Pantograph

A Machine-to-Machine interaction system for Lean 4.

Pantograph provides interfaces to execute proofs, construct expressions, and examine the symbol list of a Lean project for machine learning.

Installation

For Nix users, run

nix build .#{sharedLib,executable}

to build either the shared library or executable.

Install elan and lake, and run

lake build

This builds the executable in .lake/build/bin/pantograph-repl.

Executable Usage

pantograph MODULES|LEAN_OPTIONS

The REPL loop accepts commands as single-line JSON inputs and outputs either an Error: (indicating malformed command) or a JSON return value indicating the result of a command execution. The command can be passed in one of two formats

command { ... }
{ "cmd": command, "payload": ... }

The list of available commands can be found in Pantograph/Protocol.lean and below. An empty command aborts the REPL.

The pantograph executable must be run with a list of modules to import. It can also accept lean options of the form --key=value e.g. --pp.raw=true.

Example: (~5k symbols)

$ pantograph Init
env.catalog
env.inspect {"name": "Nat.le_add_left"}

Example with mathlib4 (~90k symbols, may stack overflow, see troubleshooting)

$ pantograph Mathlib.Analysis.Seminorm
env.catalog

Example proving a theorem: (alternatively use goal.start {"copyFrom": "Nat.add_comm"}) to prime the proof

$ pantograph Init
goal.start {"expr": "∀ (n m : Nat), n + m = m + n"}
goal.tactic {"stateId": 0, "goalId": 0, "tactic": "intro n m"}
goal.tactic {"stateId": 1, "goalId": 0, "tactic": "assumption"}
goal.delete {"stateIds": [0]}
stat {}
goal.tactic {"stateId": 1, "goalId": 0, "tactic": "rw [Nat.add_comm]"}
stat

where the application of assumption should lead to a failure.

For a list of commands, see REPL Documentation.

Project Environment

To use Pantograph in a project environment, setup the LEAN_PATH environment variable so it contains the library path of lean libraries. The libraries must be built in advance. For example, if mathlib4 is stored at ../lib/mathlib4, the environment might be setup like this:

LIB="../lib"
LIB_MATHLIB="$LIB/mathlib4/lake-packages"
export LEAN_PATH="$LIB/mathlib4/build/lib:$LIB_MATHLIB/aesop/build/lib:$LIB_MATHLIB/Qq/build/lib:$LIB_MATHLIB/std/build/lib"

LEAN_PATH=$LEAN_PATH build/bin/pantograph $@

The $LEAN_PATH executable of any project can be extracted by

lake env printenv LEAN_PATH

Troubleshooting

If lean encounters stack overflow problems when printing catalog, execute this before running lean:

ulimit -s unlimited

Library Usage

Pantograph/Library.lean exposes a series of interfaces which allow FFI call with Pantograph which mirrors the REPL commands above. It is recommended to call Pantograph via this FFI since it provides a tremendous speed up.

The executable can be used as-is, but linking against the shared library requires the presence of lean-all. Note that there isn't a 1-1 correspondence between executable (REPL) commands and library functions.

Inject any project path via the pantograph_init_search function.

Developing

A Lean development shell is provided in the Nix flake.

Testing

The tests are based on LSpec. To run tests, use either

nix flake check

or

lake test

You can run an individual test by specifying a prefix

lake test -- "Tactic/No Confuse"