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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Implements docs/QUESTIONS.md Level 1 (structural reification only). CubicalTransport/Question.lean: - CompQ structure (env, binder, body, φ, u, t) — the CCHM partial-element-filler question, reified as data. - CompQ.ask = eval env (.comp …); CompQ.Equiv = ask-equality (refl/symm/trans). - CompQ.ofTransp smart constructor — every transport is a degenerate comp (u = t). - Classifiers: IsConstLine, IsFullFace, IsEmptyFace, IsTransport, IsPathLine, IsGlueLine, IsPiLine, IsSigmaLine, IsIndLine, IsIntervalLine, IsUnivLine. - Restated as CompQ.ask theorems: ask_of_full_face (C1), ask_of_empty_face (C2), ask_of_const_line (hcomp reduction), ask_of_pi_line (vCompFun packaging), ask_of_stuck (residual). - ask_of_transport_full_face — the bridge corollary linking CompQ.ofTransp to the legacy eval_transp_top axiom under the standard typing premise (base dim-absent in the binder). - Decidable instance for IsConstLine (Bool-valued); face/body- shape decidability deferred to Level 1.5 (needs cross-package DecidableEq from Topolei.Cubical.DecEq). No new axioms; all five restated theorems derive from existing eval_comp_* axioms in Eval.lean. Levels 2 (simp routing) and 3 (question-driven proofs) deferred per QUESTIONS.md §4. CubicalTransport/FFITest.lean: 3 new CompQ smoke tests (ask delegation, ofTransp on .interval, IsConstLine decidability). Test count: 81 → 84 passing. Companion docs: QUESTIONS.md (philosophy), ALGEBRA_PLAN.md (the macro layer this enables), EULERIAN.md (poetic record). 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.