SOAP or REST or WebSocket?

This BOF is a lively discussion comparing SOAP, REST, and WebSocket architectures, asking questions such as when to use which? Should SOAP and/or REST be used in a complementary way where request/response are handled with SOAP and/or REST/XHR and push/pubsub/broadcast are provided by WebSocket?

Can REST and WebSocket coexist, given that REST is stateless (scalability via caching) whereas WebSocket connections are stateful (scalability via load-balancing)? Are WebSocket apps creating siloed applications instead of REST-like, addressable resources? If you do REST over WebSocket, how do you represent HTTP methods, URIs, URI parameters, and headers?