logger.rb

class Rack::Logger
  def initialize(app, logger)
    @app = app
    @logger = logger
  end

  def call(env)
    env["rack.logger"] = @logger
    result = @app.call(env)
    @logger.flush if @logger.respond_to?(:flush)
    result
  end
end

use Rack::Logger, Logger.new(STDOUT)
# or
use Rack::Logger, ActiveSupport::BufferedLogger.new("rack.log")

run lambda { |env|
  env["rack.logger"].warn "Hey Logger"
  [200, {"Content-Type" => "text/html"}, "Hello, World!"]
}