Problems for Section 7.5

I'm giving a few different problems for the ML material covered on Apr 5, approximately corresponding to Section 7.5. Enter these in the automated grading system as "7.5.a" etc.

7.5.a Use map to write a function sumPairs that takes a list of pairs and returns a list of the sum of those pairs. For example, sumPairs([(1,2), (3,4), (5,6)]) would return [3,7,11]. (This is like Exercise 2.2.14, which we did in class on Sept 6, but using map.)

7.5.b Use filter to write a function keepLessThan that takes an int and a list of ints and returns a list like the one given but including only those ints that are less than the given one. For example, keepLessThan(5, [3,7,2,9,8,1]) would return [3,2,1].

7.5.c Use map and filter to write a function halveEvens that takes a list of ints and returns a list containing only the halves of the even elements (so, odd elements are removed completely). For example, halveEvens([8,14,17,6,9,11,4]) would return [4,7,3, 2]. (This is like a problem from Test 1, but using map and filter.)

For convenience, here are map and filter:

fun map(f, []) = []
  | map(f, a::rest) = f(a)::map(f, rest);

fun filter(f, []) = []
  | filter(f, a::rest) = if f(a) then a::filter(f, rest) else filter(f, rest);

Also, you can find all the code from class here.