I’m not sure why the connection of REST to HTTP is so commonly misunderstood, but after hearing an architect say REST is implemented with HTTP, I’ve had just about enough.
HTTP is a transfer protocol that implements the four verbs in REST (under different names). HTTP is thus a convenient foundation for RESTful services. It is not the only possible foundation. Wanna implement REST over JMS? Over CORBA? Over carrier pigeon? Go nuts!