Exercise 1 Consider an unknown language with a left-associate + operator that is overloaded to have the following types: int * real -> real, int * int -> int, real * int -> real, and real*real -> real. Suppose the variable i has type int and the variable r has type real. For each + operator in each of the following expressions, say which type of + is used:

a. i + r

b. i + r + i

c. i + (r + i)

d, i + i + r + (r + i)