Lean 4 cubical-transport HoTT engine + Rust naga-IR FFI. The backend that powers topolei. Cells-spec implementation; the proof IS the implementation.
f27211f73f
Adds schema-based inductive type encoding to the engine, supporting both
plain inductives (Nat, List, Bool) and HITs (S¹, propositional truncation,
suspensions) via a single CTypeSchema/CtorSpec/CTypeArg structure.
New CType constructor:
- .ind (S : CTypeSchema) (params : List CType)
New CTerm constructors:
- .dimExpr (r : DimExpr)
- .ctor (S, ctorName, params, args)
- .indElim (S, params, motive, branches, target)
New CVal constructors:
- .vctor (S, ctorName, params, evaluatedArgs)
- .vdimExpr (DimExpr)
New CNeu constructor:
- .nIndElim (S, params, motive, branches, neuTarget)
Five-way mutual block in Syntax.lean (CType, CTerm, CTypeArg, CtorSpec,
CTypeSchema) with Repr derivation post-hoc. Tag layout per
docs/INDUCTIVE_TYPES.md §6: old tags preserved (no shifting). Existing
62/62 smoke + property tests pass unchanged through Rust.
Substitution / dim-absent / endpoint handling:
Subst.lean — substDim, substDimExpr, equation lemmas,
substDim_eq_substDimExpr (mutual with .params helpers).
DimLine.lean — CTerm.dimAbsent + CType.dimAbsent (mutual w/ helpers
for list / branches / params). Plus all five
auxiliary mutual blocks: substDim_absent_aux,
substDimExpr_absent_aux, dimAbsent_after_substDim_aux,
substDim_comm_aux — for both CTerm and CType.
Eval.lean: ctor → vctor (eval'd args); indElim β-reduces on canonical
vctor target via vApp chain over branch body, otherwise stuck via
.nIndElim; dimExpr → vdimExpr. Path-ctor boundary firing and
recursive-arg IH wiring marked TODO REL1.1 (β-reduction works for
non-recursive ctors today).
Readback.lean: vctor → .ctor, vdimExpr → .dimExpr, nIndElim → .indElim.
FFITest.lean: cvalSummary / ctermSummary extended with new constructor
arms.
Topolei (sibling repo) has not yet been migrated — see
docs/INDUCTIVE_TYPES.md §9.1 for the per-file impact map.
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/libtopolei_cubical.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.