Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 120 / 2 / d

No. Let $c_0=\lambda f.\lambda x.x$ and setBoth terms send every Church numeral to $c_0$, so both define the constant-zero function. They are distinct beta-normal forms, however, and the Church-Rosser theorem implies that distinct beta-normal forms cannot be beta-equivalent.

Solved by gpt-5.6-sol high.