cfabca3404
Some checks are pending
Lean Action CI / build (push) Waiting to run
Removes the transient alias block (CType.flat/.sharp/.shape +
6 CTerm modal abbrev) and rewrites the substantive content using
the unified .modal/.modalIntro/.modalElim constructors directly.
Three modal CFunctor witnesses → one ModalityKind-parameterised
function:
forModalityKind (ℓ : ULevel) (k : ModalityKind) :
CFunctor (CType_as_Category ℓ) (CType_as_Category ℓ)
The body is uniform in k (no internal `match k with` branches);
obj/arr fields use `.modalIntro k` / `.modalElim k` directly;
preserves_id/preserves_comp parameterised in k.
Six rfl-lemmas + 2 dependence theorems → 2 each, parameterised.
Crisp predicate constructors generalised from flat-only to all
kinds (semantic widening — documented in source as a deliberate
generalisation from spatial-TT's flat-only canonical Crisp;
sound because every modal eliminator extracts from a modalised
subuniverse):
· flatElimBody → modalElimBody (k) (f m)
· flatIntroOfCrisp → modalIntroOfCrisp (k) {a} (h)
· appPropagation unchanged
· Crisp.var_not_immediate restated to ∃ k existential
Three adjoint-triple theorems restated using `forModalityKind ℓ
.flat/.sharp/.shape`. All three sorries preserved with rephrased
waits-on annotations.
Three β-soundness theorems → one:
modal_beta_sound (env) (k) (f a) := eval_modalElim_beta env k f a
Net: -68 lines. Build clean (48 + 43 jobs). Runtime 95/95.
3 sorries unchanged (the three adjoint-triple theorems).
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
|
||
|---|---|---|
| .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/libcubical_transport.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.