add implementaion for Luhn algorithm.

Author: thma

src/Luhn.hs

@@ -1,11 +1,10 @@
---{-# LANGUAGE ScopedTypeVariables #-}
-
 module Luhn where
 
 import Data.Char (digitToInt)
 import Control.Arrow ((>>>))
+import Data.Natural (Natural)
 
-{--
+{-- From Rosetta Code:
 Reverse the order of the digits in the number.
 Take the first, third, ... and every other odd digit in the reversed digits and sum them to form the partial sum s1
 Taking the second, fourth ... and every other even digit in the reversed digits:
@@ -40,22 +39,33 @@ use it to validate the following numbers:
    1234567812345670
 --}
 
+divisibleBy10 :: Int -> Bool
+divisibleBy10 = (0 ==) . (`mod` 10)
 
+sumDigits :: [Int] -> Int
+sumDigits = sum . map (uncurry (+) . (`divMod` 10))   -- map (uncurry (+) . (`divMod` 10)) [6,2,7,16,9,6,7,4,9,18,4] -> [6,2,7,7,9,6,7,4,9,9,4]
 
-{--
-luhn :: String -> Bool
-luhn = (0 ==) . (`mod` 10) . sum . map (uncurry (+) . (`divMod` 10)) . zipWith (*) (cycle [1,2]) . map digitToInt . reverse
----}
+double2nd :: [Int] -> [Int]   
+double2nd = zipWith (*) (cycle [1,2])                 -- zipWith (*) [6,1,7,8,9,3,7,2,9,9,4] [1,2,1,2,1,2,1,2,1,2,1] -> [6,2,7,16,9,6,7,4,9,18,4]
 
-luhn :: String -> Bool
-luhn = 
-  reverse >>> map digitToInt >>>
-  zipWith (*) (cycle [1,2]) >>>
-  map (uncurry (+) . (`divMod` 10)) >>>
-  sum >>>
-  (`mod` 10) >>>
-  (0 ==)
+toDigits :: Natural -> [Int]
+toDigits = map digitToInt . show                      -- toDigits 49927398716 -> [4,9,9,2,7,3,9,8,7,1,6]
 
+luhn1 :: Natural -> Bool
+luhn1 = divisibleBy10 . sumDigits . double2nd . reverse . toDigits
+
+luhn2 :: Natural -> Bool
+luhn2 n = divisibleBy10 (sumDigits (double2nd (reverse (toDigits n))))
+
+luhn3 :: Natural -> Bool
+luhn3 = toDigits  >>> 
+        reverse   >>>
+        double2nd >>>
+        sumDigits >>>
+        divisibleBy10
+       
+luhn4 :: Natural -> Bool
+luhn4 = (0 ==) . (`mod` 10) . sum . map (uncurry (+) . (`divMod` 10)) . zipWith (*) (cycle [1,2]) . map digitToInt . reverse . show       
 
 {--
 1. Reverse the order of the digits in the number.
@@ -65,13 +75,16 @@ luhn =
 5. Sum the partial sums of the even digits to form s2
 6. If s1 + s2 ends in zero then the original number is in the form of a valid credit card number as verified by the Luhn test.
 --}
-luhnTest :: String -> Bool
+luhnTest :: Natural -> Bool
 luhnTest n =
-  let (odds, evens) = (oddsEvens . map digitToInt . reverse) n           -- 1. and 3. 
+  let (odds, evens) = (oddsEvens . map digitToInt . reverse . show ) n   -- 1. and 3.
       s1 = sum odds                                                      -- 2.
       s2 = sum (map (crossSum . (* 2)) evens)                            -- 4. and 5.
-   in (s1 + s2) `rem` 10 == 0                                            -- 6.
-
+  in (s1 + s2) `rem` 10 == 0                                             -- 6.
+  where 
+    crossSum :: Int -> Int
+    crossSum = uncurry (+) . (`divMod` 10)
+    
 oddsEvens :: [Int] -> ([Int], [Int])
 oddsEvens xs = foldr collectOddsEvens ([], []) (zip xs [1 ..])
   where
@@ -80,11 +93,12 @@ oddsEvens xs = foldr collectOddsEvens ([], []) (zip xs [1 ..])
       | odd i     = (x : odds, evens)
       | otherwise = (odds, x : evens)
 
-crossSum :: Int -> Int
-crossSum = uncurry (+) . (`divMod` 10) --sum . map digitToInt . show
 
 main :: IO ()
 main = do
-  let testcases = ["49927398716", "49927398717", "1234567812345678", "1234567812345670"]
+  let testcases = [49927398716, 49927398717, 1234567812345678, 1234567812345670]
   print $ map luhnTest testcases
-  print $ map luhn testcases
+  print $ map luhn1 testcases
+  print $ map luhn2 testcases
+  print $ map luhn3 testcases
+  print $ map luhn4 testcases