CMSC 331
Spring 2014
Prepare a Haskell program that includes the following function
definitions and PutStrLn calls to show that they work as
intended. The program needs to run on the GL platforms. As before,
use the UNIX script command to list the program and the
results. Email the file to me and the TA
Atul {nicholas,atul7}@umbc.edu no later than
midnight Thursday May 8. Work submitted
before Tuesday May 6 will be eligible for extra credit.
1. Define a function elem that decides if a value is an element of a list. (Note that elem is already a built-in function in Haskell.) The signature would be:
elem :: Eq a => a -> [a] -> Bool
2. Using a high order function, define a
function replicate :: Int -> a -> [a] that
produces a list of identical elements. For example,
> replicate 3 "tsk"
["tsk","tsk","tsk"]
3. Define a function halve :: [a] → ([ a], [a]) that
splits any list into two halves. Extra credit may be awarded for solutions that don't use the !! operator, or the take function. For example:
> halve [1,2,3,4,5,6]
([1, 2, 3], [4, 5,
6])
> halve [1, 2, 3]
([1, 2], [3])
>
halve []
([],[])
4. For any positive integer k, we can compute the sum of the
divisors of k. For example, sumOfDivisors 8 would be 1+2+4=7.
But sumOfDivisors 6 is 6, since 1+2+3=6. A number that equals the
sum of its divisors is said to be
5. Define a recursive function merge :: Ord a ⇒ [a] → [a]
→ [a] that merges two sorted lists to give a single sorted
list. Your definition should be defined using explicit
recursion. For example,
> merge [2,5,6] [1,3,4]
[1,2,3,4,5,6]
6. Using the merge and halve functions from other exercises,
define a recursive function msort :: Ord a ⇒ [a] →
[a] that implements merge sort. In the merge sort, the
empty list and singleton lists are already sorted, and any other
list is sorted by merging together the two lists that result from
sorting the two halves of the list separately.