Memoizing in Ruby without ivars and defined?

memoize.rb

class Memoizer < Module
  def initialize(method_name)
    define_method(method_name) do
      super().tap do |value|
        puts "memoizing"
        define_singleton_method(method_name) { value }
      end
    end
  end
end

module Memoize
  def memoize(method_name)
    prepend Memoizer.new(method_name)
  end
end

class ProofItWorks
  @@num = 0
  extend Memoize
  def foo
    puts "expensive"
    @@num = @@num + 1
  end
  memoize(:foo)
end

class YourThing
  extend Memoize
  def v
    $1 if xml =~ /blah/
  end
  memoize :v
end

could (should?) have written ProofItWorks as a test, but I was mucking around in a REPL session