31d19f655e
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Restructure to engine-only contents. Application code (Topolei.*
namespace, canvas-rs / render Rust crates, Main / ProbeTest, naga IR
pipeline, Selection / Subobject / Trace / Obs.Ctx hypothesis stack,
cells-spec / HYPOTHESES / STATUS / NAGA_IR_PLAN docs) moves to the
sibling repo max/topolei.
What moved:
- `Topolei/Cubical/*.lean` (22 files) → `CubicalTransport/*.lean`
with namespace `Topolei.Cubical.*` renamed to `CubicalTransport.*`.
Fully-qualified test types `TopoleiCubical{FFI,Property}Test` →
`CubicalTransport{FFI,Property}Test` for consistency.
- New root file `CubicalTransport.lean` re-exporting all 22 modules.
- Lakefile: package `cubicalTransport`; lib `CubicalTransport`; only
`cubical-test` and `cubical-bench` exes (no GPU link path).
The split criterion: anything an AI shortcut could break that would
cascade-corrupt downstream proofs lives here. Anything that would
only break the application stays in the topolei interface repo.
cubical-test passes 62/62 (smoke + properties) on the renamed engine.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
51 lines
2.4 KiB
Text
51 lines
2.4 KiB
Text
/-
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Topolei.Cubical.CompLaws
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========================
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Residual step-level axiom for composition: subject reduction (C4).
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C1 (`comp_full`) and C2 (`comp_empty`), formerly stated here as
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step-level axioms, are now NbE theorems in `Cubical/Readback.lean`
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(`readback_comp_full` / `readback_comp_empty`). The Rust backend's
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discharge obligations for composition reduce to: the eval-level
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axioms in `Eval.lean`, the readback-level axioms in `Readback.lean`,
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and the C4 residual below.
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Note on CCHM C3 (`transp = comp_{[φ↦t₀]} t₀`):
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CCHM expresses transport as a specialised composition. That
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specialisation is only *typed* when the system body coincides with
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the base (u = t₀) and the compatibility `t₀[i:=0] = t₀` holds —
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i.e. `L.binder` is absent from `t₀`. Stating it would duplicate
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the constant-line transport identity (`readback_transp_const_id`).
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The real CCHM reduction (`transp = hcomp + fill`) lives at the
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eval level; see `vCompFun` / `vApp_vCompFun` in `Eval.lean`.
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Why C4 stays step-level: same reason as T3 — needs a typing-
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preservation lemma on `eval`/`readback` (Stream B #2a).
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-/
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import CubicalTransport.System
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import CubicalTransport.TransportLaws
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import CubicalTransport.ValueTyping
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-- ── Subject reduction for composition ────────────────────────────────────────
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/-- **C4 (composition subject reduction)** — stepping a well-typed
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composition preserves the output type.
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**Now a theorem, not an axiom.** Stage 2.3 consolidation: follows
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from `HasType.comp` and `CTerm.step_preserves_type` (ValueTyping.lean).
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Parallel to `transp_step_preserves` (T3).
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The `HasType.comp` constructor requires a compatibility side-condition
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on the system body (`u[i:=0] = t₀` wherever `φ ∩ (i=0)` is inhabited).
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Callers that cannot produce this side-condition should fall through
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to a per-callsite argument rather than using this theorem. -/
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theorem comp_step_preserves (Γ : Ctx) (L : DimLine) (φ : FaceFormula)
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(u t₀ : CTerm)
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(ht : HasType Γ t₀ L.at0)
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(hu : HasType Γ u L.at1)
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(hc : ∀ env : DimVar → Bool,
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φ.eval env = true → env L.binder = false →
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CTerm.substDimBool L.binder false u = t₀) :
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HasType Γ (CTerm.step (.comp L.binder L.body φ u t₀)) L.at1 :=
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CTerm.step_preserves_type Γ _ _ (HasType.comp L ht hu hc)
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