I'm wondering first, exactly what axioms pg settled on. And I'm also curious as you've described it, if the hardware were built for the language and rather than the language being built for the hardware, "what is the least number of axioms need for a practical language".
I can't really answer that. Somebody would need to write an "eval" function in Arc. That would give you a pretty good starting point for figuring out how many axioms you need.