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The aim of the lab is to practice function definitions using pattern matching and guarded equations together with the list comprehension.

**Exercise 1:** Write a function `separate :: [Int] -> ([Int], [Int])`

taking a list and returning a pair of lists. The first
containing elements on indexes 0,2,4,… and the second on the indexes 1,3,5,… E.g.

separate [1,2,3,4,5] => ([1,3,5], [2,4])

*Hint:* Using pattern matching `x:y:xs`

and recursion.

separate :: [Int] -> ([Int], [Int]) separate [] = ([], []) separate [x] = ([x], []) separate (x:y:xs) = let (evs, ods) = separate xs in (x:evs, y:ods)

**Exercise 2:** Write a function `numToStr :: Int -> Int -> String`

taking as input an integer `n`

together with a `radix`

denoting the number of symbols used to represent the number `n`

(for example 2,10,16 for binary, decimal, hexadecimal representation respectively). This function returns a string containing the representation of `n`

in the corresponding numerical system. For the representation use the standard symbols `0123456789ABCDEF`

.

Examples:

numToStr 52 10 => "52" numToStr 5 2 => "101" numToStr 255 16 => "FF".

*Hint:* The representation can be obtained by consecutive division of `n`

by `radix`

and collecting the remainders. The integer division can be computed by the function `div`

and the remainder after integer division can be computed by the function `mod`

.

numToStr :: Int -> Int -> String numToStr n radix = if n < radix then [chars !! n] else (numToStr d radix) ++ [chars !! r] where chars = ['0'..'9'] ++ ['A'..'F'] d = n `div` radix r = n `mod` radix

**Exercise 3:** Write a function `split n xs`

that takes a natural number `n`

and a list `xs :: [Int]`

and splits `xs`

into a list of
lists of `n`

-many consecutive elements. The last chunk of numbers can be shorter than `n`

. E.g.

split 3 [1..10] => [[1,2,3],[4,5,6],[7,8,9],[10]] split 3 [1,2] => [[1,2]]Use the function

`split`

to implement a function `average_n n xs`

taking a list of integers and returning the list of the averages of `n`

consecutive elements.
E.g.
average_n 3 [-1,0,1,2,3] => [0.0,2.5]

*Hint:* You can use functions `take n xs`

and `drop n xs`

. The first one returns the list of the first `n`

elements of `xs`

. The second returns the remaining list after stripping the first `n`

elements off. Further, use function `length xs`

returning the length of `xs`

.

The function `split`

can be written recursively. If the length of `xs`

is less than or equal to `n`

then return just `xs`

.
If it is bigger then take the first `n`

elements and cons them to the result of the recursive call of `split`

after dropping the first `n`

elements.

split :: Int -> [Int] -> [[Int]] split n xs | (length xs) <= n = [xs] | otherwise = take n xs : (split n (drop n xs))

The function `average_n`

can be easily written via the list comprehension using `split`

. The only caveat is the division operation involved in the computation of averages. Even though the inner lists after applying `split`

are of the type `[Int]`

, their averages are floating numbers. So the type of `average_n`

is `Int -> [Int] -> [Float]`

. We can compute the sum of an inner list by the function `sum`

and its length by `length`

but the type system would complain if we want to divide them. To overcome this problem, one has to convert the integer arguments into floating-point numbers. This can be done by the function `fromIntegral`

converting an integer into any more general numeric type.

average_n :: Int -> [Int] -> [Float] average_n n ys = [fromIntegral (sum xs) / fromIntegral (length xs) | xs <- xss] where xss = split n ys

**Task 1:** Write a function `copy :: Int -> String -> String`

that takes an integer `n`

and a string `str`

and returns
a string consisting of `n`

copies of `str`

. E.g.

copy 3 "abc" => "abcabcabc"

copy :: Int -> String -> String copy n str | n <= 0 = "" | otherwise = str ++ copy (n - 1) str -- tail recursive version copy2 :: Int -> String -> String copy2 n str = iter n "" where iter k acc | k <= 0 = acc | otherwise = iter (k-1) (acc ++ str)

**Task 2:** 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, e.g. 1 7 8 4 ⇒ 2 7 16 4;
- 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.

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 7 => 5

Using `luhnDouble`

and the integer remainder function `mod`

, define a function
`luhn :: [Int] -> Bool`

that decides if a list of numbers representing a bank card number is valid. For
example:

luhn [1,7,8,4] => True luhn [4,7,8,3] => False

*Hint:* Since the numbers are processed from right to left, reverse first the list by the function `reverse`

. Then apply the function `separate`

from Exercise 1 to split the list into the numbers
to be luhnDoubled and the rest.

courses/fup/tutorials/lab_8_-_haskell_basics.txt · Last modified: 2022/04/08 12:01 by xhorcik