Lean Beam

Lean Beam

Use this skill for Lean projects when you want the AI to replace repeated lake build loops with cheap speculative Lean probes, optional follow-up handle execution, and targeted file checkpoints.

This is the Lean-only skill. It should stay focused on Lean and should not require Rocq setup or Rocq concepts. Do not factor shared Lean/Rocq skill instructions into a common helper; duplicate short guidance if both skills need it.

Setup

From the lean-beam repo root:

./scripts/install-beam.sh --codex

Use --claude, --pi, --opencode, or --vibe instead when installing for Claude Code, Pi Agent, OpenCode, or Mistral Vibe. Use --all-skills when you want every supported agent skill target.

The installer puts lean-beam, lean-beam-search, and lean-beam-mcp in ~/.local/bin, stages the self-contained runtime under BEAM_INSTALL_ROOT (default ~/.local/share/beam), requires elan on PATH, prebuilds the pinned lean-toolchain bundle by default, and installs the bundled Lean skill only for the agent flags you request. Use the setup docs for additional supported or custom toolchain prebuilds.

Use lean-beam --version for CLI bug reports and installed runtime identity checks. Use lean-beam-mcp --version to verify which installed MCP server wrapper, server binary, runtime payload hash, manifest, and source commit a client command resolves. Source checkout runs also report git commit/branch/dirty state when available. From a live MCP session, call beam_version to report the running server process identity as structured content. lean_init_workspace with mode: "reset" restarts the Lean runtime inside the current MCP server process; it does not prove the MCP server binary itself was refreshed.

Restart active agent or MCP client sessions after installation.

For the authoritative install and bundle-resolution order, see the repo [docs/SETUP.md](../../docs/SETUP.md) and [Supported Toolchains](../../docs/SETUP.md#supported-toolchains-and-bundles) sections.

Skill Surface

This skill documents the current Lean-facing lean-beam workflow surface. Use the smallest command family that fits the task.

Agents may access Beam through the lean-beam wrapper or through a registered lean-beam-mcp server. This skill names wrapper commands because they are always available after installation. When your client exposes the matching MCP tools, use them with the same saved-file, version, update, sync, and isolation rules; do not treat MCP as a raw Lean LSP proxy.

Supported command families:

• bootstrap the Lean backend: lean-beam ensure
• keep a sandboxed daemon owner alive across separate commands: lean-beam ensure --hold
• inspect existing code, navigation data, or proof state: lean-beam hover,

lean-beam signature-help, lean-beam definition, lean-beam references, lean-beam document-symbols, lean-beam workspace-symbols, lean-beam goals before, lean-beam goals after

• inspect actionable Lean items in a range: lean-beam todo
• inspect file or daemon state: lean-beam open-files, lean-beam doctor, lean-beam stats,

lean-beam reset-stats

• produce a pasteable bug report card from JSON input: lean-beam feedback
• try one isolated speculative Lean snippet: lean-beam run-at
• continue from one exact speculative state: lean-beam run-at-handle, lean-beam run-with,

lean-beam run-with-linear, lean-beam release

• refresh or checkpoint one tracked workspace module: lean-beam sync, lean-beam refresh,

lean-beam save, lean-beam close-save

• run shell-oriented search loops over the same handle APIs: lean-beam-search

What to treat as the normal agent workflow surface:

• default workflow commands: lean-beam hover, lean-beam signature-help,

lean-beam definition, lean-beam references, lean-beam document-symbols, lean-beam workspace-symbols, lean-beam goals, lean-beam todo, lean-beam run-at, lean-beam sync, lean-beam refresh

• operational commands: lean-beam open-files, lean-beam doctor,

lean-beam stats, lean-beam reset-stats, lean-beam feedback, lean-beam save, lean-beam close-save

• pre-stable support APIs: lean-beam run-at-handle, lean-beam run-with, lean-beam run-with-linear,

lean-beam release, lean-beam-search

Core workflow contract:

• use lean-beam, not raw JSON and not raw LSP
• lean-beam only sees the on-disk file, not unsaved editor buffers
• in transient PID-sandboxed command runners, start one foreground lean-beam ensure --hold

process when you need daemon reuse across separate shell invocations; interrupt it when finished

• after every real Lean source edit: save the file normally, then run lean-beam update before the

next version-bound probe; run lean-beam sync when you need diagnostics/readiness

• use lean-beam save only for a synced workspace module path in the current Lake workspace package

graph, for example MyPkg/Sub/Module.lean

• lean-beam save validates and checkpoints only the module you save; it does not validate importers of

that module

• lean-beam save currently supports only Lake module setups Beam can replay from the LSP snapshot

without custom batch setup; modules with custom Lean options, Lean arguments, dynamic libraries, or plugins fail with saveUnsupportedSetup and should be rebuilt with lake build

• treat wrapper stderr as human-facing only; use stdout JSON or beam-client request-stream

for machine-readable automation

• lean-beam feedback does not accept free-form notes; pass a JSON object with required string

fields title, summary, reproduction, expected, and actual

• use optional feedback triage fields kind (bug, ux, perf, docs, question) and

severity (low, medium, high, critical) when they help route the report

• do not assume hidden mutable session state carries across unrelated requests

Agent Cost Model

Prefer Beam probes over detached scratch Lean files for project-local questions.

A standalone scratch file has a high fixed cost: it starts from a detached module, reloads imports and environment, and encourages simplified contexts that may not match the real source position.

A lean-beam run-at probe has low marginal cost once the per-project daemon and module context are warm: it asks one speculative question against an explicit broker document version and the real module environment.

This changes the right agent behavior:

• prefer many small run-at probes at the source position over one large scratch experiment
• use goals before, goals after, hover, signature-help, definition, references, and

symbol queries instead of reconstructing semantic state elsewhere

• issue independent run-at probes or handle-rooted search sequences in parallel when you have many

candidates to check; use distinct request IDs if you need per-request cancellation or tracing

• do not batch unrelated questions just to amortize Lean startup; future batch APIs may reduce

per-call overhead, but high-bandwidth clients can already get most of the throughput benefit by keeping independent probe sequences in flight

• after a real source edit, run lean-beam update before later probes; run

lean-beam sync when you need diagnostics/readiness

• use lake build for dependency-cone or final validation, not as the inner loop
• use scratch files only for context-free Lean syntax checks or Beam incident isolation

Prompting Contract

Prefer the smallest command that matches the actual task:

• use lean-beam hover when you want semantic information about existing code at one position
• use lean-beam signature-help when you want callable-argument signature information at one

position

• use lean-beam definition or lean-beam references when you want navigation targets for an

existing symbol

• use lean-beam document-symbols for file-local symbol outlines and lean-beam workspace-symbols

for workspace-wide symbol search

• use lean-beam goals before or lean-beam goals after when you want existing proof state at one

tactic position

• use lean-beam todo when you want actionable items in a saved file range, such as sorries, holes,

diagnostics, code actions, or incomplete proofs

• use lean-beam run-at when you want to try one speculative Lean snippet without editing the file
• before lean-beam run-at, lean-beam run-at-handle, lean-beam hover,

lean-beam signature-help, lean-beam definition, lean-beam references, lean-beam document-symbols, lean-beam goals, or lean-beam todo, call lean-beam update and pass the returned version; lean-beam workspace-symbols takes only a query

• if a versioned request fails with contentModified and

error.data.reason = "documentVersionMismatch", use error.data.acceptedVersion for the next retry or run lean-beam update / lean-beam sync again; do not guess a version

• for lean-beam run-at, lean-beam hover, lean-beam signature-help,

lean-beam definition, lean-beam references, lean-beam goals, and lean-beam todo, treat line and character arguments as Lean/LSP coordinates: line 0 is the first line, character 0 is the first UTF-16 code unit, and on a truly empty line only character 0 is valid

• use lean-beam run-at-handle and then lean-beam run-with or lean-beam run-with-linear only when exact

speculative continuation matters

• for multiline speculative text, prefer --stdin as the normal path; use --text-file

when the text already lives in a file

• for handle-based continuation, prefer --handle-file as the normal path; deeper shell-loop

variants such as stdin handle piping live in the reference docs

• do not expect one lean-beam run-at call to become the basis of the next one automatically
• parallel probes are fine when they are independent; do not concurrently reuse a linear handle or

assume ordered side effects between separate speculative sequences

• use lean-beam update right after every real saved edit before the next speculative probe
• use lean-beam sync when you need diagnostics/readiness before saving or checkpointing
• use lean-beam save or lean-beam close-save only for a synced workspace module path such as

MyPkg/Sub/Module.lean

Stop probing and change tactics when:

• the speculative result now needs to become real source: edit the file, save it, then lean-beam sync
• repeated lean-beam run-at probes are no longer clarifying the problem
• you edited a dependency and now need trustworthy downstream results; lean-beam save only validates

the module you save, not downstream importers

• stale-state, contentModified, or rebuild trouble keeps appearing; inspect with lean-beam open-files

and lean-beam doctor

• if lean-beam sync fails with syncBarrierIncomplete: inspect error.data.staleDirectDeps,

error.data.saveDeps, and error.data.recoveryPlan; save only the listed direct deps that still need checkpointing, then lean-beam refresh "Target.lean" if the plan says to; if this repeats across multiple dependency hops, escalate to lake build

When those conditions hold, prefer a real edit plus lean-beam sync, or escalate to lake build when the task has become dependency freshness or final validation across importers rather than one-file probing.

Lean-Run-At Semantics

lean-beam run-at is a speculative execution request against one explicit broker document version. Read it as "try this Lean text here", not as "edit the file here".

What lean-beam run-at does not do:

• it does not edit the source file or create a new on-disk baseline for the next request
• it does not make the speculative text become the basis of the next lean-beam run-at call
• it does not wait for or return the full diagnostics barrier for the rest of the file
• it does not replay full-file diagnostics in its final JSON payload
• it does not auto-indent or synthesize leading spaces when you probe at an indented empty line
• it does not reinterpret blank-line coordinates; if the line is truly empty then character 1 is

already out of range

• in command mode, one run-at request accepts one Lean command, not a complete top-level command

sequence; use run-at-handle plus run-with for explicit sequencing, or make a real edit and sync

Use the right tool for each goal:

• if you made a real edit and want fresh file diagnostics: save the file, then use lean-beam sync
• if you want exact continuation from speculative state: mint a handle with lean-beam run-at-handle,

then continue with lean-beam run-with or lean-beam run-with-linear

• if you want to test several top-level commands together: write them to the file and sync, or split

the experiment into explicit handle continuations

• for handle-based commands, --handle-file is the easiest way to avoid inlining handle json
• if surface syntax depends on indentation or layout: pass the exact text you want Lean to parse, or

make a real edit in the file instead of expecting the wrapper to fill whitespace for you

Open [references/lean-run-at-semantics.md](references/lean-run-at-semantics.md) when the task needs concrete examples for:

• full-file diagnostics after a speculative probe
• chaining speculative state across multiple calls
• indentation-sensitive or newline-sensitive probes on blank or layout-sensitive lines

Open [references/workflow-details.md](references/workflow-details.md) when the task needs the shell-oriented details for:

• --text-file, --, or stdin-handle piping variants
• handle-file versus stdin-handle tradeoffs
• debugging-oriented wrapper details instead of the normal path

Open [references/commit-speculative.md](references/commit-speculative.md) when the task needs the current workflow for turning a good speculative probe into a real saved edit.

Open [references/anti-patterns.md](references/anti-patterns.md) when you want a short checklist of what Lean agents should not assume about lean-beam run-at, lean-beam sync, handles, or dependency edits.

Lean Wrapper

Use lean-beam, not raw JSON and not raw LSP.

lean-beam for Lean:

• infers the target project root from the current directory or --root
• keeps one Beam daemon per project root and records it in /.beam/beam-daemon.json
• in sandboxed or read-only project trees, set BEAM_CONTROL_DIR to a writable directory; lean-beam uses a per-root subdirectory there
• resolves a toolchain-keyed Lean bundle, preferring the installed beam bundle cache and

falling back to a project-local runtime bundle under /.beam/bundles or BEAM_BUNDLE_DIR

• serves Lean toolchains listed in supported-lean-toolchains plus exact custom names recorded by

the installer in custom-lean-toolchains

• owns Beam daemon startup, shutdown, and registry handling
• resolves Lean with elan which lean
• builds a local fallback bundle only when no matching installed bundle exists for the target

supported or explicitly custom Lean toolchain

• fails early on Lean toolchains that are neither supported nor explicitly custom; use

lean-beam supported-toolchains to inspect the validated allowlist and lean-beam doctor to inspect custom acceptance state

• restarts the Beam daemon if the effective Lean startup configuration for that root changes
• lean-beam shutdown, lean-beam stats, and lean-beam reset-stats apply to the current project only
• wrapper commands talk to the per-project Beam daemon over localhost TCP; they are not direct in-process Lean calls
• lean-beam ensure --hold prints the usual JSON ensure response on stdout, keeps the wrapper

process alive until interrupted, and is only for environments that reap background daemons when each command exits; later wrappers recover from same-namespace stale lease files left by killed wrapper processes

lean-beam is more than a one-shot probe:

• the common path is stil

…

Source & license

This open-source skill is cataloged on AgentStack and links to its original source — we do not rehost the code.

• Author: ejgallego
• Source: ejgallego/lean-beam
• License: Apache-2.0

Install and usage instructions live in the source repository linked above.