If you compare the steps and lessons in a Basics program of Lardy, Farmer, Aycock, Stawski, Graham, Attar, Kappes, Curtis, Rorem, Carey and others including Basics as I describe in Retrievers ONLINE, you will see a set of steps and a sequence that is fundamentally the same. That sequence was first developed by Rex by the early-mid 70's. Thus, it is reasonable to label such programs as Carr-based. It has been described as a "force-based system" but that term is loaded with baggage. There are many variants but list the steps and you will see the genesis.
When you get to Transition, a term formally introduced by Attar and Lardy and copied by others, you start to see some more variances amongst the steps as practiced above and by Rex. But again the fundamentals are there in Rex's work.
Of course, each of the above have added their own wrinkles to approach and implementation and perhaps there are the most significant differences in philosophy. However, the "basic" steps are from a Carr based training system whether they learned it from Rex or not. For example, Lardy did not visit with Rex until the 90's but he saw a certain sequence with Kappes in the early 80's.
All of the above use Operant Conditioning theory but there are considerable differences in how they emphasize + and - P and R for those that care about such things.
I can name a bunch of other pros who use a similar sytem but since they haven't publically documented their training elsewhere, I won't list them. Suffice it to say that almost all of the Field trial professionals use a similar basic sequence but implement in diverse ways.
If you study Rex and his philosophy you will see continual evolution. You will also see that he continually challenged new methods. He would turn over in his grave at the idea that revolutionary new "successful field methods" have been invented in the last 10 years. He would scoff at the idea that a dog could be trained to National levels with clickers/R+ve only. Having said that, he would applaud the refinement of methods to deal with a diversity of dogs and handlers and the challenges of today's field trials.
In his later years, Rex became very adamant about being fair and compassionate towards the dogs and how we train them. That was despite his early emphasis on a "force or compulsion based" approach. His passion and concern for the dogs was extreme.He would easily come to tears talking about some of his great dogs!!!
Unfortunately, in the hands of some, his methods were implemented with far less compassion and concern for the dogs!!
Rex was loved, hated, respected and above all misunderstood at times. He didn't have time for the casual or the unpassionates. His ego about the importance of doing what was best for the dog turned many off.
Clearly, history has already shown the impact of a Carr-based system! I doubt we'll see the likes of it again!
PS. I applaud Vicki's synopsis of Rex as linked above!!!