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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Phase D'.5 of ALGEBRA_PLAN.md and the §4.4 "Failure as a feature"
diagnostic. Closes the methodology-transport loop end-to-end.
CubicalTransport/Algebra/MetaPath.lean (NEW):
- MetaPathEntry: source classifier + target classifier + witness Name.
- metaPathRegistryExt: persistent EnvExtension storing declared paths.
- @[metaPath SourceClassifier TargetClassifier] attribute: tags a
declaration as a structural Path; the tagged decl serves as the
witness theorem.
- Lookup helpers: findPathsFromSource / findPathsToTarget.
- Diagnostic printer.
CubicalTransport/Algebra/Methodology.lean:
- deriveByTransport replaces its earlier stub. Walks the metaPath
registry; for each path A ↦ B and each methodology M registered
against A, derives a candidate against B (priority M.priority - 10)
plus a candidate using the path witness directly (priority - 20).
- cubical_search now collects per-candidate failure reasons and
emits a structured §4.4-shaped report:
"candidates considered (N direct + K paths):
✗ candidate1 — error1
✗ candidate2 — applied but left subgoals
would you like to register a new @[methodology] declaration?"
- Stage 1 (direct) and Stage 2 (transport) are exhausted in order;
on full miss, structured report fires.
CubicalTransport/Algebra/Test.lean:
- Phase D'.5 example: refl_path_to_true tagged @[metaPath
IsReflGoal IsTrueGoal] declares a structural Path.
- Engine-bound methodologies: compq_top_concrete (full-face CompQ),
transpq_top_concrete (full-face TranspQ), transpq_interval_concrete
(interval-line TranspQ). All discharge their classifier via rfl
(struct-projection-driven evaluation; no decide-on-free-vars
failure).
- Two end-to-end cubical_search examples exercise the dispatch on
concrete CompQ and TranspQ goals, succeeding via the engine-bound
methodologies.
CubicalTransport.lean: import the new MetaPath module.
93/93 tests pass. cubical_search now demonstrably closes both
trivial (True, Eq.refl, Iff.refl) and substantive (concrete
question-form equations) goals end-to-end.
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.