TLA⁺ Examples

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. A central manifest of specs with descriptions and accounts of their various models and features can be found in the manifest.json file.

List of Examples

#	Name	Description	Authors	TLAPS Proof?	TLC Model?	Module Dependencies	PlusCal?	Apalache?
1	2PCwithBTM	A modified version of P2TCommit (Gray & Lamport, 2006)	Murat Demirbas		✔	FinSet, Int, Seq	✔
2	802.16	IEEE 802.16 WiMAX Protocols	Prasad Narayana, Ruiming Chen, Yao Zhao, Yan Chen, Zhi (Judy) Fu, and Hai Zhou		✔	Int, Seq, FinSet
3	aba-asyn-byz	Asynchronous Byzantine agreement (Bracha & Toueg, 1985)	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Nat
4	acp-nb	Non-blocking atomic commitment with a reliable broadcast (Babaoğlu & Toueg, 1993)	Stephan Merz		✔	default theories
5	acp-nb-wrong	Wrong version of the non-blocking atomic commitment with a reliable broadcast (Babaoğlu & Toueg, 1993)	Stephan Merz		✔	default theories
6	acp-sb	Non-blocking atomic commitment with a simple broadcast (Babaoğlu & Toueg, 1993)	Stephan Merz		✔	default theories
7	allocator	Specification of a resource allocator	Stephan Merz		✔	FinSet
8	async-comm	The diversity of asynchronous communication (Chevrou et al., 2016)	Florent Chevrou, Aurélie Hurault, Philippe Quéinnec		✔	Nat
9	bcastByz	Asynchronous reliable broadcast - Figure 7 (Srikanth & Toeug, 1987)	Thanh Hai Tran, Igor Konnov, Josef Widder	✔	✔	Nat, FinSet
10	bcastFolklore	Folklore reliable broadcast - Figure 4 (Chandra and Toueg, 1996)	Thanh Hai Tran, Igor Konnov, Josef Widder	✔	✔	Nat
11	bosco	One-Step Byzantine asynchronous consensus (Song & Renesse, 2008)	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Nat, FinSet
12	Boulangerie	A variant of the bakery algorithm (Yoram & Patkin, 2015)	Leslie Lamport, Stephan Merz	✔	✔	Int	✔
13	byihive	Based on RFC3506 - Requirements and Design for Voucher Trading System (Fujimura & Eastlake)	Santhosh Raju		✔	default theories
14	byzpaxos	Byzantizing Paxos by Refinement (Lamport, 2011)	Leslie Lamport		✔	Int, FinSet
15	c1cs	Consensus in one communication step (Brasileiro et al., 2001)	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Int, FinSet
16	Caesar	Multi-leader generalized consensus protocol (Arun et al., 2017)	Giuliano Losa		✔	FinSet, Seq, Int	✔
17	CarTalkPuzzle	A TLA+ specification of the solution to a nice puzzle.			✔	Int
18	CASPaxos	An extension of the single-decree Paxos algorithm to a compare-and-swap type register (Rystsov)	Tobias Schottdorf		✔	Int, FinSet
19	cbc_max	Condition-based consensus (Mostefaoui et al., 2003)	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Int, FinSet
20	cf1s-folklore	One-step consensus with zero-degradation (Dobre & Suri, 2006)	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Nat
21	ChangRoberts	Leader election in a ring (Chang & Roberts, 1979)	Stephan Merz		✔	Nat, Seq	✔
22	DataPort	Dataport protocal 505.89PT, only PDF files (Biggs & Noriaki, 2016)	Geoffrey Biggs, Noriaki Ando			Int, Seq
23	detector_chan96	Chandra and Toueg’s eventually perfect failure detector	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Int, FinSet
24	DieHard	A very elementary example based on a puzzle from a movie			✔	Nat
25	dijkstra-mutex	Mutual exclusion algorithm (Dijkstra, 1965)			✔	Int	✔
26	diskpaxos	Disk Paxos (Gafni & Lamport, 2003)	Leslie Lamport, Giuliano Losa		✔	Int
27	egalitarian-paxos	Leaderless replication protocol based on Paxos (Moraru et al., 2013)	Iulian Moraru		✔	Nat, FinSet
28	ewd840	Termination detection in a ring (Dijkstra et al., 1986)	Stephan Merz	✔	✔	Nat
70	ewd998	Shmuel safra's version of termination detection	Stephan Merz, Markus Kuppe		✔	Int, FinSet
29	fastpaxos	An extension of the classic Paxos algorithm, only PDF files (Lamport, 2006)	Leslie Lamport			Nat, FinSet
30	fpaxos	A variant of Paxos with flexible quorums (Howard et al., 2017)	Heidi Howard		✔	Int
31	HLC	Hybrid logical clocks and hybrid vector clocks (Demirbas et al., 2014)	Murat Demirbas		✔	Int	✔
32	L1	Data center network L1 switch protocol, only PDF files (Thacker)	Tom Rodeheffer			FinSet, Nat, Seq
33	lamport_mutex	Mutual exclusion (Lamport, 1978)	Stephan Merz	✔	✔	Nat, Seq
34	leaderless	Leaderless generalized-consensus algorithms (Losa, 2016)	Giuliano Losa		✔	FinSet, Int, Seq	✔
35	losa_ap	The assignment problem, a variant of the allocation problem (Delporte-Gallet, 2018)	Giuliano Losa		✔	FinSet, Nat, Seq	✔
36	losa_rda	Applying peculative linearizability to fault-tolerant message-passing algorithms and shared-memory consensus, only PDF files (Losa, 2014)	Giuliano Losa			FinSet, Nat, Seq
37	m2paxos	Multi-leader consensus protocols (Peluso et al., 2016)	Giuliano Losa		✔	Int, Seq, FinSet
38	mongo-repl-tla	A simplified part of Raft in MongoDB (Ongaro, 2014)	Siyuan Zhou		✔	FinSet, Nat, Seq
39	MultiPaxos	The abstract specification of Generalized Paxos (Lamport, 2004)	Giuliano Losa		✔	Int, FinSet
40	N-Queens	The N queens problem	Stephan Merz		✔	Nat, Seq	✔
41	naiad	Naiad clock protocol, only PDF files (Murray et al., 2013)	Tom Rodeheffer		✔	Int, Seq, FinSet
42	nbacc_ray97	Asynchronous non-blocking atomic commit (Raynal, 1997)	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Nat, FinSet
43	nbacg_guer01	On the hardness of failure-sensitive agreement problems (Guerraoui, 2001)	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Nat, FinSet
44	nfc04	Non-functional properties of component-based software systems (Zschaler, 2010)	Steffen Zschaler		✔	Real, Nat
45	Paxos	Paxos consensus algorithm (Lamport, 1998)	Leslie Lamport		✔	Int, FinSet
46	Prisoners	A puzzle that was presented on an American radio program.			✔	Nat, FinSet
47	raft	Raft consensus algorithm (Ongaro, 2014)	Diego Ongaro		✔	FinSet, Nat, Seq
48	SnapshotIsolation	Serializable snapshot isolation (Cahill et al., 2010)	Michael J. Cahill, Uwe Röhm, Alan D. Fekete		✔	FinSet, Int, Seq
49	spanning	Spanning tree broadcast algorithm in Attiya and Welch’s book	Thanh Hai Tran, Igor Konnov, Josef Widder		✔	Int
50	SpecifyingSystems	Examples to accompany the book Specifying Systems (Lamport, 2002)			✔	all modules
51	Stones	The same problem as CarTalkPuzzle			✔	FinSet, Int, Seq
52	sums_even	Two proofs for showing that x+x is even, for any natural number x.		✔	✔	Int
53	SyncConsensus	Synchronized round consensus algorithm (Demirbas)	Murat Demirbas		✔	FinSet, Int, Seq	✔
54	Termination	Channel-counting algorithm (Kumar, 1985)	Giuliano Losa		✔	Integers, FiniteSets, Apalache, Sequences	✔	✔
55	Tla-tortoise-hare	Robert Floyd's cycle detection algorithm	Lorin Hochstein		✔	Nat	✔
56	tower_of_hanoi	The well-known Towers of Hanoi puzzle.	Markus Kuppe, Alexander Niederbühl		✔	Bit, FinSet, Int, Nat, Seq
57	transaction_commit	Consensus on transaction commit (Gray & Lamport, 2006)	Leslie Lamport		✔	Int
58	TransitiveClosure	The transitive closure of a relation			✔	FinSet, Int, Seq
59	TwoPhase	Two-phase handshaking	Leslie Lamport, Stephan Merz		✔	Nat
60	VoldemortKV	Voldemort distributed key value store	Murat Demirbas		✔	FinSet, Int, Seq	✔
61	Missionaries and Cannibals	Missionaries and Cannibals	Leslie Lamport		✔	FinSet, Int
62	Misra Reachability Algorithm	Misra Reachability Algorithm	Leslie Lamport	✔	✔	Int, Seq, FiniteSets, TLC, TLAPS, NaturalsInduction	✔
63	Loop Invariance	Loop Invariance	Leslie Lamport	✔	✔	Int, Seq, FiniteSets, TLC, TLAPS, SequenceTheorems, NaturalsInduction	✔
64	Teaching Concurrency	Teaching Concurrency	Leslie Lamport	✔	✔	Int, TLAPS	✔
65	Spanning Tree	Spanning Tree	Leslie Lamport		✔	Int, FiniteSets, TLC, Randomization
66	Paxos (How to win a Turing Award)	Paxos	Leslie Lamport		✔	Nat, Int, FiniteSets
67	Tencent-Paxos	PaxosStore: high-availability storage made practical in WeChat. Proceedings of the VLDB Endowment(Zheng et al., 2017)	Xingchen Yi, Hengfeng Wei	✔	✔	Int, FiniteSets
68	Blocking Queue	BlockingQueue	Markus Kuppe	✔	✔ (LiveEnv)	Naturals, Sequences, FiniteSets
69	Paxos	Paxos			✔	Int, FiniteSets
71	Echo Algorithm	Echo Algorithm	Stephan Merz		✔	Naturals, FiniteSets, Relation, TLC	✔
72	Cigarette Smokers problem	Cigarette Smokers problem	Mariusz Ryndzionek		✔	Integers, FiniteSets
73	Conway's Game of Life	Conway's Game of Life	Mariusz Ryndzionek		✔	Integers
74	Sliding puzzles	Sliding puzzles	Mariusz Ryndzionek		✔	Integers
75	Lock-Free Set	PlusCal spec of a lock-Free set used by TLC	Markus Kuppe		✔	Sequences, FiniteSets, Integers, TLC	✔
76	Chameneos	Chameneos, a Concurrency Game	Mariusz Ryndzionek		✔	Integers
77	ParallelRaft	A variant of Raft	Xiaosong Gu, Hengfeng Wei, Yu Huang		✔	Integers, FiniteSets, Sequences, Naturals
78	TLC MC	PlusCal spec of safety checking as implemented in TLC	Markus Kuppe		✔	Integers, FiniteSets, Sequences, TLC	✔
79	TLA+ Level Checking	Level-checking of TLA+ formulas as described in Specifying Systems	Leslie Lamport			Integers, Sequences
80	CRDT-Bug	CRDT algorithm with defect and fixed version	Alexander Niederbühl		✔	FiniteSets, Naturals, Sequences
81	asyncio-lock	Bugs from old versions of Python's asyncio lock	Alexander Niederbühl		✔	Sequences
82	Single Lane Bridge problem	Single Lane Bridge	Younes Akhouayri		✔	Naturals, FiniteSets, Sequences
83	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		✔	Functions, SequencesExt, FiniteSetsExt, TypedBags		✔
84	EWD687a	Detecting termination in distributed computations by Edsger Dijkstra and Carel Scholten	Stephan Merz (PlusCal spec), Leslie Lamport & Markus Kuppe (TLA+ spec)		✔	Integers, Graphs	✔
85	Huang	Termination detection by using distributed snapshots by Shing-Tsaan Huang	Markus Kuppe		✔	DyadicRationals
86	Azure Cosmos DB	Consistency models provided by Azure Cosmos DB	Dharma Shukla, Ailidani Ailijiang, Murat Demirbas, Markus Kuppe		✔	Integers, Sequences, FiniteSets, Functions, SequencesExt	✔
87	MET for CRDT-Redis	Model-check the CRDT designs, then generate test cases to test CRDT implementations	Yuqi Zhang		✔	Integers, Sequences, FiniteSets, TLC	✔
88	Parallel increment	Parallel threads incrementing a shared variable. Demonstrates invariants, liveness, fairness and symmetry	Chris Jensen		✔	Integers, FiniteSets, TLC
89	The Streamlet consensus algorithm	Specification and model-checking of both safety and liveness properties of Streamlet with TLC	Giuliano Losa		✔	Sequences, Integers, FiniteSets	✔
90	Petri Nets	Instantiable Petri Nets with liveness properties	Eugene Huang		✔	Integers, Sequences, FiniteSets, TLC
91	Knuth Yao & Markov Chains	Knuth-Yao algorithm for simulating a sixsided die	Ron Pressler, Markus Kuppe		✔	DyadicRationals
92	ewd426 - Token Stabilization	Self-stabilizing systems in spite of distributed control	Murat Demirbas, Markus Kuppe		✔	Naturals, FiniteSets
93	CRDT	Specifying and Verifying CRDT Protocols	Ye Ji, Hengfeng Wei		✔	Naturals, FiniteSets
94	Multi-Car Elevator System	Directory	Andrew Helwer		✔	Integers
95	Snapshot Key-Value Store	Directory	Andrew Helwer		✔
96	Nano Blockchain Protocol	Directory	Andrew Helwer		✔	Naturals, Bags
97	Coffee Can White/Black Bean Problem	Directory	Andrew Helwer		✔	Naturals
98	The Slush Protocol	Directory	Andrew Helwer		✔	Naturals, FiniteSets, Sequences	✔
99	SDP (Software Defined Perimeter)	Specifying and Verifying SDP Protocol based Zero Trust Architecture	Luming Dong, Zhi Niu		✔	FiniteSets, Sequences, Naturals
100	Simplified Fast Paxos	Simplified version of Fast Paxos (Lamport, 2006)	Lim Ngian Xin Terry, Gaurav Gandhi		✔	TLC, Naturals, FiniteSets, Integers
101	Learn TLA⁺ Proofs	Basic PlusCal algorithms and formal proofs of their correctness	Andrew Helwer	✔	✔	Sequences, Naturals, Integers, TLAPS	✔
102	Lexicographically-Least Circular Substring	Booth's 1980 algorithm to find the lexicographically-least circular substring	Andrew Helwer		✔	FiniteSets, Integers, Naturals, Sequences	✔
103	Distributed Checkpoint Coordination	Algorithm for coordinating checkpoint/snapshot leases in a Paxos ring	Andrew Helwer		✔	FiniteSets, Naturals, Sequences, TLC

License

The repository is under the MIT license. However, we can upload your benchmarks under your license.

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. Ensure your spec is released under MIT or a similarly-permissive license
2. Fork this repository and create a new directory under specifications with the name of your spec
3. Place all TLA⁺ files in the directory, along with their .cfg model files; you are encouraged to include at least one model that completes execution in less than 10 seconds
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 below table in this top-level README.md 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. Otherwise, follow these directions:

1. Ensure you have Python 3.11+ installed
2. Download & extract tree-sitter-tlaplus (zip, tar.gz) to the root of the repository; ensure the extracted folder is named tree-sitter-tlaplus
3. Open a shell and navigate to the repo root; ensure a C++ compiler is installed and on your path
   • On Windows, this might entail running the below script from the visual studio developer command prompt
4. 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)
5. Run pip install -r .github/scripts/requirements.txt
6. Run python .github/scripts/generate_manifest.py
7. 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 source: if this spec was first published elsewhere, provide a link to this location
   • 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 config:
     • "ignore deadlock" if your model should ignore deadlock
   • Model result:
     • "success" if the model completes successfully
     • "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
   • 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/.