The Writer monad is a programming design pattern which makes it possible to compose functions which return their result values paired with a log string. The final result of a composed function yields both a value, and a concatenation of the logs from each component function application.

Demonstrate in your programming language the following:

 Construct a Writer monad by writing the 'bind' function and the 'unit' (sometimes known as 'return') function for that monad (or just use what the language already provides)
 Write three simple functions: root, addOne, and half
 Derive Writer monad versions of each of these functions
 Apply a composition of the Writer versions of root, addOne, and half to the integer 5, deriving both a value for the Golden Ratio φ, and a concatenated log of the function applications (starting with the initial value, and followed by the application of root, etc.)
import Control.Monad.Trans.Writer
import Control.Monad ((>=>))
 
loggingVersion :: (a -> b) -> c -> a -> Writer c b
loggingVersion f log x = writer (f x, log)
 
logRoot = loggingVersion sqrt "obtained square root, "
logAddOne = loggingVersion (+1) "added 1, "
logHalf = loggingVersion (/2) "divided by 2, "
 
halfOfAddOneOfRoot = logRoot >=> logAddOne >=> logHalf
 
main = print $ runWriter (halfOfAddOneOfRoot 5)