Step by Step solution about How to resolve the algorithm Monads/Writer monad step by step in the Go programming language

Package Declaration:

package main

• Declares the main package of the program.

Imports:

import (
   "fmt"
   "math"
)

• Imports the necessary packages:
  • fmt: For printing to the console.
  • math: For mathematical functions.

Custom Type:

type mwriter struct {
   value float64
   log   string
}

• Defines a custom type called mwriter. It has two fields:
  • value: A float64 representing the current numerical value.
  • log: A string containing a log of the operations performed on the mwriter.

Method on mwriter Type:

func (m mwriter) bind(f func(v float64) mwriter) mwriter

• Defines a method named bind on the mwriter type. It takes a function f as an argument.
• The function f takes a float64 as input and returns an mwriter.
• bind executes f with m.value as the argument, resulting in a new mwriter instance.
• The log field of the new mwriter is appended with the log field of the current mwriter.
• The new mwriter is returned as the result of bind.

Helper Functions:

• unit(v float64, s string) mwriter: Creates an mwriter with the given value and log string.
• root(v float64) mwriter: Creates an mwriter by taking the square root of the given value.
• addOne(v float64) mwriter: Creates an mwriter by adding one to the given value.
• half(v float64) mwriter: Creates an mwriter by dividing the given value by two.

Main Function:

func main() {
   mw1 := unit(5, "Initial value")
   mw2 := mw1.bind(root).bind(addOne).bind(half)
   fmt.Println("The Golden Ratio is", mw2.value)
   fmt.Println("\nThis was derived as follows:-")
   fmt.Println(mw2.log)
}

• Defines the main function, which is the entry point of the program.
• Creates an mwriter mw1 with an initial value of 5 and a log message "Initial value".
• Uses the bind method to sequentially apply the root, addOne, and half functions to mw1. This results in a new mwriter mw2.
• Prints the final value of mw2 and the log of operations performed on it.

Flow of the Program:

• The program starts with an initial mwriter representing the value 5.
• The root function is applied to the mwriter, taking the square root of 5 (approximately 2.236).
• The addOne function is then applied, adding one to the result (approximately 3.236).
• Finally, the half function is applied, dividing the result by two (approximately 1.618).
• The final mwriter has a value of approximately 1.618, which is close to the Golden Ratio.
• The log of the operations performed on the mwriter is printed to the console, showing the derivation of the Golden Ratio from the initial value.

package main

import (
    "fmt"
    "math"
)

type mwriter struct {
    value float64
    log   string
}

func (m mwriter) bind(f func(v float64) mwriter) mwriter {
    n := f(m.value)
    n.log = m.log + n.log
    return n
}

func unit(v float64, s string) mwriter {
    return mwriter{v, fmt.Sprintf("  %-17s: %g\n", s, v)}
}

func root(v float64) mwriter {
    return unit(math.Sqrt(v), "Took square root")
}

func addOne(v float64) mwriter {
    return unit(v+1, "Added one")
}

func half(v float64) mwriter {
    return unit(v/2, "Divided by two")
}

func main() {
    mw1 := unit(5, "Initial value")
    mw2 := mw1.bind(root).bind(addOne).bind(half)
    fmt.Println("The Golden Ratio is", mw2.value)
    fmt.Println("\nThis was derived as follows:-")
    fmt.Println(mw2.log)
}