This problem set involves writing small functions working with lists and tuples. Begin by downloading the harness code. Uncompress this archive and store the resulting folder in a reasonable place. Then do any of the problems totalling 14 points. Feel free to extras totalling up to 18 points.

1. (1 Point) Write a function last : 'a list -> 'a. Given the call last([1, 2, 3]) the last function should return 3. If last is called with an empty list it should return an error message.

2. (2 Point) Write a function addEvens : int list -> int. Given the call addEvens([1, 2, 3, 4]) the addEvens function should return 6.

3. (2 Point) Write a function removeDuplicates : 'a list -> 'a list. Given the call removeDuplicates([1, 2, 3, 3, 2]) the removeDuplicates function should return [1, 2, 3].

4. (2 Point) Write a function isAscending : 'a list -> bool. Given the call isAscending([1, 4, 4]), the isAscending function should return False. Given the call isAscending([8]) or isAscending([]) the isAscending function should return True.

5. (3 Point) Write a function powerList : 'a list -> ('a list) list which returns the list of all sublists of the input argument. Given the call powerList([1, 2, 3]) the powerList function should return the list of lists [[1, 2, 3], [1, 2], [2, 3], [1, 3], [1], [2], [3], []] (no necessarily in that order).

6. (2 Point) Write a function insert : 'a -> 'a list -> 'a list. Given the call insert(20, [10, 30, 50]) the insert function should return the list [10, 20, 30, 50]. In writing the insert function, you may assume that the second argument is in ascending order.

7. (2 Point) Write a function merge : 'a list -> 'a list -> 'a list. Given the call merge([20, 60], [10, 30, 50]) the merge function should return the list [10, 20, 30, 50, 60]. In writing the merge function, you may assume that the two input lists are in ascending order.

8. (2 Point) Write a function split : 'a list -> ('a list * 'a list) that splits lists in half. Given the call split([10, 5, 20, 40, 50]) the split function should return the pair of lists ([10, 5], [20, 40, 50]).

9. (2 Point) Write a function almostInsertionSort : 'a list -> 'a list -> 'a list. Given the call almostInsertionSort([40, 20], [10, 30, 50]), the almostInsertionSort function should return the sorted list [10, 20, 30, 40, 50]. In writing the almostInsertionSort function, you may assume that the second argument is in ascending order.

10. (2 Point) Write a function antiCons : 'a list -> ('a * 'a list). Given the call antiCons(["Mary", "Alice", "Lisa"]) the antiCons function should return the pair ("Lisa", ["Mary", "Alice"]).

11. (2 Point) Write a function isPalindrome : string -> bool. Given the call isPalindrome("able was I ere I saw elba") the isPalindrome function should return True. Note that it is case-sensitive.

12. (1 Point) Write a function zip : ('a list * 'b list) -> ('a * 'b) list. Given the call zip(["A", "B"], [26, 25]), the zip function should return the list of pairs [("A", 26), ("B", 25)]. You may not assume that the input lists are of the same length.

13. (1 Point) Write a function unzip : ('a * 'b) list -> ('a list * 'b list). Given the call unzip([("A", 26), ("B", 25)]) the unzip function should return the pair of lists (["A", "B"], [26, 25]). You may not assume that the input lists are of the same length.