Tactician's API: A graph- and text-based machine learning interface for Coq

Tactician's API provides external machine learning agents with the data collected by Tactician from the Coq Proof Assistant. It is able to extract large-scale datasets from a wide variety of Coq packages for the purpose of offline machine learning. Additionally, it allows agents to interact with Coq. Proving servers can be connected to Tactician's synth tactic and prove theorems for Coq users (see below). Additionally, servers can do proof exploration through the Tactician Explore command (see below).

The data provided to agents includes definitions, theorems, proof terms and a machine-readable representation of tactical proofs. The data is provided both in Coq's standard text-based human-readable format and as a semantic graph. The semantic graph is a single interconnected object that includes the entire mathematical universe known to Coq (at a given moment in time). The graph is designed to represent the semantic meaning of a mathematical object as faithfully as possible, minimizing the amount of implicit knowledge needed to interpret the object. For example, when a definition X refers to another definition Y, such a dependency is encoded explicitly using an edge in the graph. No definition lookup table is need. We also shy away from using names or de Bruijn indices as variables. Instead, variables point directly to their binders, so that name lookup becomes a trivial operation. Such an encoding reduces alpha-equivalence between terms to the graph-theoretic notion of bisimilarity, and allows us to globally deduplicate any alpha-equivalent terms in the graph.

Communication with agents happens through the Cap'n Proto serialization format and remote procedure calling (RPC) protocol. It supports a wide variety of programming languages, including Python, OCaml, C++, Haskell, Rust and more. This serialization was chosen because it allows us to memory-map (mmap) large graph datasets, allowing fast random-access to graphs that may not fit into main memory. Furthermore, Cap'n Proto's RPC protocol, based on the distributed object-capability model, allows us to export Coq's proof states to external agents. Agents can inspect the proof states, and execute tactics on them, allowing exploration of the proof search space in arbitrary order.

PyTactician library

This repository includes a Python library that provides a layer of abstraction over Cap'n Proto to make it easier to implement agents in Python. Check its README for more information.

Installation

Before attempting installation, ensure that you have all prerequisites installed!

To install the OCaml component of this repository, make sure that you have the appropriate switch activated and run the command opam install . from the root of this repository.

If you want maximum performance, it is recommended that you use an OCaml version with flambda enabled. On newer versions of Opam you can achieve this by installing ocaml-option-flambda.

Usage of the Coq plugin

Available Commands

These commands will create a graph of some object, and write it to graph.pdf (if graphviz is available).

The following commands are always available:

[Shared] Graph [Depth <n>] Ident identifier.
[Shared] Graph [Depth <n>] Term term.

The normal commands print a fully transitive graph. Adding Depth i limits the traversal to visiting at most i nested definitions.

Additionally, in proof mode, these commands are available:

[Shared] Graph [Depth <n>] Proof.

Options that modify the graphs generated by the commands above are

[Set | Unset] Tactician Neural Visualize Ordered.
[Set | Unset] Tactician Neural Visualize Labels.
[Set | Unset] Tactician Neural Visualize Hashes.

Interaction with synth

In order to connect Tactician's synth tactic to a external tactic prediction server like the dummy pytact-server described above, the plugin makes a number of commands and settings available in Coq. In order to load the plugin, Coq needs to be started appropriately. This can be done by prefixing every invocation of a command that uses Coq, like coqc, coqide, a make command or an editor like emacs with tactician exec:

tactician exec -- coqc ...
tactician exec -- coqide ...
tactician exec -- make ...
tactician exec -- dune build ...
tactician exec -- emacs ...

To make the synth command available, your Coq file will have to start with

From Tactician Require Import Ltac1.

The following settings govern the data that Coq will send to the server:

• Set Tactician Neural Textmode determines wether Coq is communicating with a graph-based server or a text-based server (graph-based by default).
• Set Tactician Neural Metadata adds text-based metadata to when communicating in graph-mode, such as hypothesis names, textual representation of proof states and textual representations of definition. This will slow down the communication protocol, and should only be enabled for debugging, or when otherwise needed.

To let Coq take care of starting and stopping the server, use the command

Set Tactician Neural Executable "external-server-executable --argument1 --argument2".

If you have a prediction server already running somewhere over TCP, you can make Coq connect to it using

Set Tactician Neural Server "<address>:<port>".

At this point, you have the following commands available which will interact with the server:

• Tactician Neural Alignment will ask the which tactics and definitions currently in scope are unknown to it. This is meant as a sanity check.
• Suggest and Debug Suggest will ask the server for predictions for the current proof state.
• synth and debug synth will perform a proof search by repeatedly asking the server for predictions.
• Tactician Neural Cache will preemptively send a lot of required data to the prediction server and keeps that information cached. This will make the commands above run much faster. This command can be issued multiple times in a document, creating multiple nested caches.
• Set Tactician Autocache will automatically execute Tactician Neural Cache on each command. This is an experimental option, and there may be some overhead associated with this.

Client-based proof exploration

Finally, the command Tactician Explore. will initiate a proof exploration session. An example of this is available in TestReinforceStdin.v. To do this, you need to have a python client running. An example is available in the pytact-prover executable. To see how it works, run pytact-prover --pdfsequence --pdfname test This will execute a dummy proof through the proof exploration interface. Visualizations of each proof state are available in test<n>.pdf. optionally --file option to point to a source Coq .v file. Also with --interactive option the interactive shell appears where you can manually interact with the environment. Whenever a tactic is executed, the resulting proof state if visualized in the file python_graph.pdf.

Generating a dataset

To generate a dataset, you currently have to install a slightly different version of the Coq plugin that resides in the generate-dataset branch. The procedure to generate the dataset is as follows.

1. Create your switch

   opam switch create tacgen --empty

2. Install coq-tactician-api generate-dataset

   git clone -b generate-dataset --recurse-submodules git@github.com:coq-tactician/coq-tactician-api.git
   cd coq-tactician-api
   opam install .
   tactician inject # you can answer 'no' to recompiling
   opam install coq-tactician-stdlib --keep-build-dir # make sure that you have the coq-extra-dev repo enabled

3. For your Coq dataset, e.g. propositional

   cd ../propositional
   tactician exec dune build

4. With opam build of coq-package do

   opam install coq-package --keep-build-dir

   and you find the *.bin in the directory <switch>/.opam-switch/build. The recorded dependency paths are relative to <switch>/.opam-switch/build.

Prerequisites

This repository has an OCaml component that should be installed through the Opam package manager and a Python component that should be installed through the Pip package manager. Additionally, some extra dependencies are needed:

• Opam 2.1.x
• Cap'n Proto >= 0.8
• XXHash >= 0.8
• Graphviz
• A reasonable set of development packages like git, bash, gmp, c/c++ compiler toolchains that should be installed on most systems.

If your operating systems package manager does not provide these packages with the correct version, the simplest and most reliable way to install these packages is through Conda. This repository provides a environment.yml file with the required Conda dependencies. To set it up, follow these commands:

git clone --recurse-submodules git@github.com:coq-tactician/coq-tactician-api.git # Clone this repo
cd coq-tactician-api
conda env create -f environment.yml
conda activate tactician
conda env config vars set CPATH=${CONDA_PREFIX}/include:${CPATH}
conda activate tactician

On Ubuntu 22.04 or newer, you can get the required packages as follows (older versions of Ubuntu have to fall back to the Conda solutions because the bundled software is out of date)

sudo apt-get --yes install graphviz capnproto libcapnp-dev pkg-config libev-dev libxxhash-dev

After installing the prerequisites, you'll need a Python virtualenv and an Opam switch to install the software. To create the virtualenv, run python -m venv <desired-location-of-virtualenv> To activate the virtualenv run `source