finished luhn algorithm

luhn.lhs

@@ -1,13 +1,43 @@
-This is an implementation of the Luhn Algorithm. It's used to validate credit card numbers.
+This is an implementation of the Luhn Algorithm. It's used to validate
+credit card numbers.
+
+Return the last digit of an integer number
 
 > lastDigit :: Integer -> Integer
 > lastDigit n = mod n 10
 
+Remove the last digit of an integer number and return the rest
+
 > dropLastDigit :: Integer -> Integer
 > dropLastDigit n = div n 10
 
+Put all digits of an integer number in reverse order into a list
+
 > toRevDigits :: Integer -> [Integer]
 > toRevDigits n
 >   | n < 1     = []
 >   | otherwise = lastDigit(n) : toRevDigits(dropLastDigit(n))
 
+Put all digits of an integer number into a list
+
+> toDigits :: Integer -> [Integer]
+> toDigits n = reverse(toRevDigits(n))
+
+Double every second value in the input list.
+
+> doubleEveryOther :: [Integer] -> [Integer]
+> doubleEveryOther([]) = []
+> doubleEveryOther(x:[]) = [x]
+> doubleEveryOther(a:(b:xs)) = a : 2*b : doubleEveryOther(xs)
+
+Sum up all digits from all integers.
+
+> sumDigits :: [Integer] -> Integer
+> sumDigits([]) = 0
+> sumDigits(0:xs) = sumDigits(xs)
+> sumDigits(x:xs) = lastDigit(x) + sumDigits(dropLastDigit(x) : xs)
+
+Evaluate if a credit card number is 'valid'.
+
+> luhn :: Integer -> Bool
+> luhn x = lastDigit(sumDigits(doubleEveryOther(toRevDigits(x)))) == 0