Ugly pure-ruby rack app

my_rack_app.rb

class MyRackApp
  def call(env)
    case env.values_at('REQUEST_METHOD', 'PATH_INFO')
    when ['GET', '/']
      [200, {}, "This is the root"]
    when ['GET', '/greet']
      name = env['QUERY_STRING'][/name=([^&]*)/, 1] || "World"
      [200, {}, "Hello, #{name}"]
    when ['POST', '/greet']
      name = env["rack.input"].read[/name=([^&]*)/, 1] || "World"
      [200, {}, "Nice to meet you, #{name}."]
    else
      [404, {}, '']
    end
  end
end