Pantograph

An interaction system for Lean 4.

Installation

Install elan and lean4. Then, execute

lake build

Then, 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 $@

Note that lean-toolchain must be present in the $PWD in order to run Pantograph! This is because Pantograph taps into Lean's internals.

Usage

build/bin/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/Commands.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)

$ build/bin/Pantograph Init
catalog
inspect {"name": "Nat.le_add_left"}

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

$ lake env build/bin/Pantograph Mathlib.Analysis.Seminorm
catalog

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

$ env build/bin/Pantograph Init
proof.start {"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.

Commands

See Pantograph/Commands.lean for a description of the parameters and return values in Json.

• options.set { key: value, ... }: Set one or more options (not Lean options; those have to be set via command line arguments.)
• options.print: Display the current set of options
• catalog: Display a list of all safe Lean symbols in the current context
• 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.
• clear: Delete all cached expressions and proof trees
• expr.type {"expr": <expr>}: Determine the type of an expression and round-trip it
• proof.start {["name": <name>], ["expr": <expr>], ["copyFrom": <symbol>]}: Start a new proof state from a given expression or symbol
• proof.tactic {"treeId": <id>, "stateId": <id>, "goalId": <id>, "tactic": string}: Execute a tactic on a given proof state
• proof.printTree {"treeId": <id>}: Print the topological structure of a proof tree

Troubleshooting

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

ulimit -s unlimited

Testing

The tests are based on LSpec. To run tests,

test/all.sh