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Algorand Verification

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The Algorand consensus protocol is the foundation of a decentralized digital currency and transactions platform. This project provides a model of the protocol in Coq, expressed as a transition system over global states in a message-passing distributed system. Included is a formal proof of safety for the transition system.



We recommend installing the dependencies of the project via opam, for example:

opam repo add coq-released
opam install coq.8.16.0 coq-mathcomp-ssreflect.1.15.0 \
 coq-mathcomp-algebra coq-mathcomp-finmap.1.5.2 \
 coq-mathcomp-analysis.0.5.4 coq-mathcomp-zify coq-record-update

Then, run make in the project root directory. This will check all the definitions and proofs.


The project includes:

  • an abstract and timed specification in Coq of the Algorand consensus protocol as a transition system, including node-level behavior, asynchronous messaging and a model of the adversary,
  • a complete formal proof of asynchronous safety for the transition system.

For more details on the formalization, see the report:

PDF Modeling and Verification of the Algorand Consensus Protocol

Statements of some liveness properties for the transition system are also provided, but these are work-in-progress and their proofs are currently incomplete.

All Coq source files can be found under the theories directory, and their content is as follows:

  • fmap_ext.v: auxiliary definitions and results on finite maps
  • algorand_model.v: definition of the Algorand local state, global state, and transition system, along with helper functions and facts
  • safety_helpers.v: helper functions and lemmas used when proving safety of the transition system
  • quorums.v: definitions and hypotheses about quorums of nodes
  • safety.v: statement and complete formal proof of safety for the transition system
  • liveness.v: an initial attempt at specifying liveness properties for the transition system. This part is work-in-progress and thus the file contains incomplete (admitted) proofs.

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