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The CAP theorem is a very strong limit on providing both availability and consistency in any distributed system. In your sharding+replication example, what happens when the datacenters containing your master and slave lose their network link? There's no way you can maintain write availability for clients in both datacenters while also providing the ACID Consistency guarantee. (But systems like Dynamo or CouchDB can do so while guaranteeing eventual consistency.)

After seeing some real-world, big business problems solved with weakened consistency guarentees, I'm skeptical that there are as many problems that "need" ACID as most people think. Rather, I think that (a) most engineers have not yet been exposed to the reasonable alternatives to ACID, and so have not actually thought about whether they "need" it, and (b) most businesses do not yet have the knowledge they need to weigh ACID's benefits against its availability costs.

I agree with the CAP theorem and it applies to my example. In my example replication only provides a backup copy of the data and is not used by the application, that's why it's active-passive (provides reliability). This configuration provides the highest level of data protection that is possible without affecting the performance of the master database/shard. This is accomplished by allowing a transaction to commit writes to the master database. The same transaction is also written to the slave, but that transaction is optional and written asynchronously. Two-phase commit is not performed.

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