Description

Important Instructions:
• Submit your solution in a single file named loginid.1.hs on Moodle. For example, if I were to submit a solution, the file would be called spsuresh.1.hs.
• Please remember to rename your file to loginid.1.hs before submitting.
• Deviation from the instructions will result in marks being reduced.
• If your Haskell file does not compile, or if your function names differ from the ones I havespecified (ensure that you use the exact sequence of small letters and capital letters), you will receive no marks.

1. Define a function nextSquare :: Integer -> Integer such that nextSquare n returns the least square m with m >= n.
Sample cases:
nextSquare (-10) = 0
nextSquare 0 = 0
nextSquare 1 = 1
nextSquare 25 = 25
nextSquare 36 = 36
nextSquare 102 = 121
2. Define a function previousCube :: Integer -> Integer such that previousCube n returns the greatest cube m with m <= n, for n > 0. Assume that only positive inputs will be provided.
Sample cases:
previousCube 1 = 1
previousCube 100 = 64 previousCube 1000 = 1000 previousCube 5000 = 4913 previousCube 10000 = 9261
3. Define a function nextPalin :: Integer -> Integer such that nextPalin n returns the least palindromic number m with m >= n.
Sample cases:
nextPalin (-10) = 0
nextPalin 0 = 0
nextPalin 5 = 5
nextPalin 55 = 55
nextPalin 56 = 66
nextPalin 102 = 111
nexPalin 5962 = 5995
4. Define a function primesIn :: Integer -> Integer -> [Integer] such that for any integers l and u, primesIn l u returns the list of all primes in the range [l..u].
Sample cases:
primesIn (-20) (-10) = []
primesIn (-20) 0 = []
primesIn (-10) (-20) = []
primesIn 100 50 = []
primesIn 50 50 = []
primesIn 53 53 = [53]
primesIn 50 100 = [53,59,61,67,71,73,79,83,89,97]
5. Define a function isPrime :: Integer -> Bool such that isPrime n returns True if n is prime, and False if not.
Sample cases:
isPrime (-20) = False
isPrime 0 = False
isPrime 1 = False
isPrime 2 = True
isPrime 5 = True
isPrime 27 = False
isPrime 47 = True
6. Define a function decToBin :: Integer -> Integer such that decToBin n returns the binary representation of n, for any n >= 0. Assume that only nonnegative inputs will be provided.
Sample cases:
decToBin 0 = 0
decToBin 1 = 1
decToBin 25 = 11001
decToBin 63 = 111111
decToBin 64 = 1000000
decToBin 65 = 1000001
decToBin (2^24) = 1000000000000000000000000
7. Define a function binToDec :: Integer -> Integer such that for any n >= 0 which contains only the digits 0 and 1, binToDec n outputs m, where n is the binary representation of m. Assume that all the inputs provided will be nonnegative and will only contain the digits 0 and 1.
Sample cases:
binToDec 0 = 0
binToDec 1 = 1
binToDec 11001 = 25
binToDec 111111 = 63
binToDec 1000000 = 64
binToDec 1000001 = 65
binToDec 1001100011 = 611