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."
> 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!
