The following definitions:

def inc(n: Int) = n + 1 def dec(n: Int) = n 1 def isZero(n: Int) = n == 0

In the following problems, your solutions may assume that all inputs are non-negative integers (these are sometimes called the natural numbers).

Problem_1

Re-define the function:

add(n: Int, m: Int) = n + m

Your definition should only use classical recursion(not tail recursion), inc, dec, and isZero.

Problem_2

Re-define the function:

mul(n: Int, m: Int) = n * m

Your definition should only use classical recursion, add, inc, dec, and isZero.