Question

Reduce the following A expression to normal form. Show each reduction step. If already in normal form, write "normal form". Hint: function application is left-associative xy z = (х у) z. (Ах.Лу.х у г) (Лс.c) ((Ла.а) Ь)

Answer 1

To reduce the given expression to normal form, we need to apply the lambda calculus reduction rules.

1. (Ах.Лу.х у г) (Лс.c) ((Ла.а) Ь) // Apply beta reduction with x := (Лс.c)

(Лу.(Лс.c) (Лу.х у г)) ((Ла.а) Ь)

2. (Лс.c) (Лу. (Ла.а) Ь г) // Apply beta reduction with у := (Ла.а) Ь

(Лс.c) ((Ла.а) Ь г)

3. ((Ла.а) Ь г) // Apply beta reduction with c := г

(Ь г)

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Explanation: