[meowface]

Specifically just looking for a brief explanation of this line:

>For example, his "emulation cones" are a new name for a very old and extremely well-studied idea. The term "rulial space", similarly, is a new name for an idea that's well-developed in programming language theory.'

What's the old well-studied idea, and the well-developed programming theory idea? A one sentence reply is fine.

[covidacct]

The idea of defining a set of transition rules and then analyzing the properties of some closure (e.g., think reflexive and transitive) of those rules. For transition rules of various orders, expressiveness, etc. And then stepping back and realizing that's what you're studying and generalizing it by thinking rigorously about the relationships between those systems and so on. That's really pretty much then entire modus operandi of a huge chunk of PL research, and there's a ton of mathematical and actual technology built up for doing so. The algorithms that are core components of Stephen's "standard library" for this project scratch the surface.