An Introduction to Functional Programming Through Lambda Calculus

- 66 -Applicative order reduction notation-> - applicative order β reduction-> ... -> - multiple applicative order β reductionRecursion functiondef recursive f = λs.(f (s s)) λs.(f (s s))For:def = ... ( ... ) ...write:def f = ... (f ... ) ...def = recursive Note that:recursive => ... => (recursive )Recursion notationrec = ==def = recursive λf.4.10. Exercises1) The following function finds the sum of the numbers between n and zero:def sum1 f n =if iszero nthen zeroelse add n (f (pred n))def sum = recursive sum1Evaluate:sum three2) Write a function that finds the product of the numbers between n and one:def prod1 f n = ...def prod = recursive prod1 (*)so that:prod nin lambda calculus is equivalent to: