Step by Step solution about How to resolve the algorithm Map range step by step in the Haskell programming language

The provided Haskell program demonstrates the process of mapping values from one range to another. It does this for both floating-point numbers and rational numbers.

The mapRange function takes four parameters:

1. (a1, a2): The original range from which the value is being mapped.
2. (b1, b2): The target range to which the value is being mapped.
3. s: The value to be mapped.

The mapRange function uses linear interpolation to calculate the mapped value using the following formula: b1 + (s - a1) * (b2 - b1) / (a2 - a1)

The main function is the entry point of the program. It performs the following steps:

1. It prints a header for the floating-point mapping.
2. It uses mapM_ to iterate over a range of integers from 0 to 10 and applies the mapRange function to each integer, with the mapping from (0, 10) to (-1, 0) and converting the result to a double-precision floating-point number.
3. It prints each mapped value using the prtD function, which formats the output as an integer followed by the mapped value with three decimal places.
4. It prints a header for the rational mapping.
5. It performs the same mapping as before, but this time using rational numbers instead of floating-point numbers.
6. It prints each mapped value using the prtR function, which formats the output as an integer followed by the mapped value as a string.

In summary, this program demonstrates the process of mapping values from one range to another, using both floating-point numbers and rational numbers, and shows the results in a formatted manner.

import Data.Ratio
import Text.Printf (PrintfType, printf)

-- Map a value from the range [a1,a2] to the range [b1,b2].  We don't check
-- for empty ranges.
mapRange
  :: Fractional a
  => (a, a) -> (a, a) -> a -> a
mapRange (a1, a2) (b1, b2) s = b1 + (s - a1) * (b2 - b1) / (a2 - a1)

main :: IO ()
main
-- Perform the mapping over floating point numbers.
 = do
  putStrLn "---------- Floating point ----------"
  mapM_ (\n -> prtD n . mapRange (0, 10) (-1, 0) $ fromIntegral n) [0 .. 10]
  -- Perform the same mapping over exact rationals.
  putStrLn "---------- Rationals ----------"
  mapM_ (\n -> prtR n . mapRange (0, 10) (-1, 0) $ n % 1) [0 .. 10]
  where
    prtD
      :: PrintfType r
      => Integer -> Double -> r
    prtD = printf "%2d -> %6.3f\n"
    prtR
      :: PrintfType r
      => Integer -> Rational -> r
    prtR n x = printf "%2d -> %s\n" n (show x)