Talk:Monad (functional programming): Difference between revisions

Revision as of 19:11, 28 November 2024

Revision as of 15:18, 29 November 2024

Line 195:

:::The obvious 4th piece would be ''ordered'' selections ''without'' replacement, which I guess would technically be partial permutations? The symmetry is really easy to see combinatorically, but our current table lists the property of the monoid, which isn't nearly as elegant.

:::Per your specific question about a well-defined join, if I'm thinking through this right, both full and partial permutations would have a well-defined join ''on their respective domains''. In a full permutation, there's no restriction on the ___domain so the join yields [a,b,a] without any issues. For a partial permutation though, listing 'a' twice is prohibited at the monoid level so in your example, the ++ would yield a type error at the 2nd 'a' prior to any join. As long as nothing is repeated though, there's no reason the naive join wouldn't work just like with the full permutation / free monoid. -- [[User:Zar2gar1|Zar2gar1]] ([[User talk:Zar2gar1|talk]]) 19:11, 28 November 2024 (UTC)

::::[a, b] + [a] does need to be defined as long as both [a, b] and [a] are in the monad. To get permutations, we need a relation that identifies [a, b, a] to either [a, b] or [b, a], that is, a choice of left- or right-bias for each element. We don't have a unique but multiple valid concrete structures, which seems kind of unfortunate. Otherwise, we might simply accept [a, b, a] = error as a monadic value, which would be without a homomorphism to sets and fit worse in the table. Do I make sense?

::::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)

== Rust example ==