I hadn’t thought that I would blog, but since Jekyll makes it so easy, I’m feeling like I need to give it a whirl. No promises about how often this will happen, of course, because the virtual world is littered with dead blogs of the well-intentioned.
I thought I would try to clear up, if only for myself, the terminology surrounding consistency and isolation, or, more specifically, operation and transaction ordering. Of course, there have been a large number of discussions and blog posts that are a rabbit-hole of the illuminating and horrifying.
I’ve been thinking and talking about this stuff a lot lately because I am TA'ing UW’s undergraduate distributed systems class and working on TAPIR, where we are grappling with how to explain providing consistency with inconsistency (with any consistency). Of course, this also serves as dinner conversation for me and Dan, so it is good that we have the right words to use, at least until we have a few glasses of wine.
Before we dive into the different levels of isolation and consistency provided by distributed systems and databases, I will try to define the guarantees themselves.
Consistency, as in the CAP theorem, defines how copies of the set of data items in a system relate to each other. Does the system ensure that they appear as if they are a single copy (to an application or an external observer)? Or do they appear to have some other apparent behavior (i.e., after some period of time they converge to a single copy)?
Edit: Coherence Someone pointed out to me that I should also define coherence, as how copies of a single item relate to each other (assuming that the system holds more than one data item). Architects tend to define this differently from consistency due to reasoning about a single cache line vs. multiple cache lines. As a result, it is possible to have consistency bugs that are not coherence bugs.
Isolation, in ACID, defines the how sets of multiple operations on the set of data items in a system relate to each other. Does the system ensure that a set of operations (grouped together in a transaction) appear as if they ran at a single point in time? Do transactions then appear as if they each ran sequentially on a single copy of the database? Or some other behavior (i.e., each transaction ran on its own snapshot of the database)?
In summary, (1) coherence dictates how a system orders operations for a single data item in the system, (2) consistency dictates how a system orders operations for the entire set of data items in the system, and (3) isolation dictates how a system orders sets of operations grouped in transactions over the entire set of items in the system. As a side effect, consistency is a total ordering guarantee for a set of replicas, while isolation is a partial ordering guarantee (because not every transaction touches every data item).
Unlike isolation and CAP consistency, the ACID type of consistency is not a system guarantee, but an application-specific invariant (e.g., bank account balance must be greater than 0). Enforcing this type of consistency depends on the application as well as the system. For example, the A, I & D system guarantees ensure that application doesn’t see uncommitted or other intermediate state, but the application needs to ensure that it does not violate its own invariants (e.g., the application needs to check the bank account balance before withdrawing).
I’ve been reading some great old database papers recommended by Phil Bernstein, and Thomas  defines, internal consistency as the C in ACID and mutual consistency as the C in CAP (both of which should not be confused with external consistency!), which I think is a great way to differentiate the two.
As Thomas says,
The notion of internal consistency is somewhat more difficult to define precisely. It concerns the preservation of invariant relations that exist among items within a database. As such, internal consistency is related to the interpretation or semantics of items in the database. Therefore, most of the responsibility for the internal consistency of a database must rest with the application processes which update it.
Support for this kind of consistency is available in modern database systems, but rarely discussed. When people are talking about the consistency of transactional storage systems like Spanner, they are almost always talking about isolation.
OK, now back to how we order operations and transactions in a storage system. There are so many different types of ordering guarantees that this is a huge topic. I will primarily talk about the strongest variants because these are the best defined.
Sequential (or serializable) consistency ensures that the same operations are applied in the same order to every copy of a set of data items.
Serializable isolation ensures that transactions execute as if they were executing one at a time on a single copy of the database.
Linearizable consistency ensures that the same operations are applied in the same order to every copy of the data item and that the order reflects the order in which the operations appear to execute to an external observer (like the application).
Strict serializable isolation ensures that transactions execute as if they were executing one at a time on a single copy of the database and that the order matches the order in which the transactions appear to execute to an external observer (like the application).
There has been much discussion of externally consistent (or linearizable) transactions since the publication of Google’s Spanner system . Traditionally, the guarantees provided by Spanner and applied to transactions would be called strict serializability. Practically, it doesn’t matter: linearizability is just strict serializability for single operations.
As many people have observed, we just ended up with different words for the same thing because two research communities separately developed the terminology. Now the two communities have collided (not literally but that would be fun!), as distributed transactional storage systems require both consistency and isolation guarantees, and everyone is thoroughly confused.
It might seem that, despite the database and systems communities inability to coordinate, consistency and isolation are tied together. If a storage system has one level of isolation (e.g., strict serializability) for transactions, then it typically replicates single data items with a matching level of consistency (e.g., linearizability). Or put another way, if you want a strict serial ordering of transactions, you need to start with a strict serial ordering of operations, right? (See why this is confusing?)
Interestingly (to me anyway), this is not necessary. In the TAPIR project, we are designing a new protocol to provide strong isolation guarantees without any consistency guarantees. Our observation is that there is no need to enforce both isolation and consistency in a transactional storage system that uses replication. This has all kinds of benefits, like letting us get away without using an expensive replication protocol like Paxos.
Explaining consistency is hard and it doesn’t help that we don’t have consistent terminology! Trying to convince people that they might want strong isolation but not need consistency (in CAP) and probably don’t care about that other kind of consistency (in ACID) is really hard.
 R. H. Thomas. A majority consensus approach to concurrency control for multiple copy databases. ACM Transactions on Database Systems, 4(2):180–209, June 1979.
 J. C. Corbett et al. Spanner: Google’s globally-distributed database. In Proceedings of OSDI, 2012.