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 feedback "tooling possible, not tools — highly selective". Each former opinionated wrapper either reduces to a Lean-standard mechanism or splits into stated-contract primitives. CubicalTransport/Question.lean: - Drop the `cubical_simp` and `cubical_simp [..]` macros. They baked in a fixed lemma list with a fixed expansion order. - Drop the proposed `register_simp_attr question_simp` named-set too — strictly more curation than the foundation principle calls for. Anyone wanting a named bundle can register one downstream. - The genuinely-equational classifier-conditioned theorems remain `@[simp]`-tagged; existential-conclusion theorems (`ask_of_pi_line`, `ask_of_path_line`, HCompQ pi) lose their `@[simp]` tag (they don't rewrite goals — they produce witnesses). - Examples now use Lean's standard `simp` against the `@[simp]` database — no special tactic involved. CubicalTransport/Algebra/Methodology.lean: - New foundation primitive `tryEntryAsClosed : MethodologyEntry → TacticM Bool` with stated contract: tries `exact` then `apply`, restores tactic state on failure, never throws, returns whether goal closed. Order fixed to those two attempts in that sequence; alternative orders are user-side compositions of the primitive. - `cubical_search` rewritten using `tryEntryAsClosed` + `findMethodologies` + `getMetaPaths` + `findMethodologies` (for source classifiers). Docstring reframes it explicitly as a *reference-composition demonstrator* — exposes one obvious order for stages 1 (direct) and 2 (transport), with a "register your own dispatcher" pointer for users wanting different ordering / retry / failure shape. CubicalTransport/Algebra/EngineMethodologies.lean: - Drop the `cubical_close` macro entirely. A `simp; (rfl | cubical_search)` composition is one line at the call site; baking it in imposed an opinionated default. CubicalTransport/Algebra/Test.lean: - Remove the three `cubical_close` examples (the macro is gone). - Engine-bound methodologies remain (they exercise the @[methodology] registration mechanism). AlgebraRestructure.lean: - Docstring reframed as "thin labeled shell over `Algebra.print*` registry-printer functions, not a normative CLI." The four subcommands are this demonstrator's choice; underlying printers accept any other shell equally. 93/93 tests pass. No new functionality removed, just the opinion layer between user code and the foundations. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> |
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| .forgejo/workflows | ||
| CubicalTransport | ||
| docs | ||
| native/cubical | ||
| .gitignore | ||
| AlgebraRestructure.lean | ||
| 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.