Toroid

AI that writes and proves correctness properties for chips.

Toroid reads a spec and a small RTL module, synthesizes formal properties with an LLM, runs an open-source model checker (Yosys + SymbiYosys), and iterates on counterexamples — automating the hardware-verification engineer's inner loop. The LLM proposes; the solver disposes, so hallucination cannot pass verification. Every reported result is a bounded proof to depth k, an unbounded proof, or a concrete counterexample waveform — never the model's unverified say-so.

The demo: point it at a FIFO with an injected off-by-one in its full flag. Toroid checks the flag/occupancy invariant full ⟺ count==DEPTH, proves it on the correct FIFO and falsifies it on the buggy one with a solver counterexample — a state where the flag disagrees with the true occupancy at the DEPTH boundary — and narrates the failing cycle deterministically.

Status: M1–M5 built — verifies real RTL end-to-end, catches an injected FIFO bug, and checks RTL-to-RTL equivalence, all on a real solver. The LLM synthesis path ran live against claude-opus-4-8 and is replayed from a recorded fixture in CI. See ROADMAP.md for the plan and PROGRESS.md for what's shipped.

The whole thing in one screen — the injected FIFO bug, caught by a real solver, with the failing cycle narrated (make demo; regenerate with make screenshot, which paints the command's actual stdout — nothing here is typed by hand):

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See it work

1 — The AI writes the properties; the solver proves them (recorded live, claude-opus-4-8). Claude reads the spec + the Yosys-extracted interface and synthesizes properties; they pass a Yosys compile gate, then the model checker discharges each one. This run produced 9 properties — 5 safety asserts + 4 reachability covers — which compiled on the first attempt; every assert proves:

# recorded synthesis: 9 properties (5 asserts + 4 covers), compiled in 1 attempt
| Property                                       | Verdict   | Engine              |
|------------------------------------------------|-----------|---------------------|
| P1  After synchronous reset, count is 0        | ✅ PROVEN | yosys-sat (minisat) |
| P2  Enabled below max increments by 1          | ✅ PROVEN | yosys-sat (minisat) |
| P3  Enabled at max saturates at 15 (no wrap)   | ✅ PROVEN | yosys-sat (minisat) |
| P4  Disabled out of reset holds value          | ✅ PROVEN | yosys-sat (minisat) |
| P5  count never exceeds 15                      | ✅ PROVEN | yosys-sat (minisat) |

Recorded to tests/fixtures/counter.synth.json and replayed offline with no API key — pytest -m integration -k recorded_synthesis reproduces the table above (the 4 covers are anti-vacuity witnesses; yosys-sat reports unknown for cover mode, so only the 5 asserts carry a verdict). A fresh live run (needs ANTHROPIC_API_KEY, and is non-deterministic run to run): toroid verify designs/counter.v --spec designs/counter.md --top counter.

2 — It catches a real bug, with a solver counterexample. The buggy FIFO computes its full flag one slot early — assign full = (cnt == 3'd3) instead of == 4. The structural invariant full ⟺ count==DEPTH(4) proves on the correct FIFO and is falsified on the buggy one; the solver returns a state where count == 4 yet full == 0, exactly the dropped boundary:

$ toroid verify designs/fifo_buggy.v --top fifo --no-llm --props designs/fifo.props.json
| F1  full is asserted exactly when count == DEPTH (4) | ❌ FALSIFIED | yosys-sat | depth 20 |
| F2  empty is asserted exactly when count == 0        | ✅ PROVEN    | yosys-sat |    —     |

step |  rst  wr_en  rd_en  full  empty  count
   0 |   1     0      1      0     0      4    ← count==4 but full==0: the off-by-one boundary
   1 |   1     0      0      0     1      0
   ⋮   (steps 2–18 identical: rst=1, count=0, full=0, empty=1)
  19 |   0     0      0      0     1      0    ← counterexample ends

On the lightweight yosys-sat backend the counterexample lands at the unconstrained initial state, because that backend ignores assume cells (ADR-0004). The sby + Bitwuzla backend lifts that limit and is live and green in CI (--backend sby): it honors assumptions and discharges covers, so assume-dependent properties prove and a pass whose witness is unreachable is caught as VACUOUS — see designs/counter_assume.props.json and designs/counter_vacuous.props.json, which the formal-sby CI job runs on every push.

3 — It proves (or disproves) RTL-to-RTL equivalence. A miter with shared symbolic inputs — the hardware sibling of Congruent:

$ toroid equiv designs/max2.v designs/max2_alt.v     --top-a max2 --top-b max2_alt      → ✅ PROVEN
$ toroid equiv designs/max2.v designs/max2_min_bug.v --top-a max2 --top-b max2_min_bug  → ❌ FALSIFIED
    distinguishing input at step 0:  a=4  b=2  →  max2 y=4   impostor y=2

Every verdict is tied to a real solver run — never the model's say-so. A pass with an unreachable witness is reported VACUOUS, and PROVEN is only awarded by an unbounded engine (k-induction / PDR); BMC alone is an honest BOUNDED-PASS.

The solver runs (2, 3, and the bug-catch chart) need nothing but pip install (Yosys via yowasp-yosys) and run on Windows; the live-LLM synthesis in (1) needs an ANTHROPIC_API_KEY, and its output is recorded as a fixture so CI replays the AI path with no key.

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What it can't do

The honest limits, so the claims above aren't read wider than they are:

• No full concurrent SVA. Properties use the open-Yosys subset (immediate assertions
  • $past/$rose/$stable/$anyseq/$anyconst). Sequences and the full temporal layer need the commercial Verific frontend — a deliberate non-goal (ADR-0002).
• Small, single-clock modules. Counter/FIFO/arbiter scale (≲500 lines). No multi-clock or CDC, no full-chip, no industrial IP.
• Safety properties only — no liveness or fairness.
• The lightweight backend ignores assumptions. yosys-sat (the pip-only default) ignores assume cells (ADR-0004), so assume-dependent properties can't be proven and covers aren't discharged — use --backend sby for those. Both backends narrate counterexamples cycle-by-cycle.
• It never edits your RTL. An rtl_bug verdict is terminal: Toroid diagnoses and pinpoints, it does not rewrite the design under test.
• LLM synthesis is non-deterministic. A live re-run may propose a different (still gated) property set; the committed fixture is the pinned, reproducible artifact.
• The benchmarks are illustrative, not a benchmark claim. Three tiny designs, no confidence intervals and no named external baseline — they show the flow works and the bug is caught, nothing more.
• No floating-point, analog, gate-level, or timing verification.

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Run it

Prerequisites: Python ≥ 3.11 (check: python --version). For the actual verification you need a model checker — pick one:

• Lightweight (works on Windows, no admin): pip install yowasp-yosys — Yosys as WebAssembly. Drives the built-in sat backend (internal minisat, no external solver). This is what the dev install (.[dev]) pulls in.
• Full stack: the OSS CAD Suite (Yosys + SymbiYosys + Bitwuzla) on PATH — https://github.com/YosysHQ/oss-cad-suite-build — for the sby backend, which honors assume cells and discharges covers (see ADR-0004). Linux is the supported path (it's what CI runs; use WSL2 on Windows); the native Windows build also works — see the "H2" entry in PROGRESS.md for a packaging caveat.

The offline demo and the unit tests need neither.

python -m venv .venv && source .venv/Scripts/activate   # Windows Git Bash
                                                        # (Linux/macOS: .venv/bin/activate)
pip install -e ".[dev]"     # once (includes yowasp-yosys)

make demo                   # ONE COMMAND: prove real RTL, catch a real bug with a
                            # counterexample, and check equivalence. No key, no OSS CAD
                            # Suite. (`make check` = lint + typecheck + tests.)

toroid demo               # offline showcase: render a wrapper + a sample report
# Verify real RTL (run from the repo root; yowasp-yosys is sandboxed to the CWD):
toroid verify designs/counter.v --spec designs/counter.md --top counter --no-llm
# → P1, P2 ✅ PROVEN.  Try the over-strong property to see a counterexample:
toroid verify designs/counter.v --top counter --no-llm --props designs/counter_bad.props.json
# → PB ❌ FALSIFIED, with a waveform written under designs/_build/.

pytest                      # unit tests (fast, offline)
pytest -m integration       # runs a real proof via Yosys (needs a Yosys on PATH)

The demo that lands

# Clean FIFO: the flag/occupancy invariants hold.
toroid verify designs/fifo.v --top fifo --no-llm --props designs/fifo.props.json
#   → F1 (full ⟺ count==4), F2 (empty ⟺ count==0)  ✅ PROVEN

# Buggy FIFO (off-by-one `full`): the bug is caught with a counterexample.
toroid verify designs/fifo_buggy.v --top fifo --no-llm --props designs/fifo.props.json
#   → F1 ❌ FALSIFIED (waveform shows full=0 at count==4); F2 ✅ PROVEN

# Benchmarks (charts need the `bench` extra: pip install -e ".[bench]"):
python -m benchmarks.bugcatch          # per-design verdicts + bug-catch chart
python -m benchmarks.depth_vs_time     # bounded-proof time vs BMC depth

# RTL-to-RTL equivalence:
toroid equiv designs/max2.v designs/max2_alt.v    --top-a max2 --top-b max2_alt     # ✅ PROVEN
toroid equiv designs/max2.v designs/max2_min_bug.v --top-a max2 --top-b max2_min_bug # ❌ distinguishing input

Commands

Command	What it does
toroid demo	Offline: render the formal wrapper + a sample verdict report.
toroid verify <rtl…> --top <name> --no-llm	Discharge a hand-written property file against the RTL.
toroid verify … --backend {auto,sby,yosys-sat}	Pick the engine (auto: sby if present, else yosys-sat).
toroid equiv <a.v> <b.v> --top-a A --top-b B	Prove two designs equivalent, or find a distinguishing input.
toroid extract <rtl…> --top <name>	Print the extracted interface model (debug).
pytest / pytest -m integration	Unit tests / live end-to-end tests.
ruff check . && mypy	Lint + typecheck.

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How to give feedback

You mainly test and report. Every milestone in ROADMAP.md ends with explicit Test steps — run them, then:

• Describe what happened in plain language.
• Paste any errors verbatim (the single most useful thing).
• For verification runs, the report (--report out.md) is the artifact to share.

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Project docs

Doc	What's in it
DESIGN.md	The full design and rationale — the single source of truth.
ROADMAP.md	The milestone checklist (the plan + what's done).
PROGRESS.md	Build log: what shipped each milestone and why.
docs/	Architecture decision records (ADRs) and long-form notes.
Toroid-Foundational-Doc.md	The origin thesis and positioning.

Tech stack

Python 3.11 · Yosys + SymbiYosys + Bitwuzla (open formal stack, ISC/MIT) · Anthropic SDK (claude-opus-4-8) · pytest / ruff / mypy. Pairs with Congruent (software equivalence) as the formal-methods-meets-AI portfolio spine.

License

MIT — see LICENSE.