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A highly-available move operation for replicated trees

This repository contains work on move operations in conflict-free replicated data types (CRDTs), by Martin Kleppmann, Dominic P. Mulligan, Victor B. F. Gomes, and Alastair R. Beresford.

For background and details, please see these two papers:

  • Martin Kleppmann, Dominic P. Mulligan, Victor B. F. Gomes, and Alastair R. Beresford. A highly-available move operation for replicated trees. IEEE Transactions on Parallel and Distributed Systems, 2021. (PDF, doi:10.1109/TPDS.2021.3118603)
  • Martin Kleppmann. Moving elements in list CRDTs. 7th Workshop on Principles and Practice of Consistency for Distributed Data (PaPoC), April 2020. (PDF, doi:10.1145/3380787.3393677, workshop presentation)


The Isabelle/HOL formalisation and proof of correctness can be found in the following files in the proof directory:

  • proof.pdf contains a PDF rendering of the whole proof.
  • Move.thy contains the definition of the move algorithm for trees, a proof that a tree node has at most one parent, and a proof that the move operation is commutative.
  • Move_Acyclic.thy contains a proof that the tree contains no cycles.
  • Move_SEC.thy contains a proof that the algorithm provides Strong Eventual Consistency, as formalised in our proof framework.
  • Move_Code.thy contains an alternative definition of the algorithm that is efficiently executable, and a proof that it is equivalent to the earlier, more abstract algorithm.
  • Move_Create.thy contains a proof that it is safe for node creation operations to use an optimised code path.

To check the proofs, download Isabelle and install it. The Move_SEC theory depends on the definition of Strong Eventual Consistency in the Isabelle Archive of Formal Proofs. Download a release of the AfP and configure your Isabelle installation to use it.

You can either run the Isabelle GUI interactively, or you can run it from the command line. This is how you run it on Mac OS (adjust the path to your Isabelle installation):

/Applications/ build -D .

The Isabelle-generated Scala source is written to Move_Code.scala. To use it in the evaluation, copy that file to evaluation/src/main/scala/.


There are two papers in the paper directory:

  • A highly-available move operation for replicated trees is in paper/move-op.tex
  • Moving elements in list CRDTs is in paper/list-move.tex

To build PDFs of the papers with LaTeX:

cd paper
make move-op.pdf list-move.pdf


In evaluation/src/main/scala/TestReplica.scala there is a simple network server and client that is used to evaluate the performance of the algorithm. To build it, you need sbt installed; then you can run:

cd evaluation
sbt compile

Note: annoyingly, the Isabelle-generated code contains classes whose name differs only in case. For this reason, it cannot be compiled and run on a case-insensitive filesystem (macOS, Windows): the class files generated by the compiler would clash. You need to build it on Linux instead. For people running other OSes, there is a Docker setup in evaluation/Dockerfile that installs sbt and compiles the source. After installing Docker you can run this:

# Run this in the root directory of this repository,
# not in the `evaluation` directory
docker build -t move-op:latest evaluation
docker run -it --rm move-op /bin/bash

# Then run this inside the container to watch source files for changes:
cd evaluation && sbt ~compile

# Edit a file outside of the container, and then copy it into the
# container to compile it, like this:
docker cp evaluation/src/main/scala/TestReplica.scala 10c36574237a:/evaluation/src/main/scala
# Replace 10c36574237a with the running container ID (see `docker ps`)

To run on AWS, log into the AWS Management Console in us-west-1, eu-west-1, and ap-southeast-1 respectively. In each region, launch a c5.large instance running Ubuntu 18.04. (Hint: using the request spot instance feature can be considerably cheaper, but the user interface is a nightmare.)

Configure their security groups so that you can log in via SSH (TCP port 22), and so that the three instances can talk to each other on TCP port 8080.

Modify the script evaluation/ to contain the IP addresses of your instances, and the location of the SSH private keys on your filesystem. Manually log in to each of the instances as shown in that script, and run the following one-off setup on each:

sudo apt-get update && sudo apt-get upgrade -y && sudo apt-get install -y apt-transport-https gnupg wget unzip
echo "deb /" | sudo tee -a /etc/apt/sources.list.d/sbt.list
sudo apt-key adv --keyserver hkp:// --recv 2EE0EA64E40A89B84B2DF73499E82A75642AC823
sudo apt-get update && sudo apt-get install -y openjdk-8-jdk-headless sbt
git clone && cd move-op/evaluation && sbt compile

Once that setup is done, you can run the script evaluation/ from your local machine to perform a test run on all three instances concurrently. It takes one argument: the interval between successive move operations generated on each replica, in microseconds.

The script logs into the instances by SSH, updates the configuration, runs the experiment, and copies the logs off the instances into evaluation/data/logs/*.log.gz. Each test run lasts for 10 minutes and then automatically shuts down. This repository contains the logs from our evaluation in the following directories:

  • evaluation/data/logs-crdt-generated: Running in CRDT mode, using the code extracted from Isabelle.
  • evaluation/data/logs-crdt-optimised: Running in CRDT mode, using the hand-optimised (not verified) implementation.
  • evaluation/data/logs-leader-generated: Running in state machine replication mode, using the code extracted from Isabelle.
  • evaluation/data/logs-leader-optimised: Running in state machine replication mode, using the hand-optimised (not verified) implementation.

Those logs are then analysed by the scripts evaluation/data/ (for mode USE_LEADER=false) and evaluation/data/ (for USE_LEADER=true). Pass a directory name to these scripts and they will write a file called in that directory. Those data files are then used to plot the graphs in the paper using Gnuplot. To refresh the graphs:

gnuplot crdt-generated.gnuplot
gnuplot crdt-optimised.gnuplot
gnuplot leader-vs-crdt.gnuplot


This project is made available under the terms of the MIT License.


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