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.)
USING: kernel math math.functions monads prettyprint ;
FROM: monads => do ;
 
{
    [ 5 "Started with five, " <writer> ]
    [ sqrt "took square root, " <writer> ]
    [ 1 + "added one, " <writer> ]
    [ 2 / "divided by two." <writer> ]
} do .