Question: 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,

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]

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