We can define numbers in lambda calculus with Church Numerals, where numbers are represented as lambda expressions. Below are some lambda expressions representing 0, 1, 2, and 3. 0 = f . x . x 1 = f . x . f x 2 = f . x . f (f x) 3 = f . x . f (f (f x)) The following implements a succ function on Church Numerals that takes in n as input and returns the next number (i.e., n 1 ). succ = n . f . x . f (n f x) succ 2 = (n . f . x . f (n f x) ) 2 f . x . f (2 f x) = f . x . f (( f . x . f (f x) ) f x) f. x. f ( (f (f x))) -> 3 a. Write the reduction for sum 3 2 where sum = j.k.f .x. j f ( k f x) [10 Points]