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 based workflow, see below.

Install elan and lake. Execute

make build/bin/pantograph

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,

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 provided flake.nix has a develop environment with Lean already setup.

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.

Commands

See Pantograph/Protocol.lean for a description of the parameters and return values in JSON.

• reset: Delete all cached expressions and proof trees
• expr.echo {"expr": <expr>, "type": <optional expected type>}: Determine the type of an expression and round-trip it
• env.catalog: Display a list of all safe Lean symbols in the current environment
• env.inspect {"name": <name>, "value": <bool>}: Show the type and package of a given symbol; If value flag is set, the value is printed or hidden. By default only the values of definitions are printed.
• options.set { key: value, ... }: Set one or more options (not Lean options; those have to be set via command line arguments.), for options, see Pantograph/Protocol.lean
• options.print: Display the current set of options
• goal.start {["name": <name>], ["expr": <expr>], ["copyFrom": <symbol>]}: Start a new goal from a given expression or symbol
• goal.tactic {"stateId": <id>, "goalId": <id>, ["tactic": <tactic>], ["expr": <expr>]}: Execute a tactic string on a given goal
• goal.continue {"stateId": <id>, ["branch": <id>], ["goals": <names>]}: Continue from a proof state
• goal.remove {"stateIds": [<id>]}": Remove a bunch of stored goals.
• goal.print {"stateId": <id>}": Print a goal state
• stat: Display resource usage

Errors

When an error pertaining to the execution of a command happens, the returning JSON structure is

{ error: "type", desc: "description" }

Common error forms:

• command: Indicates malformed command structure which results from either invalid command or a malformed JSON structure that cannot be fed to an individual command.
• index: Indicates an invariant maintained by the output of one command and input of another is broken. For example, attempting to query a symbol not existing in the library or indexing into a non-existent proof state.

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.

Developing

Testing

The tests are based on LSpec. To run tests,

make test

Nix based workflow

The included Nix flake provides build targets for sharedLib and executable. The executable can be used as-is, but linking against the shared library requires the presence of lean-all.

To run tests:

nix build .#checks.${system}.test

For example, ${system} could be x86_64-linux. Using nix develop drops the current session into a development shell with fixed Lean version.