Step by Step solution about How to resolve the algorithm Pythagorean quadruples step by step in the Haskell programming language

The goal of this Haskell code is to find the unrepresentable numbers that cannot be represented within a certain range. These are numbers that exceed the limits of the representable data type used in the program.

Here's a breakdown of the code:

1. powersOfTwo: This is a list of powers of two, starting from 1. It is an infinite list generated using the iterate function, which applies a function repeatedly to a value to create a list. In this case, the function is (2 *), which multiplies the current value by 2, and the initial value is 1.

2. unrepresentable: This is a list of unrepresentable numbers. It is created by merging two lists:

   • powersOfTwo, as defined above.
   • ((5 *) <$> powersOfTwo), which is a list of numbers obtained by multiplying each element of powersOfTwo by 5. This is done using the (<$>) function, which applies a function to each element of a list.

3. merge: This is a function that merges two sorted lists into a single sorted list. It takes two lists, xxs and yys, as input and compares their first elements. If the first element of xxs is less than the first element of yys, it adds the first element of xxs to the merged list and recursively calls merge with the tails of xxs and yys. Otherwise, it does the same with the first element of yys and the tails of xxs and yys.

4. main: This is the entry point of the program. It first prints a message to the console and then uses takeWhile to filter out the elements of unrepresentable that are greater than 2200. Finally, it prints the resulting list of unrepresentable numbers.

Overall, the program generates a list of powers of two and multiplies them by 5 to create a set of unrepresentable numbers. It then merges these two lists and prints the numbers that are less than or equal to 2200 but cannot be represented.

powersOfTwo :: [Int]
powersOfTwo = iterate (2 *) 1

unrepresentable :: [Int]
unrepresentable = merge powersOfTwo ((5 *) <$> powersOfTwo)

merge :: [Int] -> [Int] -> [Int]
merge xxs@(x:xs) yys@(y:ys)
  | x < y = x : merge xs yys
  | otherwise = y : merge xxs ys

main :: IO ()
main = do
  putStrLn "The values of d <= 2200 which can't be represented."
  print $ takeWhile (<= 2200) unrepresentable