I’ll go with Taran’s idea there, I think. Something like Douglas Hofstadter’s BlooP language, perhaps, which only allows primitive recursive functions. Would BlooP allow for chained arrow notation, or would it be too restrictive for that? More generally, what is the fastest growing primitive recursive function possible, and what limits would that give us in terms of the scope of problems that can be solved by our magic box?
I’ll go with Taran’s idea there, I think. Something like Douglas Hofstadter’s BlooP language, perhaps, which only allows primitive recursive functions. Would BlooP allow for chained arrow notation, or would it be too restrictive for that? More generally, what is the fastest growing primitive recursive function possible, and what limits would that give us in terms of the scope of problems that can be solved by our magic box?