Pantograph

An interaction system for Lean 4.

Installation

Install elan and lean4. Then, execute

lake build

In order to use mathlib, its binary must also be built

lake build Qq
lake build aesop
lake build std
lake build mathlib

Usage

The binary must be run inside a lake env environment. i.e. lake env build/bin/pantograph. 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/Commands.lean. An empty command aborts the REPL.

Example: (~5k symbols)

$ lake env build/bin/Pantograph
create {"imports": ["Init"]}
catalog {"id": 0}
inspect {"id": 0, "symbol": "Nat.le_add_left"}

Example with mathlib (~90k symbols)

$ lake env build/bin/Pantograph
create {"imports": ["Mathlib.Analysis.Seminorm"]}
catalog {"id": 0}

Example proving a theorem: (alternatively use proof.start {"id": 0, "name": "aa", "copyFrom": "Nat.add_comm", "expr": ""}) to prime the proof

$ lake env build/bin/Pantograph
create {"imports": ["Init"]}
proof.start {"id": 0, "expr": "∀ (n m : Nat), n + m = m + n"}
proof.tactic {"treeId": 0, "stateId": 0, "goalId": 0, "tactic": "intro n m"}
proof.tactic {"treeId": 0, "stateId": 1, "goalId": 0, "tactic": "assumption"}
proof.printTree {"treeId": 0}
proof.tactic {"treeId": 0, "stateId": 1, "goalId": 0, "tactic": "rw [Nat.add_comm]"}
proof.printTree {"treeId": 0}

where the application of assumption should lead to a failure.

create {"imports": ["Init"]}
proof.start {"id": 0, "expr": "∀ (p q: Prop), p ∨ q → q ∨ p"}
proof.tactic {"treeId": 0, "stateId": 0, "goalId": 0, "tactic": "intro p q h"}
proof.tactic {"treeId": 0, "stateId": 1, "goalId": 0, "tactic": "cases h"}
proof.tactic {"treeId": 0, "stateId": 2, "goalId": 0, "tactic": "apply Or.inr"}
proof.tactic {"treeId": 0, "stateId": 2, "goalId": 0, "tactic": "apply Or.inl"}

Troubleshooting

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

ulimit -s unlimited

Due to a current bug in Lean (which existed in Lean 3), the default value of structures are not honoured when parsing Json's.

Testing

The tests are based on LSpec. To run tests,

test/all.sh