Problem 2 [20pt] In the Church encoding of natural numbers, we have used the n-fold composition of f. written f". Intuitively, f means applying function f for n times. a) (6pt) Implement a function funPower, which takes a function f, an integer n and returns the function b) (4pt) Implement a function encode, which takes a natural number n and returns the church encoding of c) (4pt) Implement a function decode, which takes n (the church encoding of some natural number n) and d) (6pt) Implement a function MULT, which takes two church numbers n1, n2 and returns the church number f. For example, ((funPower sqrt 2) 16) should return 2. n. For example, (encode 2) should return 2 (i.e., the function Af. Az. f (J z)). returns n. For example, (decode (encode 2)) should return 2. of ni x n2 (i.e., ni n2). For example, (decode (MULT (encode 2) (encode 3)) should be 6