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Really cool post! I'm wondering if this could be used for dependently typed languages somehow? I'm guessing that Would need to figure out a good evaluation and conversion checking algorithm though… 🤔
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For perf, there are many options. Intern identifiers. Scopes are unique integers. Intern scope sets. Cache lookup results. Cache subset check results. There's also the question of multithreading. I don't have a good sense of where the bottlenecks would be.
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Without more details it's hard to tell, that sounds like it'd very much depend on how your typing judgements are set up... That said, the paper does discuss recursive definition contexts, so the system can certainly handle those.
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I guess the complication I'm having right now is how I'm using debruijn indices+levels for my NbE -based elaborator. It's very quick for elaboration, but makes being flexible with the ordering of binders tricky. Dunno if sets of scopes helps or hinders here…
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