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pufferffish / agda-symmetries

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Move isOfHLevel from Free to struct and rename ext #33

Open pufferffish opened 10 months ago

pufferffish commented 10 months ago

ext in Free should be renamed to sharp, but to make it work nicely with infix we should move (H : isOfHLevel h (𝔜 .carrier)) to struct instead

pufferffish commented 10 months ago

Turns out this would involve a lot of refactoring, a lot of arbitrary types in Sig, EqSig, struct, and such would need to be changed so that they are accompanied with a proof that states they are of a certain h-level, which would then involve spamming implicit h-level arguments everywhere. This would then add a lot of proof burden since we now need to constantly prove certain types are of the specified h-level, which is annoying because isOfHLevel h (𝔜 .carrier) isn't really used anywhere aside from defining Free definition anyway (e.g. the free monoid definition, where trunc is not used once outside of proving theorems about sharp).

Probably best to put this on hold until we find a nicer way to deal with general h-level for Free. One potential solution would be instance arguments, however this does not follow the convention of the cubical library since instance arguments aren't really used in the library.

vikraman commented 10 months ago

It's not clear how to handle the trunc for sets and groupoids, what we can say for sure is that for sets, eqs should be a proposition, and for groupoids, cohs should be a proposition.