use Symfony\Component\HttpKernel\HttpCache\Store;
$app = new Silex\Application();
$app->get('/', function () {
    return 'Hello World!';
});
$app = new Stack\Session(
    new Symfony\Component\HttpKernel\HttpCache\HttpCache(
        $app,
        new Store(__DIR__.'/cache')
    )
);

$stack = (new Stack\Builder())
    ->push('Stack\Session')
    ->push('Symfony\Component\HttpKernel\HttpCache\HttpCache', new Store(__DIR__.'/cache'));
$app = $stack->resolve($app);

use Symfony\Component\HttpFoundation\Request;
$request = Request::createFromGlobals();
$response = $app->handle($request)->send();
$app->terminate($request, $response);

$stack = (new Stack\Builder())
    ->push('Stack\Session')
    ->push(function ($app) {
        $cache = new HttpCache($app, new Store(__DIR__.'/cache'));
        return $cache;
    })
;