[madhadron]

I wish semilattices got more play. They're so ubiquitous when talking about distributed systems. I remember a keynote on eventual consistency in databases that could have been replaced with "make your merge operation the join of a semilattice."

[infogulch]

Any resources for semilattices that you do like? I'm also finding them mentioned around CRDT & distributed systems threads.

[Twisol]

My all-time favorite is the original LVars paper: https://users.soe.ucsc.edu/~lkuper/papers/lvars-fhpc13.pdf

[infogulch]

> Conclusion ... monotonicity serves as the foundation of deterministic parallelism

That's what the recent CALM Theorem [1] paper uses as the first theorem:

> Monotonicity is the key property underlying the need for coordination to establish consistency, as captured in the CALM Theorem:

> THEOREM 1. Consistency As Logical Monotonicity (CALM). A problem has a consistent, coordination-free distributed implementation if and only if it is monotonic.

Unsurprisingly, this paper is reference 32 in CALM. Maybe I should check out some other papers referenced here... Thanks for the recommendation!

[1]: https://cacm.acm.org/magazines/2020/9/246941-keeping-calm/fu...

[madhadron]

I read Birkhoff's "Lattice Theory" many years ago, then wandered down some idiosyncratic path, so, no, I'm sorry. I really don't have anything.