http://www.seas.upenn.edu/~cis194/spring13/hw/01-intro.pdf

HW01.hs

-- Exercise 1 

-- We need to first find the digits of a number. 
-- Define the functions
 
--   toDigits :: Integer -> [Integer]
--   toDigitsRev :: Integer -> [Integer]
--   toDigits should convert positive Integers to a list of digits. (For 0 or
--   negative inputs, toDigits should return the empty list.) toDigitsRev
--   should do the same, but with the digits reversed.

--   Example: toDigits 1234 == [1,2,3,4]
--   Example: toDigitsRev 1234 == [4,3,2,1]
--   Example: toDigits 0 == []
--   Example: toDigits (-17) == []

toDigits :: Integer -> [Integer]
toDigits 0 = []
toDigits n = toDigits (div n 10) ++ [mod n 10]

toDigitsRev :: Integer -> [Integer]
toDigitsRev n = reverse (toDigits n)

-- Exercise 2 

-- Once we have the digits in the proper order, we need to
-- double every other one. 

-- Define a function
--   doubleEveryOther :: [Integer] -> [Integer]
--   Remember that doubleEveryOther should double every other number
--   beginning from the right, that is, the second-to-last, fourth-to-last,
--   numbers are doubled.

--   Example: doubleEveryOther [8,7,6,5] == [16,7,12,5]
--   Example: doubleEveryOther [1,2,3] == [1,4,3]


double :: Integer -> Integer
double n = n + n

doubleEveryOther :: [Integer] -> [Integer]
doubleEveryOther xs = reverse (doubleEveryOtherFromLeft (reverse xs))

doubleEveryOtherFromLeft :: [Integer] -> [Integer]
doubleEveryOtherFromLeft [] = []
doubleEveryOtherFromLeft [x] = [x]
doubleEveryOtherFromLeft (x:y:zs) = x : double y : doubleEveryOtherFromLeft zs

-- Exercise 3 
-- The output of doubleEveryOther has a mix of one-digit
-- and two-digit numbers. Define the function
-- sumDigits :: [Integer] -> Integer
-- to calculate the sum of all digits.
-- Example: sumDigits [16,7,12,5] = 1 + 6 + 7 + 1 + 2 + 5 = 22

sumDigits :: [Integer] -> Integer
sumDigits [] = 0
sumDigits xs = sum (concatMap (toDigits) xs)

-- Exercise 4 Define the function
-- validate :: Integer -> Bool
-- that indicates whether an Integer could be a valid credit card number.
-- This will use all functions defined in the previous exercises.
-- Example: validate 4012888888881881 = True
-- Example: validate 4012888888881882 = False

validate :: Integer -> Bool
validate n = mod (sumDigits (doubleEveryOther (toDigits n))) 10 == 0