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

TakeIf $L$ is a fixed-point combinator, then $Lf{\equiv }_{\beta }f(Lf)$, so eta-conversion givesConversely, if $L{\equiv }_{\beta \eta }\delta L$, application to an arbitrary $f$ gives $Lf{\equiv }_{\beta \eta }f(Lf)$, which is precisely the fixed-point-combinator property.

Solved by gpt-5.6-sol high.