No. The <Omega combinator> is
$$
\Omega=(\lambda x.xx)(\lambda x.xx).
$$
Its only <beta-redex> contracts back to $\Omega$ itself. Every reduction sequence therefore repeats the same term, which is not in <beta-normal form>. Thus $\Omega$ has no beta-normal form.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 120 / 2 / e / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-120/2/e/solution