The Tactician

A Seamless, Interactive Tactic Learner and Prover for Coq

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What is Tactician?

Tactician is a tactic learner and prover for the Coq Proof Assistant. The system will help users make tactical proof decisions while they retain control over the general proof strategy. To this end, Tactician will learn from previously written tactic scripts, and either gives the user suggestions about the next tactic to be executed or altogether takes over the burden of proof synthesis. Tactician’s goal is to provide the user with a seamless, interactive, and intuitive experience together with strong, adaptive proof automation.

Can I use Tactician in a complex project with many dependencies?

Yes, the system has first-class support for Opam, Coq’s package manager. When you install dependencies, Tactician can automatically instrument those developments and learn from them. When you work on your project, Tactician will have background knowledge on all modules you Require.

On the flip side, using Tactician in your project does not mean you now have a hard dependency on Tactician. When the system finds a proof, it presents you with a caching witness that you can copy into your source file. As long as this witness remains valid, you can compile your project without having the main Tactician code-base installed. You only need 10 lines of helper tactics, which you can install through the coq-tactician-dummy package, or simply copy them into your development.

Is Tactician useful for teaching?

We have not yet performed a large-scale test on students, but we believe that the system may indeed be used in this capacity. Installation is straightforward and the system functions on Linux, macOS and Windows. The automation is push-button style without needing any configuration, and when a proof cannot be found, Tactician can still suggest tactics that may be useful.

I have a great Machine Learning idea; can I implement it on top of Tactician?

Yes! Tactician is an extensible platform that can incorporate multiple machine learning models and search procedures. If you want to contribute your ideas, you can either work on the Tactician code-base directly, or you can create a plugin for Tactician in a separate repository. We are always searching for people that want to develop new ideas, either independently or in collaboration with us. If you’d like more information, please reach out to us!

How good is Tactician?


What tools related to Tactician exist?

  • CoqHammer is an automated reasoning tool for Coq. It translates Coq’s Calculus of Constructions into first-order logic and calls several external automatic theorem provers to prove a goal. When the external prover succeeds, an CoqHammer attempt to reconstruct this proof within Coq. Although CoqHammer and Tactician have similar goals (automatically proof lemmas for Coq), their way of achieving this goal is quite different. As such, it has been shown before that these tools are quite complementary and we highly recommend you try CoqHammer out.