learn

An interactive Lean 4 teaching and exploration command. Lean 4 is a programming language and proof checker used to write and verify mathematical proofs.

In plain words
What is it for?
Use it to study a topic or theorem, explore a project or mathlib, learn from a PDF, work through guided exercises, or write explanations backed by Lean.
Why use it?
It helps you learn Lean or mathlib—the library of ready-made Lean mathematics—without having to know where to start.

Command

Install

Getting it into your agent

One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.

agentmods
npx agentmods add commands/frenzymath/archon/learn
Clone the repo
git clone --depth 1 https://github.com/frenzymath/Archon
Per session 8 Only the description is in the session, so the agent can decide to use it. The body loads when it is invoked.
When invoked 3,777 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. Scan, not verified.
Origin original No closer match found in the catalogue.
Token cost

What it costs to keep this loaded

Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.

ModelPer sessionOnce invoked
Fable 5 $0.00008 $0.03777
Opus 5 $0.00004 $0.01888
Sonnet 5 $0.00002 $0.00755
Haiku 4.5 $0.00001 $0.00378

Measured 2d ago against content hash 205bb61f3709, method: parsed. Prices are Anthropic first-party input rates as of 2026-08-30, from the pricing page.

Security

Grade A, and why

learn scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 2d ago.

A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.

Nothing flagged

None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.

src/archon/.archon-src/skills/lean4/commands/learn.md · 179 lines

How it starts

The opening of the file, as written. The whole thing — 179 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Lean4 Learn

Interactive teaching and mathlib exploration. Adapts to beginner, intermediate, and expert audiences.

Usage

/lean4:learn                                 # Start conversational discovery
/lean4:learn Finset.sum                      # Auto-detect mode from topic
/lean4:learn --mode=repo                     # Explore current project
/lean4:learn --mode=mathlib topology         # Navigate mathlib for a topic
/lean4:learn --style=socratic --interactive  # True Socratic method
/lean4:learn --style=game --track=nng-like   # Game-style natural numbers track
/lean4:learn --source ./paper.pdf            # Learn from a paper/PDF
/lean4:learn --presentation=informal "Bolzano-Weierstrass"  # Prose, Lean-backed
/lean4:learn --output=scratch                # Write results to scratch file
/lean4:learn --style=socratic --adaptive=off  # Socratic, no style/level drift

Inputs

Arg Required Default Description
topic no Free-text topic, theorem name, file path, or natural-language claim. If omitted, start conversational discovery; set --mode after first user reply.
--mode no auto auto | repo | mathlib
--level no intermediate beginner | intermediate | expert
--scope no auto auto | file | changed | project | topic
--style no tour tour | socratic | exercise | game
--output no chat chat | scratch | file
--out no Output path. Required when --output=file; hard error if missing.
--overwrite no false Allow overwriting existing files with --output=file. Without flag, existing target → hard error.
--interactive no false True Socratic method (withhold answers, ask questions). Valid only with --style=socratic; ignored with warning otherwise.
--intent no auto auto | usage | internals | authoring | math. See learn-pathways.md.
--presentation no auto informal | supporting | formal | auto. Controls user-facing display, not Lean backing. See learn-pathways.md.
--verify no best-effort best-effort | strict. Verification strictness for key claims. See learn-pathways.md.
--track no Exercise ladder: nng-like | set-theory-like | analysis-like | proofs-reintro. Valid only with --style=game. See learn-pathways.md.
--source no File path, URL, or PDF to seed learning. See learn-pathways.md.
--adaptive no on on | off. Controls whether the debate can change style/level. See learn-pathways.md.

Read the full file on GitHub · 179 lines

Changes

What this file has done since we first saw it

Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.

  1. 2d ago First seen · 179 lines · 8 tokens per session scan A 205bb61f3709

Subscribe to this mod's changes

learn is a command published in the GitHub repository frenzymath/Archon (213 stars, last pushed 16d ago), licensed Apache-2.0. It adds 8 tokens to every session and 3,777 once invoked, about $0.0000 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.