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::::Regarding the whole table, I would see this table as a commutative diagram of "list → multiset → set", "list → permutation → set". The combinatoric interpretation is interesting. For the permutations, choosing universal left-bias might correspond to enforcing causality (the items selected earlier is removed from the pool and forbidden).
::::I don't think full permutation allowing duplicates is a standard terminology. Also, I stand by just permutation instead of partial permutation, as there is nothing to disambiguate in the context, and [[Partial permutation#Restricted partial permutations|being partial can mean many things]]! [[User:J824h|Junghyeon Park]] ([[User talk:J824h|talk]]) 15:18, 29 November 2024 (UTC)
:::::{{outdent|4}} Ahhh, you're right, I totally forgot about the closure there. I also think you're exactly right about biasing the operator so that it's well-defined.
:::::Because the join is a natural transformation, that would probably still remain naive, and the + would need to implement the bias. I would think either direction could work though; the append would just need to directly compare the items, then drop duplicates from either the left or the right. And like you said, you could interpret the left-bias causally like selection without replacement (and the right-bias is... anti-causal?)
:::::''That said'', I also think you're right that we're getting into the weeds about the permutation bit. There's actually not even a citation either so while I think technical articles (especially hard topics) need some flexibility to work out the math / logic oneself, we're probably veering into [[WP:SYNTHESIS]] at this point.
:::::So I just cut any mention of the permutations from the table for now. I also consolidated the table layout a bit, but noted the combinatoric properties (so the potential symmetry I mentioned is still implied). If you think it needs more work though or that it should be cut, you should probably go for it. This article definitely needs more attention to the technical details. -- [[User:Zar2gar1|Zar2gar1]] ([[User talk:Zar2gar1|talk]]) 17:26, 3 December 2024 (UTC)
== Rust example ==
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