Tradeoff of defining types as subobjects

[YaelDillies]

Zulip

[adomani]

Thanks for writing this!

[riccardobrasca]

Can you mention that the subobject approach has sometimes performance issues? Like what happened for the ring of integers (see #12386).

Also, I think that it is worth mentioning that the anonymous constructor can make the projections' name issue less important.

[YaelDillies]

#12386 was in fact the impetus for me to write this blogpost, but it seems that the issue has been fixed by making the discrimination keys more thorough, see #86 (comment)

I am not sure why anonymous dot notation is relevant here.

[YaelDillies]

#12386 was in fact the impetus for me to write this blogpost, but it seems that the issue has been fixed by making the discrimination keys more thorough, see #86 (comment)

I am not sure why anonymous dot notation is relevant here.

[riccardobrasca]

I mean ⟨x, by simp⟩ (isn't this called anonymous constructor?) to build a term of a subtype.

[YaelDillies]

Ah sure, but anonymous constructor notation is useless when working with highly nested structures such as subobjects. Eg to build a subring one needs to do \<\<\<_, _\>, _\>, _\>, which I think isn't worth the trouble unless you are trying to write very compact code.

[Vierkantor]

My concerns are addressed, this is good to go as far as I'm concerned. I'll merge in a few days unless we get objections.

[bryangingechen]

Are there some examples in mathlib of each design that would be illuminating to discuss?

[bryangingechen]

Thanks!