The issue is this:
I have a web application that runs on a PHP server. I\'d like to build a REST api for it.
I did some research and I figured out that REST api uses HTT
Another framework which has not been mentioned so far is Laravel. It's great for building PHP apps in general but thanks to the great router it's really comfortable and simple to build rich APIs. It might not be that slim as Slim or Sliex but it gives you a solid structure.
See Aaron Kuzemchak - Simple API Development With Laravel on YouTube and
Laravel 4: A Start at a RESTful API on NetTuts+