Student grades

Consider the following type to represent student grades:

type grade = Val of int | CumLaude;;

Write functions with the following types:

is_valid : grade -> bool

which evaluates to true iff the grade is included between 18 and 30, or it is CumLaude.

int_of_grade : grade -> int

which transforms a valid grade into an integer (where CumLaude counts for 32), and fails if the grade is not valid.

avg : grade list -> float

which computes the average of a list of valid grades (it fails if some grade in the list is not valid).