Trying to get to grips with Haskell. The problem is taken from here.

{-
Given Credit Card number: 49927398716

• Reverse the digits: 61789372994
• Sum the odd digits: 6 + 7 + 9 + 7 + 9 + 4 = 42 = s1
• The even digits: 1, 8, 3, 2, 9
•  Two times each even digit: 2, 16, 6, 4, 18
•  Sum the digits of each multiplication: 2, 7, 6, 4, 9
•  Sum the last: 2 + 7 + 6 + 4 + 9 = 28 = s2
• s1 + s2 = 70
• which, as it ends in zero, means that 49927398716 passes the Luhn test
-}

import Data.Char

data Validity = Valid | Invalid deriving Eq
type CardNumber = String

luhnCheck :: CardNumber -> Validity
luhnCheck s =
let r = revDigits s
(os,es) = oddsAndEvens r
s1 = sum os
s2 = sum $map sumDigits$ map (*2) es
in if (s1 + s2) mod 10 == 0 then Valid
else Invalid

revDigits :: CardNumber -> [Int]
revDigits s = map digitToInt (reverse s)

oddsAndEvens :: [Int] -> ([Int],[Int])
oddsAndEvens is =
let digitsWithIdx = zip is (cycle [1,2])
odds = map fst $filter (\d -> (snd d) == 1) digitsWithIdx evens = map fst$ filter (\d -> (snd d) == 2) digitsWithIdx
in (odds,evens)

sumDigits:: Int -> Int
sumDigits i = sum $map digitToInt$ show i

test :: Bool
test = let testData = ["49927398716", "49927398717", "1234567812345678","1234567812345670"]
in  (map luhnCheck testData) == [Valid,Invalid,Invalid,Valid]


One thing that immediately pops out (and happens a lot with beginner Haskell programmers, IME):

s2 = sum $map sumDigits$ map (*2) es


This means (reads as for me) "map (*2) on es, then map sumDigits on it, then sum the numbers."

What you typically want to do is to stay on the "function side" on things as long as possible:

s2 = sum . map sumDigits . map (*2) $es  Meaning you compose as much as you can, and put only one application at the end. That makes it easier to eta-reduce and in general is considered more idiomatic. You could also compose the mapped operation, bringing it down to classic "map-reduce" scenario (where "map" part is sumDigits . (*2), and "reduce" part is the sum). s2 = sum . map (sumDigits . (*2))$ es


I'd also flip the order of Valid and Invalid:

data Validity = Invalid | Valid deriving Eq


This way, when you derive Ord, Valid > Invalid, which is sometimes helpful and in general you'll see that it holds "intuitively", for Maybe (Just _ > Nothing), Either (Right _ > Left _) and similar values.

• I guess the function composition comment would apply to the oddsAndEvens function too?
– jb77
Commented Feb 19, 2015 at 9:19
• @jb77 Yep. It applies generally. Commented Feb 19, 2015 at 9:41