Lean 4 cubical-transport HoTT engine + Rust naga-IR FFI. The backend that powers topolei. Cells-spec implementation; the proof IS the implementation.
50bb6660d6
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Typing.lean: minimal-viable typing rules for the three new CTerm
constructors (REL1 first cut; REL2 will refine to dependent
formulations).
- HasType.ctor : .ctor S c params args : .ind S params
(no per-arg premises; runtime enforces)
- HasType.indElim : non-dependent form — motive : .pi (.ind …) C,
result : C; branch coherence checked at eval
- HasType.dimExpr : placeholder typing at .univ (real interval-
typing requires a CType.interval primitive,
deferred to REL2)
HasType.weaken_core extended with the three new arms.
TransportLaws.lean: derived theorems for transport over .ind (T1,
T2, stuck), all reducing to existing axioms (eval_transp_top,
eval_transp_const, eval_transp_nonpath + vTransp_stuck). Pointwise
distribution through ctor args is REL1.1 future work.
CompLaws.lean: derived theorems for composition over .ind (C1, C2,
const-line, stuck) — corollaries of the existing eval_comp_*
axioms. Same REL1.1 deferral for pointwise distribution.
native/cubical/src/subst.rs: critical Rust fix. The previous
fallback `_ => mk_term_var(ctor_field(t, 0))` corrupted the new
TERM_DIMEXPR / TERM_CTOR / TERM_INDELIM tags by extracting field 0
(a CTypeSchema for ctor) and wrapping it as a malformed .var,
causing infinite recursion / OOM in subst-driven paths
(eval_comp_top calls substDim). Proper arms for all three new
tags + cterm_subst_dim_list and cterm_subst_dim_branches helpers.
Unknown-tag fallback now safely returns the input unchanged
instead of synthesising a malformed .var.
FFITest.lean: three new smoke arms exercising T1/T2 transport and
C1 composition over .ind natC. Result: 28/28 smoke + 46/46
properties = 74/74.
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.