The Luhn algorithm is used to check bank card numbers for simple errors such as mistyping a digit, and proceeds as follows: consider each digit as a separate number; • moving left, double every other number from the second last; • subtract 9 from each number that is now greater than 9; add all the resulting numbers together; • if the total is divisible by 10, the card number is valid. See also the Wikipedia entry on the Luhn algorithm. Define a function luhnDouble :: Int -> Int that doubles a digit and subtracts 9 if the result is greater than 9. For example: > luhnDouble 3 6 > luhnDouble 6 3 Using luhnDouble and the integer remainder function mod, define a function luhn: Int -> Int -> Int -> Int -> Bool that decides if a four digit bank card number is valid (according to the Luhn algorithm described above). For example: > luhn 1 784 True > luhn 4 783 False

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