Step by Step solution about How to resolve the algorithm Horner's rule for polynomial evaluation step by step in the Haskell programming language

The provided code defines a function horner that evaluates a polynomial using Horner's method:

horner :: (Num a) => a -> [a] -> a

where:

• a: The type of the coefficients in the polynomial. It must be a numeric type that supports addition and multiplication (Num).
• x: The value to be evaluated at.
• [a]: A list of coefficients representing the polynomial, with the coefficients in decreasing order of their exponents.

The horner function uses the foldr function to iteratively evaluate the polynomial using Horner's method. foldr takes three arguments: a function to apply to each element of the list, an initial value, and the list itself. In this case, the function is:

(\a b -> a + b*x)

which takes two arguments:

• a: The accumulator, which initially starts with the value 0.
• b: The current coefficient in the polynomial.

The function adds b*x to the accumulator and returns the result. The foldr function applies this function to every element of the list, accumulating the result in the accumulator variable.

The initial value for the accumulator is 0, which represents the constant term in the polynomial.

The main function simply calls the horner function with the value 3 and the list [-19, 7, -4, 6], which represents the polynomial -19x^3 + 7x^2 - 4x + 6. The result of the evaluation is then printed to the console.

In this case, the result will be -33, which is the value of the polynomial -19x^3 + 7x^2 - 4x + 6 when evaluated at x=3.

horner :: (Num a) => a -> [a] -> a
horner x = foldr (\a b -> a + b*x) 0

main = print $ horner 3 [-19, 7, -4, 6]