Question

Reduce the following lambda-calculus term to the normalform. Show all intermediate steps, with one beta reduction at a time. In the reduction, assume that you are supplied with extra rules thatallow you to reduce the multiplication of two natural numbers into thecorresponding result.

(λf.λx.f(f x))(λy.y≠3) 2

Answer 1

Decrease to typical from utilizing lambda-decrease:

The given lambda - math terms is, (λf.λx.f(f(fx)))(λy.y×3)2

The of taking the terms is significant in lambda - math,

For the term, (λy, y×3)2, we can substitute the incentive to the capacity.

Therefore apply beta-decrease on “(λy, y×3)2,“ will return 2 × 3 = 6

Presently the tem becomes, (λf λx f(f(fx)))6

The main term, (λf λx f(f(fx))) takes a capacity and a contention and substitute the contention in the capacity.

Here it is given that it is conceivable to substitute, the subsequent increase in the outcome.

In this way by applying next level beta - decrease, the term becomes f(f(f(6))), which is in ordinary structure.