1. Write a function count_list with type

int list -> int

that returns the number of items in a list. An item that is repeated is counted each time it appears in the list.

2. Write an ML function sum_list with type

int list -> int

that returns the sum of all the elements within a list

3. Write a function countdown with the type

int -> int list

that returns a list of numbers from its argument down to 1.

countdown (5) = [5, 4, 3, 2, 1]

countdown (10) = [10, 9, 8, 7, 6, 5, 4, 3, 2, 1]

4. Write a function countup with type

int * int -> int list

that takes two arguments (start and finish) and returns a list with all the numbers between start and finish.

countup (1, 10) = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

countup (2, 7) = [2, 3, 4, 5, 6, 7]

5. Write a function find_last with type

int list -> int

that returns the last element in a list:

findlast [1, 3, 5, 7, 9] = 9

findlast [2, 3, 4, 5] = 5