Lean 4 cubical-transport HoTT engine + Rust naga-IR FFI. The backend that powers topolei. Cells-spec implementation; the proof IS the implementation.
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Per the elegance pass: 9 ad-hoc per-modality constructors collapse into
3 ModalityKind-parameterised constructors. Future modalities (Phase
4's ʃ_EML, ℑ infinitesimal) extend ModalityKind by adding cases —
no new constructors, no new ABI bump.
New Lean enum (Syntax.lean):
inductive ModalityKind | flat | sharp | shape
deriving DecidableEq, Repr, Inhabited
Constructor unification:
· CType: 3 (.flat / .sharp / .shape) → 1 (.modal k A)
· CTerm: 6 (.flatIntro / .sharpIntro / .shapeIntro / .flatElim /
.sharpElim / .shapeElim) → 2 (.modalIntro k a, .modalElim k f m)
· CVal: 3 (vFlatIntro / vSharpIntro / vShapeIntro) → 1 (vModalIntro)
· CNeu: 3 (nflatElim / nsharpElim / nshapeElim) → 1 (nModalElim)
· SkeletalCType: 3 (skFlat / skSharp / skShape) → 1 (skModal k)
Engine cascade across 12 files (DecEq, DimLine, Eval, FFITest, Modal,
Question, Readback, Reflect, Subst, Syntax, Typing, Value): every
match site collapsed from 3-per-modality arms to 1 k-parameterised arm.
Reflect.lean: new `reflectModalityKind` / `reifyModalityKind` helpers
+ ModalityKind dispatch arm in classifyFieldType. The Phase 1 macro
auto-derived per-constructor reflect/reify for the new unified
constructors — no manual cascade needed there.
Eval.lean β-rule: `.modalElim k f (.modalIntro k' a)` β-reduces only
when k = k' (kind-discrimination preserves cross-kind correctness even
if typing is bypassed); cross-kind case produces a marker neutral.
Modal.lean transient alias block (top of file, outside namespace) for
backward dot-syntax reference (`.flatIntro a` resolves to
`.modalIntro .flat a` via abbrev). Phase 3 will rewrite Modal.lean
properly to use the unified constructors directly + forModalityKind-
derived functor.
Net: −145 lines across the cascade (-478 deletions, +333 insertions).
Build: lake build (48 jobs) + lake build CubicalTransport (43 jobs) PASS.
Runtime: lake exe cubical-test 49/49 + 46/46 = 95/95 PASS.
Sorry count: Modal.lean 3 (unchanged), total engine 33 (no new sorries
from this phase, all annotated).
The Rust ABI v6 still uses 9 modal tags — diverges from the Lean side
after this commit but FFI tests don't exercise modal paths so no
runtime regression. Phase 4 will sync to ABI v7.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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|---|---|---|
| .forgejo/workflows | ||
| CubicalTransport | ||
| docs | ||
| native/cubical | ||
| .gitignore | ||
| build.sh | ||
| CubicalBench.lean | ||
| CubicalTest.lean | ||
| CubicalTransport.lean | ||
| lake-manifest.json | ||
| lakefile.toml | ||
| lean-toolchain | ||
| LICENSE | ||
| NOTICE | ||
| README.md | ||
cubical-transport-hott-lean4
A Lean 4 implementation of cubical-transport homotopy type theory (CCHM-flavor), with a fast Rust kernel exposed through C ABI.
The Lean side defines the syntax, semantics, and soundness theorems.
The Rust side discharges the per-step β-rules of the evaluator.
Lean axioms are routed through @[implemented_by] to Rust functions
that return Lean objects in the same shape Lean would have produced;
the soundness layer (CubicalTransport/Soundness.lean) certifies the
backend at the boundary, so the kernel speed of the Rust code
preserves the Lean-level proofs.
What's here
CubicalTransport/— 22 Lean modules for syntax, substitution, dimensional structure, faces, typing, evaluation (eval / value / readback), transport, Glue, composition, and the soundness theorems.native/cubical/— Rust kernel (#![no_std], dual-target native staticlib + cdylib, wasm32 cdylib).CubicalTest.lean,CubicalBench.lean— engine smoke + property tests (62/62 passing) and microbenchmarks.
Consuming the engine (with permission)
This Software is proprietary. See LICENSE — no use is granted
by virtue of the repository being public. The instructions below
are for the copyright holder and any party with prior written consent
from mgorog@gmail.com.
Add as a Lake dependency from another Lean 4 project:
[[require]]
name = "cubicalTransport"
path = "../cubical-transport-hott-lean4" # or git = "..."
Then import CubicalTransport.Syntax, import CubicalTransport.Eval,
etc. Link against native/cubical/target/release/libcubical_transport.a
in your own moreLinkArgs so the FFI symbols resolve.
Build
(cd native/cubical && cargo build --release)
lake build
./.lake/build/bin/cubical-test # 62/62 tests pass
Reference
docs/FFI_DESIGN.md— C ABI contract between Lean and the Rust kernel.docs/FFI_COMPLETENESS.md— per-function axiom audit.docs/KERNEL_BOUNDARY.md— what this delivers in unmodified Lean 4 vs. what would need upstream Lean kernel work.docs/NUMERICAL.md— numerical implementation principles.docs/PHASE1_HISTORY.md— original transport/composition formalisation plan (archived; Phase 1 closed; preserved as methodology template for future phases).docs/ZIGZAG_PORT.md— step-by-step Lean port plan for the n-category combinatorial engine (Phase 2+ higher-cell backend). Lands here in the engine. Read the cascade caveat at the top before editing: changes in the ported zigzag layer cascade to the siblingtopoleirepo.native/cubical/README.md— Rust crate build + dev guide.native/cubical/WASM.md— wasm32 ABI integration contract.
Used by
max/topolei— the cells-spec workspace interface, built on this engine. See itsdocs/cells-spec.mdanddocs/STATUS.mdfor the application-side picture.