175 lines
6.2 KiB
Markdown
175 lines
6.2 KiB
Markdown
# Pantograph
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A Machine-to-Machine interaction system for Lean 4.
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Pantograph provides interfaces to execute proofs, construct expressions, and
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examine the symbol list of a Lean project for machine learning.
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## Installation
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For Nix based workflow, see below.
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Install `elan` and `lake`, and run
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``` sh
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lake build
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```
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This builds the executable in `.lake/build/bin/pantograph`.
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To use Pantograph in a project environment, setup the `LEAN_PATH` environment
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variable so it contains the library path of lean libraries. The libraries must
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be built in advance. For example, if `mathlib4` is stored at `../lib/mathlib4`,
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the environment might be setup like this:
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``` sh
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LIB="../lib"
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LIB_MATHLIB="$LIB/mathlib4/lake-packages"
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export LEAN_PATH="$LIB/mathlib4/build/lib:$LIB_MATHLIB/aesop/build/lib:$LIB_MATHLIB/Qq/build/lib:$LIB_MATHLIB/std/build/lib"
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LEAN_PATH=$LEAN_PATH build/bin/pantograph $@
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```
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The `$LEAN_PATH` executable of any project can be extracted by
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``` sh
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lake env printenv LEAN_PATH
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```
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## Executable Usage
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``` sh
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pantograph MODULES|LEAN_OPTIONS
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```
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The REPL loop accepts commands as single-line JSON inputs and outputs either an
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`Error:` (indicating malformed command) or a JSON return value indicating the
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result of a command execution. The command can be passed in one of two formats
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```
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command { ... }
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{ "cmd": command, "payload": ... }
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```
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The list of available commands can be found in `Pantograph/Protocol.lean` and below. An
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empty command aborts the REPL.
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The `pantograph` executable must be run with a list of modules to import. It can
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also accept lean options of the form `--key=value` e.g. `--pp.raw=true`.
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Example: (~5k symbols)
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```
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$ pantograph Init
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env.catalog
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env.inspect {"name": "Nat.le_add_left"}
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```
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Example with `mathlib4` (~90k symbols, may stack overflow, see troubleshooting)
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```
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$ pantograph Mathlib.Analysis.Seminorm
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env.catalog
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```
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Example proving a theorem: (alternatively use `goal.start {"copyFrom": "Nat.add_comm"}`) to prime the proof
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```
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$ pantograph Init
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goal.start {"expr": "∀ (n m : Nat), n + m = m + n"}
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goal.tactic {"stateId": 0, "goalId": 0, "tactic": "intro n m"}
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goal.tactic {"stateId": 1, "goalId": 0, "tactic": "assumption"}
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goal.delete {"stateIds": [0]}
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stat {}
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goal.tactic {"stateId": 1, "goalId": 0, "tactic": "rw [Nat.add_comm]"}
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stat
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```
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where the application of `assumption` should lead to a failure.
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### Commands
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See `Pantograph/Protocol.lean` for a description of the parameters and return values in JSON.
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* `reset`: Delete all cached expressions and proof trees
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* `stat`: Display resource usage
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* `expr.echo {"expr": <expr>, "type": <optional expected type>, ["levels": [<levels>]]}`: Determine the
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type of an expression and format it.
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* `env.catalog`: Display a list of all safe Lean symbols in the current environment
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* `env.inspect {"name": <name>, "value": <bool>}`: Show the type and package of a
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given symbol; If value flag is set, the value is printed or hidden. By default
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only the values of definitions are printed.
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* `options.set { key: value, ... }`: Set one or more options (not Lean options; those
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have to be set via command line arguments.), for options, see `Pantograph/Protocol.lean`
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One particular option for interest for machine learning researchers is the
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automatic mode (flag: `"automaticMode"`). By default it is turned on, with
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all goals automatically resuming. This makes Pantograph act like a gym,
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with no resumption necessary to manage your goals.
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* `options.print`: Display the current set of options
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* `goal.start {["name": <name>], ["expr": <expr>], ["levels": [<levels>]], ["copyFrom": <symbol>]}`:
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Start a new proof from a given expression or symbol
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* `goal.tactic {"stateId": <id>, "goalId": <id>, ...}`: Execute a tactic string on a
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given goal. The tactic is supplied as additional key-value pairs in one of the following formats:
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- `{ "tactic": <tactic> }`: Execute an ordinary tactic
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- `{ "expr": <expr> }`: Assign the given proof term to the current goal
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- `{ "have": <expr>, "binderName": <name> }`: Execute `have` and creates a branch goal
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- `{ "calc": <expr> }`: Execute one step of a `calc` tactic. Each step must
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be of the form `lhs op rhs`. An `lhs` of `_` indicates that it should be set
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to the previous `rhs`.
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- `{ "conv": <bool> }`: Enter or exit conversion tactic mode. In the case of
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exit, the goal id is ignored.
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* `goal.continue {"stateId": <id>, ["branch": <id>], ["goals": <names>]}`:
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Execute continuation/resumption
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- `{ "branch": <id> }`: Continue on branch state. The current state must have no goals.
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- `{ "goals": <names> }`: Resume the given goals
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* `goal.remove {"stateIds": [<id>]}"`: Drop the goal states specified in the list
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* `goal.print {"stateId": <id>}"`: Print a goal state
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### Errors
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When an error pertaining to the execution of a command happens, the returning JSON structure is
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``` json
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{ "error": "type", "desc": "description" }
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```
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Common error forms:
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* `command`: Indicates malformed command structure which results from either
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invalid command or a malformed JSON structure that cannot be fed to an
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individual command.
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* `index`: Indicates an invariant maintained by the output of one command and
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input of another is broken. For example, attempting to query a symbol not
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existing in the library or indexing into a non-existent proof state.
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### Troubleshooting
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If lean encounters stack overflow problems when printing catalog, execute this before running lean:
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```sh
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ulimit -s unlimited
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```
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## Library Usage
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`Pantograph/Library.lean` exposes a series of interfaces which allow FFI call
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with `Pantograph` which mirrors the REPL commands above. It is recommended to
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call Pantograph via this FFI since it provides a tremendous speed up.
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Note that there isn't a 1-1 correspondence between executable (REPL) commands
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and library functions.
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## Developing
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A Lean development shell is provided in the Nix flake.
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### Testing
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The tests are based on `LSpec`. To run tests,
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``` sh
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lake test
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```
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You can run an individual test by specifying a prefix
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``` sh
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lake test -- "Tactic/No Confuse"
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```
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## Nix based workflow
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The included Nix flake provides build targets for `sharedLib` and `executable`.
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The executable can be used as-is, but linking against the shared library
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requires the presence of `lean-all`.
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To run tests:
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``` sh
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nix flake check
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```
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