[Solved] CS40032 Assignment 2 -Calculus

1. Reduce the following -expressions. Show every step of -, -, and [2 * 7 = 14]
   • (z. z) (y. y y) (x. x a)
   • (z. z) (z. z z) (z. z y)
   • (x. y. x y y) (a. a) b
   • (x. y. x y y) (y. y) y
   • (x. x x) (y. y x) z
   • (x. (y. (x y)) y) z
   • (((x. (y. (x y)) (y. y)) w)
2. Solve the following using Y combinator [2 + 4 = 6]
   • Write the recursive definition for TriProduct where TriProduct(n) can be defined as

TriProduct(n) = n* (TriProduct(n 1) if n > 3

+ TriProduct(n 2)

TriProduct(n 3)),

= 5, if n = 3

= 2, if n = 2

= 1 if n = 1

Using Y combinator, encode the above recursive definition of TriProduct as -expressions

• Reduce TriProduct Show every step of and reductions. You may skip -reduction steps with a mention of the step.