Step by Step solution about How to resolve the algorithm Dot product step by step in the Haskell programming language

There are two functions with same name but different type signatures:

1. dotp Function:

   • Takes two lists of numeric elements ([a]) and returns a single numeric value (a).
   • Calculates the dot product of the two lists by multiplying corresponding elements and summing the results.
   • Has a strict requirement that the input lists must have the same length, otherwise it generates an error.

2. dotProduct Function:

   • Also takes two lists of numeric elements ([a]) and returns a Maybe a.
   • Calculates the dot product similarly to dotp, but returns Just with the result if the input lists have the same length, or Nothing if they don't match.

In the main function, two different scenarios are shown:

• For dotp, the input lists [1, 3, -5] and [4, -2, -1] have the same length, so it calculates the dot product and prints the result, which is 3.

• For dotProduct, the same input lists are used. Since they still have the same length, it calculates the dot product, stores it in a Maybe, and prints the value wrapped in Just.

The main difference between the two functions is that dotp strictly enforces the same-length requirement and generates an error if it's violated, while dotProduct allows for different-length lists and handles the case gracefully by returning Nothing.

dotp :: Num a => [a] -> [a] -> a 
dotp a b | length a == length b = sum (zipWith (*) a b)
         | otherwise = error "Vector sizes must match"
 
main = print $ dotp [1, 3, -5] [4, -2, -1] -- prints 3


dotProduct :: Num a => [a] -> [a] -> Maybe a
dotProduct a b 
  | length a == length b = Just $ dp a b
  | otherwise = Nothing
    where
      dp x y = sum $ zipWith (*) x y


main :: IO ()
main = print n
  where
    Just n = dotProduct [1, 3, -5] [4, -2, -1]