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This week there was a nice HoTT/UF workshop + EuroProofNet workshop, here's my slides: https://t.co/EWutfkdOQ5 In a nutshell, it's about a type theory where you can specify and use any number of two-level type theories over various object languages, at the same time.
@gergo_erdi We don't get all relevance info from elaboration btw, that's because elaboration works under bound vars, while conversion works under arbitrary instantiations of bound vars to values. E.g. while checking the body of "f : (A : U) -> ..." we know nothing about A's relevance.
@gergo_erdi Computing no types is cheaper than computing some types. If a source program doesn't depend on unit eta, the best we can do is to compute no types. The question is, how often do people depend on unit eta. If rarely, the lazy relevance checking is better, if often, it's worse.
@kmett@scheminglunatic I wouldn't say that; tbh it's on my TODO list to look into staging + substructural object languages but right now I don't know much about it. I worked recently a bit on regions + staging, which looks quite promising already without substructural types. https://t.co/GpnLqA2LBQ
@Iceland_jack Lots of big changes would be needed. Stage-indexing in kinds, proper dependent types and non-erased generated types in code intended for compile time, polarized types in code intended for runtime. And ofc the RTS has a different structure than what I described.
I wrote about a design for region memory management: https://t.co/GpnLqA2LBQ
I'm pretty excited about it. Hopefully I'll be able to actually implement it not too far in the future.
Pierre-Marie Pédrot recently explained to me a nice and simple proof that function extensionality is not provable in MLTT. I wrote some Agda and explanations for it here: https://t.co/gkCA0ti6Z1