How to call express middleware in a Google Cloud Function

gcloud-express-middleware.js

function cors(req, res, next) {
  console.log('in cors middleware:');
  req.cors = 'enabled';
  console.log(req);
  next();
}

function logger(req, res, next) {
  console.log('in logger middleware:');
  req.logged = true;
  console.log(req);
  next();
}

function doStuff(req, res) {
  console.log('in final handler:');
  req.sent = 'data';
  console.log(req);
}

function callMiddleware(req, res, middleware) {
  if (middleware.length === 0) {
    return;
  }
  const currentMiddleware = middleware.shift();
  currentMiddleware(req, res, () => callMiddleware(req, res, middleware));
}

// function deployed to GCF
module.exports.handler = function(req, res) {
  callMiddleware(req, res, [cors, logger, doStuff]);
};

module.exports.handler({}, {});

// $ node gcloud-express-middleware.js
// in cors middleware:
// { cors: 'enabled' }
// in logger middleware:
// { cors: 'enabled', logged: true }
// in final handler:
// { cors: 'enabled', logged: true, sent: 'data' }