lean-formalization-intake - SKILL.md Agent Skill

name: lean-formalization-intake description: Use when deciding whether a research claim should enter the optional Lean formalization lane.

Lean Formalization Intake

Windows Runtime Commands

On native Windows, use the managed Windows runner and the native runtime command target. Set $runtime to the installed runtime root. Multi-agent installs usually use %LOCALAPPDATA%\ai-agents-skills\runtime. Then run:

$runtime = if ($env:AAS_RUNTIME_ROOT) { $env:AAS_RUNTIME_ROOT } else { "$env:LOCALAPPDATA\ai-agents-skills\runtime" }
& "$runtime\run_skill.bat" "skills/lean-formalization-intake/run_lean_formalization_intake.bat" doctor

PowerShell runner target:

& "$runtime\run_skill.ps1" "skills/lean-formalization-intake/run_lean_formalization_intake.ps1" doctor

POSIX examples below use run_skill.sh and .sh command targets; use the Windows command target above on native Windows.

Use this skill before spending effort on Lean formalization. It decides whether a research claim is suitable for the optional formal lane and records a conservative decision:

proceed: definitions and scope look suitable enough to try formalization
defer: formalization is relevant but blocked by definitions, toolchain, library support, semantic alignment, or budget
not_applicable: Lean is not useful for this claim or outside scope
blocked: formal support was required but cannot proceed without clarification or missing tooling

defer, not_applicable, and missing Lean are not failed theorem evidence. They are only formal-lane status.

Runtime Helper

Check the local tool status:

bash "$AAS_RUNTIME_ROOT/run_skill.sh" \
  skills/lean-formalization-intake/run_lean_formalization_intake.sh doctor

Run non-installing version/toolchain probes when you need reproducibility metadata:

bash "$AAS_RUNTIME_ROOT/run_skill.sh" \
  skills/lean-formalization-intake/run_lean_formalization_intake.sh doctor --probe

Assess a claim:

bash "$AAS_RUNTIME_ROOT/run_skill.sh" \
  skills/lean-formalization-intake/run_lean_formalization_intake.sh assess \
  --claim "Every finite tree has a leaf" \
  --claim-id C1 \
  --output formal/intake-C1.json

Set AAS_LEAN or AAS_LAKE to select a specific already-installed local executable. Invalid explicit paths are reported as unavailable instead of being masked by another tool on PATH.

The helper never installs Lean, Lake, mathlib, Python packages, Node packages, credentials, services, or MCP servers.

Output Contract

The runtime emits JSON with:

formalization_decision
reason
required_definitions
expected_cost
recommended_next_step
formal_check_requirement
tool_status
limitations

The result can be copied into a v2 evidence.jsonl row or attached as a run artifact, but it does not itself prove the research claim.

Recommended templates

When this skill is involved, consider these workflow templates (install via the workflow-templates artifact profile, or --with-deps to pull backing skills):

informal-to-lean-formalization-runbook -- Local-first intake mapping an informal proof to Lean declarations with a scanner-first verification gate separating typecheck status from claim support.