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

The provided Ruby code demonstrates the use of the Writer class to perform a series of mathematical operations on a value while keeping track of the operations performed.

Here's a detailed explanation:

1. Writer Class: The Writer class is defined with two instance variables: @value, which holds the current value, and @log, which records the operations performed on the value. It has an initialize method that takes two parameters: value and log. If value is a Proc (a Ruby closure), @log is set to the provided log string. Otherwise, @log is set to the concatenation of log and the string representation of value.

2. Writer::unit Method: This class method creates a new Writer object with the given value and log.

3. bind Method: This method is defined on the Writer class and takes a mwriter argument, which is another Writer object. It returns a new Writer object with the following:

   • new_value: The result of calling the mwriter.value Proc with the current @value as the argument.
   • new_log: The concatenation of the current @log and mwriter.log.

4. Lambda Functions: The code defines three lambda functions:

   • lam_sqrt: Calculates the square root of a number.
   • lam_add_one: Adds one to a number.
   • lam_half: Divides a number by 2.

5. Creating Writer Objects: The code creates three Writer objects using the Writer::unit method:

   • sqrt: Represents the square root operation.
   • add_one: Represents the addition operation.
   • half: Represents the division operation.

6. Chain of Operations: A chain of operations is performed on the initial Writer object m1 (with an initial value of 5) by using the bind method:

   • m1.bind(sqrt) applies the square root operation.
   • m1.bind(add_one) applies the add one operation.
   • m1.bind(half) applies the division by 2 operation.
   • The result is stored in m2.

7. Accessing Value and Log: The code prints the final value (m2.value), which is the result of the combined operations. It also prints the m2.log, which shows the sequence of operations performed to derive the final value.

In summary, this code uses the Writer class to create a chain of mathematical operations and keep track of the operations performed during the calculation. This approach allows for a clear and auditable record of the operations and the resulting value.

# 20220720 Ruby programming solution
class Writer
  attr_reader :value, :log

  def initialize(value, log = "New")
    @value = value
    if value.is_a? Proc
      @log = log
    else
      @log = log + ": " + @value.to_s 
    end
  end

  def self.unit(value, log)
    Writer.new(value, log)
  end

  def bind(mwriter)
    new_value = mwriter.value.call(@value)
    new_log = @log + "\n" + mwriter.log
    self.class.new(new_value, new_log)
  end
end

lam_sqrt = ->(number) { Math.sqrt(number) }
lam_add_one = ->(number) { number + 1 }
lam_half = ->(number) { number / 2.0 }

sqrt = Writer.unit( lam_sqrt, "Took square root")
add_one = Writer.unit( lam_add_one, "Added one")
half = Writer.unit( lam_half, "Divided by 2")

m1 = Writer.unit(5, "Initial value")
m2 = m1.bind(sqrt).bind(add_one).bind(half)

puts "The final value is #{m2.value}\n\n"
puts "This value was derived as follows:"
puts m2.log