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Staring at this until my brain goes fuzzy, but it looks like a kind of sequent calculus. Is that far off the mark?

I don't think so, but I wouldn't know enough to tell you. I can tell you that I am not very interested in 20th-century formal logic, at least as a way of defining programming, but you knew that. I think it seems like a logical equivalent that my approach is not very interesting from the standpoint of 20th-century formal logic.

Must be my monkey-brain trying to explore the unfamiliar by finding similarities to what I already know.

I may of course simply be looking through a bottle (and constrained by backwards-tracking logicians).

All of this is starting to smell of an Incompleteness Theorem of Programming Languages.

I think I get it now. Sort of like a sequent calculus without the logic backtracking. Instead of proving anything Hoon just defaults it to something. Or crashes. :)

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