I'm interested in implementing a Forth system, just so I can get some experience building a simple VM and runtime.
When starting in Forth, one typically learns about the stack and its operators (DROP, DUP, SWAP, etc.) first, so it's natural to think of these as being among the primitive operators. But they're not. Each of them can be broken down into operators that directly manipulate memory and the stack pointers. Later one learns about store (!) and fetch (@) which can be used to implement DUP, SWAP, and so forth (ha!).
So what are the primitive operators? Which ones must be implemented directly in the runtime environment from which all others can be built? I'm not interested in high-performance; I want something that I (and others) can learn from. Operator optimization can come later.
(Yes, I'm aware that I can start with a Turing machine and go from there. That's a bit extreme.)
Edit: What I'm aiming for is akin to bootstrapping an operating system or a new compiler. What do I need do implement, at minimum, so that I can construct the rest of the system out of those primitive building blocks? I won't implement this on bare hardware; as an educational exercise, I'd write my own minimal VM.
This thread covers your exact question. Here is a soup-to-nuts implementation with complete documentation.
I wrote a subroutine threaded Forth targeting 68K when I was in college. I defined the runtime environment and dictionary format, then wrote some C code that boot strapped a Macintosh application that loaded a default dictionary, populated some I/O vectors and got the code running. Then I took the Leo Brodie book Starting Forth and started implementing the basic dictionary in 68K assembly language. I started with arithmetic/logic words, then did control structures then word definition/manipulation words. My understanding is that at a minimum you need @, !, +, -, * and /. The rest can be implemented in terms of those, but that's like trying to write an entire graphics library based on SetPixel and GetPixel: it will work, but yikes, why?
I enjoyed the process as there were some really interesting puzzles, like getting DOES> exactly right (and once I had a solid DOES> implementation, I was creating closures that turned into tiny, tiny amounts of code).