Can the compiler decide the noexcept'ness of a function?

Question

Let's do an example

class X
{
    int value;
public:
    X (int def = 0) : value (def) {}

    void add (int i)
    {
        value += i;
    }
};

Clearly, the function void X::add (int) will never throw any exception.

My question is, can the compiler analyze the code and decide not to generate machine code to handle exceptions, even if the function is not marked as noexcept?

Answer 1

If the compiler can prove that a function will never throw, it is allowed by the "As-If" rule (§1.9, "Program execution" of the C++ standard) to remove the code to handle exceptions.

However it is not possible to decide if a function will never throw in general, as it amounts to solving the Halting Problem.