used), which has the same effect, though: You cannot argue from within the language how your program will behave.

Compilers can use UB to "optimize" code generation aggressively. In your case, the compiler sees that the second branch will cause UB (I assume that this is known statically, even though you didn't spell it out), and so it can assume further that that branch is never taken, since that's indistinguishable: If you did enter the second branch, then the behaviour would be undefined, and that includes behaving like you entered the first branch. So the compiler can simply consider the entire code path that leads to UB as dead and remove it.

There's no way for you to prove that something is wrong.