FP101x Section 5 lab 2

lab2.hs

module Lab2 where

import Data.Char
import Test.QuickCheck

-------------------------------------------------------------------------------
-- Lab 2: Validating Credit Card Numbers
-------------------------------------------------------------------------------

(|>) :: a -> (a -> b) -> b
x |> f = f x

-- ===================================
-- Ex. 0
-- ===================================

toDigits :: Integer -> [Integer]
toDigits x
    | x < 0 = error "less than zero"
    | otherwise = x |> show |> map (toInteger . digitToInt)

prop_eval n = n > 0 ==> (eval . toDigits) n == n where
    eval = foldl (\x y -> y + (10 * x)) 0
prop_all n = n > 0 ==> all (\d -> d >= 0 && d < 10) (toDigits n)
prop_length n = n > 0 ==> (length . show) n == (length . toDigits) n


-- ===================================
-- Ex. 1
-- ===================================

toDigitsRev :: Integer -> [Integer]
toDigitsRev x
    | x < 0 = error "less than zero"
    | otherwise = x |> show |> map (toInteger . digitToInt) |> reverse

prop_evalrev n = n >= 0 ==> n == evalRev (toDigitsRev n) where
    evalRev = foldr (\x y -> x + (10 * y)) 0
prop_allrev n = n >= 0 ==> all (\d -> d >= 0 && d < 10) (toDigitsRev n)
prop_lengthrev n = n >= 0 ==> length (toDigitsRev n) == length (show n)

-- ===================================
-- Ex. 2
-- ===================================

doubleSecond :: [Integer] -> [Integer]
doubleSecond [] = []
doubleSecond [n] = [n]
doubleSecond (x1:x2:xs) = x1:x2*2:doubleSecond xs

-- ===================================
-- Ex. 3
-- ===================================

sumDigits :: [Integer] -> Integer
sumDigits [] = 0
sumDigits (x:xs)
    | x >= 10 = x `div` 10 + x `mod` 10 + sumDigits xs
    | otherwise = x + sumDigits xs


-- ===================================
-- Ex. 4
-- ===================================

isValid :: Integer -> Bool
isValid x = x |> toDigitsRev |> doubleSecond |> sumDigits |> (`mod` 10) |> (== 0)

-- ===================================
-- Ex.  5
-- ===================================

numValid :: [Integer] -> Integer
numValid xs = sum . map (const 1) $ filter isValid xs


creditcards :: [Integer]
creditcards = [ 4716347184862961,
                4532899082537349,
                4485429517622493,
                4320635998241421,
                4929778869082405,
                5256283618614517,
                5507514403575522,
                5191806267524120,
                5396452857080331,
                5567798501168013,
                6011798764103720,
                6011970953092861,
                6011486447384806,
                6011337752144550,
                6011442159205994,
                4916188093226163,
                4916699537435624,
                4024607115319476,
                4556945538735693,
                4532818294886666,
                5349308918130507,
                5156469512589415,
                5210896944802939,
                5442782486960998,
                5385907818416901,
                6011920409800508,
                6011978316213975,
                6011221666280064,
                6011285399268094,
                6011111757787451,
                4024007106747875,
                4916148692391990,
                4916918116659358,
                4024007109091313,
                4716815014741522,
                5370975221279675,
                5586822747605880,
                5446122675080587,
                5361718970369004,
                5543878863367027,
                6011996932510178,
                6011475323876084,
                6011358905586117,
                6011672107152563,
                6011660634944997,
                4532917110736356,
                4485548499291791,
                4532098581822262,
                4018626753711468,
                4454290525773941,
                5593710059099297,
                5275213041261476,
                5244162726358685,
                5583726743957726,
                5108718020905086,
                6011887079002610,
                6011119104045333,
                6011296087222376,
                6011183539053619,
                6011067418196187,
                4532462702719400,
                4420029044272063,
                4716494048062261,
                4916853817750471,
                4327554795485824,
                5138477489321723,
                5452898762612993,
                5246310677063212,
                5211257116158320,
                5230793016257272,
                6011265295282522,
                6011034443437754,
                6011582769987164,
                6011821695998586,
                6011420220198992,
                4716625186530516,
                4485290399115271,
                4556449305907296,
                4532036228186543,
                4916950537496300,
                5188481717181072,
                5535021441100707,
                5331217916806887,
                5212754109160056,
                5580039541241472,
                6011450326200252,
                6011141461689343,
                6011886911067144,
                6011835735645726,
                6011063209139742,
                379517444387209,
                377250784667541,
                347171902952673,
                379852678889749,
                345449316207827,
                349968440887576,
                347727987370269,
                370147776002793,
                374465794689268,
                340860752032008,
                349569393937707,
                379610201376008,
                346590844560212,
                376638943222680,
                378753384029375,
                348159548355291,
                345714137642682,
                347556554119626,
                370919740116903,
                375059255910682,
                373129538038460,
                346734548488728,
                370697814213115,
                377968192654740,
                379127496780069,
                375213257576161,
                379055805946370,
                345835454524671,
                377851536227201,
                345763240913232
              ]