eml-lab — compile, lookup, and inspect EML trees

Read ../shared/emlcore/ for the underlying types. This skill is a thin CLI on top of that package. compile-render output-bundle schema, auto-domain rules, and Mermaid fallback thresholds live in [references/compile-render.md](references/compile-render.md).

When this skill triggers (and when it doesn't)

Triggers on: "compile sin(x)+cos(x) into EML", "lower this sympy expression", "how many tokens does the mult witness take?", "render this tree as Mermaid", "look up the atan witness", "give me an artifact bundle for exp(x+y)".

Does not trigger on: verifying a tree against a named claim (use /eml-check), searching for a shorter tree (/eml-optimize), fitting a law from data (/eml-fit), or checking arbitrary elementary identities (/math-identity-check).

Modes

• Compile (--compile EXPR) — lower a sympy-parseable formula into an EML tree by substituting library witnesses (e, exp, ln, add, mult, sub, pow, neg, inv, div, pi, i, sin, cos, tan, sqrt, asin, acos, atan, log10).
• Lookup (--lookup NAME) — fetch a witness; emit metadata (K, depth, minimal flag, proof URL) and tree body if stored.
• Inspect (--tree STR) — parse any EML tree (nested, RPN, JSON) and emit stats + alternate representations.
• Compile-render (compile-render --expr EXPR --out-dir DIR) — one-shot stitch: compile → render Mermaid/SVG → audit against sympy.lambdify(..., modules='cmath') → emit tree.txt, diagram.md/diagram.svg, audit.json, audit.md, and summary.md. See [references/compile-render.md](references/compile-render.md) for the bundle schema.

Compile/lookup/inspect share emits: stats, rpn, json, graphviz, mermaid, nested.

How to run

All commands below assume cwd is the repo root. From an installed plugin's root, drop the leading eml-skill/; from this skill's own directory, drop eml-skill/skills/eml-lab/.

# legacy (flag-driven):
python eml-skill/skills/eml-lab/scripts/lab.py \
  ( --compile EXPR | --lookup NAME | --tree "eml(...)" | --list ) \
  [--emit stats,rpn,json,graphviz,mermaid,nested] [--out-dir <path>] [--title "label"]

# one-shot compile-render:
python eml-skill/skills/eml-lab/scripts/lab.py compile-render \
    --expr "sin(sqrt(x) + cos(x))" --out-dir /tmp/demo --domain positive-reals \
    [--render mermaid|svg] [--format md|json|blog] [--samples N] [--seed S] [--tolerance T]

Exit codes: 0 OK, 1 lookup-not-found / compile blocked, 2 parse error, 3 usage error.

Examples

python eml-skill/skills/eml-lab/scripts/lab.py --list
python eml-skill/skills/eml-lab/scripts/lab.py --compile "x*y"                              # mult, K=17
python eml-skill/skills/eml-lab/scripts/lab.py --lookup exp --emit stats,rpn,graphviz
python eml-skill/skills/eml-lab/scripts/lab.py compile-render --expr "exp(x+y)" --out-dir /tmp/demo

Non-goals

• Not a minimizer. x*y → K=17 mult every time. For shorter trees use /eml-optimize.
• Not a verifier. Branch-cut + equivalence audits live in /eml-check. compile-render's audit is a numerical sanity check, not a proof.
• Not a fitter. That's /eml-fit.

Don't reimplement

All logic lives in skills/shared/emlcore/ — CLI is a thin wrapper: compile.compileformula, parse, {ktokens, depth, leafcounts, torpn}, viz.{tographviz, tomermaid, tomermaiddoc, rendergraphvizsvg}, witnesses.{lookup, names, WITNESSES}.

Gotchas

• **--list marks proven-minimal entries with *.** Upper-bound entries show depth=-1 (only K published).
• compile inlines library witnesses. x*y returns K=17 every time; use /eml-optimize for shorter trees.
• Triple-nesting LN uses principal-branch cmath. /eml-check audits the +iπ branch choice on the negative real axis.
• RPN is space-tokenized. The paper's compact form (x1E) is display-only.
• compile-render autodetects --domain when omitted — narrowest named domain that all witnesses support. See [references/compile-render.md](references/compile-render.md) for the full priority rules.
• compile-render is K-faithful, not K-minimal. Flagship sin(sqrt(x) + cos(x)) lowers to K=1151; /eml-optimize search can often shorten it.
• Graphviz optional. --render svg needs dot; missing binary yields a clean "install graphviz or use --render mermaid" exit, not a crash.
• Mermaid auto-falls-back to RPN for K > 500. GitHub grays out large diagrams; see [references/compile-render.md](references/compile-render.md) for the threshold.

Test scenarios

1. --compile "x*y" → nested mult witness, K=17 (exit 0).
2. --lookup atan --emit stats,rpn → K=403, proof URL present (exit 0).
3. --lookup zzz → lookup-not-found (exit 1).
4. compile-render --expr "exp(x+y)" --out-dir /tmp/d → 5 files written to /tmp/d (exit 0).
5. --compile "x + unknown_symbol" → parse error (exit 2).