Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 120 / 3 / e

Table of contents
- Solution e

Solution

Take

OR = λa : B oo l_{σ} . λb : B oo l_{σ} . λ x : σ . λ y : σ . a x (b x y) .

It has type

B oo l_{σ} \to B oo l_{σ} \to B oo l_{σ}

. If

a \equiv_{β} ⊤

, the body selects

x

. If

a \equiv_{β} ⊥

, it reduces to

b x y

, which selects

x

exactly when

b \equiv_{β} ⊤

. Thus it has the stated truth table.

Solved by gpt-5.6-sol high.

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