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CALM Theorem

Last updated Aug 12, 2022 Edit Source

Consistency As Logical Monotonicity

Logically monotonic distributed code is eventually consistent without any need for consensus protocols (distributed locks, two-phase commit, etc.)

See also: CRON Theorem, I-Confluence

Logically monotonic state is something that can be represented using a join semi-lattice.

Basically, avoid coordination where possible. It’s the dominant term in the Universal Scaling Law.

# Monotonicity and Datalog

Monotonic properties arise from things in the form of a $\exists$ question (the presence of one positive example gives us an answer in the affirmative and additional positive examples don’t change that fact). Non-monotonic properties arise from things in the form of a $\forall$ question (can only answer a question like that once we’ve looked at every example). Example of the later also include $! \exists$, the negation property.

What we’ve learned from these examples is that negation and universal quantification mess with monotonicity. Thus, we can also express CALM in terms of a programming language like Datalog:

A program has an eventually consistent, coordination-free execution strategy if and only if it is expressible in (monotonic) Datalog.

In fact, this is what Bloom is based off-of. Bloom is underpinned by a programming language called Dedalus which is a Datalog variant that cleanly captures what we see as the salient semantic issues for parallel and distributed computing