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TLA+ Examples

Gitpod ready-to-code Validate Specs & Models

This is a repository of TLA+ specifications and models covering applications in a variety of fields. It serves as:

  • a comprehensive example library demonstrating how to specify an algorithm in TLA+
  • a diverse corpus facilitating development & testing of TLA+ language tools
  • a collection of case studies in the application of formal specification in TLA+

All TLA+ specs can be found in the specifications directory. The table below lists all specs and their features, such as whether they are suitable for beginners, come with an additional PlusCal variant (✔), or use PlusCal exclusively. The manifest.json file is the source of truth for this table, and is a detailed human- & machine-readable description of the specs & their models. Its schema is manifest-schema.json. All specs in this repository are subject to CI validation to ensure quality.

Examples Included Here

Here is a list of specs included in this repository, with links to the relevant directory and flags for various features:

Name Author(s) Beginner TLAPS Proof PlusCal TLC Model Apalache
Teaching Concurrency Leslie Lamport
Loop Invariance Leslie Lamport
Learn TLA⁺ Proofs Andrew Helwer
Boyer-Moore Majority Vote Stephan Merz
Proof x+x is Even Stephan Merz
The N-Queens Puzzle Stephan Merz
The Dining Philosophers Problem Jeff Hemphill
The Car Talk Puzzle Leslie Lamport
The Die Hard Problem Leslie Lamport
The Prisoners & Switches Puzzle Leslie Lamport
Specs from Specifying Systems Leslie Lamport
The Tower of Hanoi Puzzle Markus Kuppe, Alexander Niederbühl
Missionaries and Cannibals Leslie Lamport
Stone Scale Puzzle Leslie Lamport
The Coffee Can Bean Problem Andrew Helwer
EWD687a: Detecting Termination in Distributed Computations Stephan Merz, Leslie Lamport, Markus Kuppe (✔)
The Boulangerie Algorithm Leslie Lamport, Stephan Merz
Misra Reachability Algorithm Leslie Lamport
Byzantizing Paxos by Refinement Leslie Lamport
EWD840: Termination Detection in a Ring Stephan Merz
EWD998: Termination Detection in a Ring with Asynchronous Message Delivery Stephan Merz, Markus Kuppe (✔)
The Paxos Protocol Leslie Lamport
Asynchronous Reliable Broadcast Thanh Hai Tran, Igor Konnov, Josef Widder
Distributed Mutual Exclusion Stephan Merz
Two-Phase Handshaking Leslie Lamport, Stephan Merz
Paxos (How to Win a Turing Award) Leslie Lamport
Dijkstra's Mutual Exclusion Algorithm Leslie Lamport
The Echo Algorithm Stephan Merz
The TLC Safety Checking Algorithm Markus Kuppe
Transaction Commit Models Leslie Lamport, Jim Gray, Murat Demirbas
The Slush Protocol Andrew Helwer
Minimal Circular Substring Andrew Helwer
Snapshot Key-Value Store Andrew Helwer, Murat Demirbas
Chang-Roberts Algorithm for Leader Election in a Ring Stephan Merz
MultiPaxos in SMR-Style Guanzhou Hu
Einstein's Riddle Isaac DeFrain, Giuliano Losa
Resource Allocator Stephan Merz
Transitive Closure Stephan Merz
Atomic Commitment Protocol Stephan Merz
SWMR Shared Memory Disk Paxos Leslie Lamport, Giuliano Losa
Span Tree Exercise Leslie Lamport
The Knuth-Yao Method Ron Pressler, Markus Kuppe
Huang's Algorithm Markus Kuppe
EWD 426: Token Stabilization Murat Demirbas, Markus Kuppe
Sliding Block Puzzle Mariusz Ryndzionek
Single-Lane Bridge Problem Younes Akhouayri
Software-Defined Perimeter Luming Dong, Zhi Niu
Simplified Fast Paxos Lim Ngian Xin Terry, Gaurav Gandhi
Checkpoint Coordination Andrew Helwer
Finitizing Monotonic Systems Andrew Helwer
Multi-Car Elevator System Andrew Helwer
Nano Blockchain Protocol Andrew Helwer
The Readers-Writers Problem Isaac DeFrain
Asynchronous Byzantine Consensus Thanh Hai Tran, Igor Konnov, Josef Widder
Folklore Reliable Broadcast Thanh Hai Tran, Igor Konnov, Josef Widder
The Bosco Byzantine Consensus Algorithm Thanh Hai Tran, Igor Konnov, Josef Widder
Consensus in One Communication Step Thanh Hai Tran, Igor Konnov, Josef Widder
One-Step Consensus with Zero-Degradation Thanh Hai Tran, Igor Konnov, Josef Widder
Failure Detector Thanh Hai Tran, Igor Konnov, Josef Widder
Asynchronous Non-Blocking Atomic Commit Thanh Hai Tran, Igor Konnov, Josef Widder
Asynchronous Non-Blocking Atomic Commitment with Failure Detectors Thanh Hai Tran, Igor Konnov, Josef Widder
Spanning Tree Broadcast Algorithm Thanh Hai Tran, Igor Konnov, Josef Widder
The Cigarette Smokers Problem Mariusz Ryndzionek
Conway's Game of Life Mariusz Ryndzionek
Chameneos, a Concurrency Game Mariusz Ryndzionek
PCR Testing for Snippets of DNA Martin Harrison
RFC 3506: Voucher Transaction System Santhosh Raju, Cherry G. Mathew, Fransisca Andriani
Yo-Yo Leader Election Ludovic Yvoz, Stephan Merz
TCP as defined in RFC 9293 Markus Kuppe
TLA⁺ Level Checking Leslie Lamport
Condition-Based Consensus Thanh Hai Tran, Igor Konnov, Josef Widder
Buffered Random Access File Calvin Loncaric
Disruptor Nicholas Schultz-Møller

Examples Elsewhere

Here is a list of specs stored in locations outside this repository, including submodules. They are not covered by CI testing so it is possible they contain errors, the reported details are incorrect, or they are no longer available. Ideally these will be moved into this repo over time.

Spec Details Author(s) Beginner TLAPS Proof TLC Model PlusCal Apalache
Blocking Queue BlockingQueue Markus Kuppe (✔)
IEEE 802.16 WiMAX Protocols 2006, paper, specs Prasad Narayana, Ruiming Chen, Yao Zhao, Yan Chen, Zhi (Judy) Fu, Hai Zhou
On the diversity of asynchronous communication 2016, paper, specs Florent Chevrou, Aurélie Hurault, Philippe Quéinnec
Caesar Multi-leader generalized consensus protocol (Arun et al., 2017) Giuliano Losa
CASPaxos An extension of the single-decree Paxos algorithm to a compare-and-swap type register (Rystsov) Tobias Schottdorf
DataPort Dataport protocal 505.89PT, only PDF files (Biggs & Noriaki, 2016) Geoffrey Biggs, Noriaki Ando
egalitarian-paxos Leaderless replication protocol based on Paxos (Moraru et al., 2013) Iulian Moraru
fastpaxos An extension of the classic Paxos algorithm, only PDF files (Lamport, 2006) Leslie Lamport
fpaxos A variant of Paxos with flexible quorums (Howard et al., 2017) Heidi Howard
HLC Hybrid logical clocks and hybrid vector clocks (Demirbas et al., 2014) Murat Demirbas
L1 Data center network L1 switch protocol, only PDF files (Thacker) Tom Rodeheffer
leaderless Leaderless generalized-consensus algorithms (Losa, 2016) Giuliano Losa
losa_ap The assignment problem, a variant of the allocation problem (Delporte-Gallet, 2018) Giuliano Losa
losa_rda Applying peculative linearizability to fault-tolerant message-passing algorithms and shared-memory consensus, only PDF files (Losa, 2014) Giuliano Losa
m2paxos Multi-leader consensus protocols (Peluso et al., 2016) Giuliano Losa
mongo-repl-tla A simplified part of Raft in MongoDB (Ongaro, 2014) Siyuan Zhou
MultiPaxos The abstract specification of Generalized Paxos (Lamport, 2004) Giuliano Losa
naiad Naiad clock protocol, only PDF files (Murray et al., 2013) Tom Rodeheffer
nfc04 Non-functional properties of component-based software systems (Zschaler, 2010) Steffen Zschaler
raft Raft consensus algorithm (Ongaro, 2014) Diego Ongaro
SnapshotIsolation Serializable snapshot isolation (Cahill et al., 2010) Michael J. Cahill, Uwe Röhm, Alan D. Fekete
SyncConsensus Synchronized round consensus algorithm (Demirbas) Murat Demirbas
Termination Channel-counting algorithm (Kumar, 1985) Giuliano Losa
Tla-tortoise-hare Robert Floyd's cycle detection algorithm Lorin Hochstein
VoldemortKV Voldemort distributed key value store Murat Demirbas
Tencent-Paxos PaxosStore: high-availability storage made practical in WeChat. Proceedings of the VLDB Endowment(Zheng et al., 2017) Xingchen Yi, Hengfeng Wei
Paxos Paxos
Lock-Free Set PlusCal spec of a lock-Free set used by TLC Markus Kuppe
ParallelRaft A variant of Raft Xiaosong Gu, Hengfeng Wei, Yu Huang
CRDT-Bug CRDT algorithm with defect and fixed version Alexander Niederbühl
asyncio-lock Bugs from old versions of Python's asyncio lock Alexander Niederbühl
Raft (with cluster changes) Raft with cluster changes, and a version with Apalache type annotations but no cluster changes George Pîrlea, Darius Foom, Brandon Amos, Huanchen Zhang, Daniel Ricketts
MET for CRDT-Redis Model-check the CRDT designs, then generate test cases to test CRDT implementations Yuqi Zhang
Parallel increment Parallel threads incrementing a shared variable. Demonstrates invariants, liveness, fairness and symmetry Chris Jensen
The Streamlet consensus algorithm Specification and model-checking of both safety and liveness properties of Streamlet with TLC Giuliano Losa
Petri Nets Instantiable Petri Nets with liveness properties Eugene Huang
CRDT Specifying and Verifying CRDT Protocols Ye Ji, Hengfeng Wei
Azure Cosmos DB Consistency models provided by Azure Cosmos DB Dharma Shukla, Ailidani Ailijiang, Murat Demirbas, Markus Kuppe

License

The repository is under the MIT license and you are encouraged to publish your spec under a similarly-permissive license. However, your spec can be included in this repo along with your own license if you wish.

Support or Contact

Do you have any questions or comments? Please open an issue or send an email to the TLA+ group.

Contributing

Do you have your own case study or TLA+ specification you'd like to share with the community? Follow these instructions:

  1. Fork this repository and create a new directory under specifications with the name of your spec
  2. Place all TLA+ files in the directory, along with their .cfg model files
  3. You are encouraged to include at least one model that completes execution in less than 10 seconds, and (if possible) a model that fails in an interesting way - for example illustrating a system design you previously attempted that was found unsound by TLC
  4. Ensure name of each .cfg file matches the .tla file it models, or has its name as a prefix; for example SpecName.tla can have the models SpecName.cfg and SpecNameLiveness.cfg, etc.
  5. Consider including a README.md in the spec directory explaining the significance of the spec with links to any relevant websites or publications, or integrate this info as comments in the spec itself
  6. Add an entry to the table of specs included in this repo, summarizing your spec and its attributes

Adding Spec to Continuous Integration

To combat bitrot, it is important to add your spec and model to the continuous integration system. To do this, you'll have to update the manifest.json file with machine-readable records of your spec files. If this process doesn't work for you, you can alternatively modify the .ciignore file to exclude your spec from validation. Modifying the manifest.json can be done manually or (recommended) following these directions:

  1. Ensure you have Python 3.11+ installed
  2. It is considered best practice to create & initialize a Python virtual environment to preserve your system package store; run python -m venv . then source ./bin/activate on Linux & macOS or .\Scripts\activate.bat on Windows (run deactivate to exit)
  3. Run pip install -r .github/scripts/requirements.txt
  4. Run python .github/scripts/generate_manifest.py
  5. Locate your spec's entry in the manifest.json file and ensure the following fields are filled out:
    • Spec title: an appropriate title for your specification
    • Spec description: a short description of your specification
    • Spec sources: links relevant to the source of the spec (papers, blog posts, repositories)
    • Spec authors: a list of people who authored the spec
    • Spec tags:
      • "beginner" if your spec is appropriate for TLA+ newcomers
    • Model runtime: approximate model runtime on an ordinary workstation, in "HH:MM:SS" format
    • Model size:
      • "small" if the model can be executed in less than 10 seconds
      • "medium" if the model can be executed in less than five minutes
      • "large" if the model takes more than five minutes to execute
    • Model mode:
      • "exhaustive search" by default
      • {"simulate": {"traceCount": N}} for a simulation model
      • "generate" for model trace generation
    • Model result:
      • "success" if the model completes successfully
      • "assumption failure" if the model violates an assumption
      • "safety failure" if the model violates an invariant
      • "liveness failure" if the model fails to satisfy a liveness property
      • "deadlock failure" if the model encounters deadlock
    • (Optional) Model state count info: distinct states, total states, and state depth
      • These are all individually optional and only valid if your model uses exhaustive search and results in success
      • Recording these turns your model into a powerful regression test for TLC
    • Other fields are auto-generated by the script; if you are adding an entry manually, ensure their values are present and correct (see other entries or the manifest-schema.json file)

Before submitted your changes to run in the CI, you can quickly check your manifest.json for errors and also check it against manifest-schema.json at https://www.jsonschemavalidator.net/.