cubical-transport-hott-lean4/CubicalTransport.lean
Maximus Gorog 6adbce0c1b
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QUESTIONS Level 1: CompQ reified + classifier-conditioned axioms
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>
2026-05-01 00:21:58 -06:00

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import CubicalTransport.Interval
import CubicalTransport.Face
import CubicalTransport.Syntax
import CubicalTransport.Subst
import CubicalTransport.DimLine
import CubicalTransport.Typing
import CubicalTransport.Equiv
import CubicalTransport.Glue
import CubicalTransport.Value
import CubicalTransport.Transport
import CubicalTransport.Line
import CubicalTransport.Eval
import CubicalTransport.EvalTest
import CubicalTransport.Readback
import CubicalTransport.FFI
import CubicalTransport.FFITest
import CubicalTransport.ValueTyping
import CubicalTransport.TransportLaws
import CubicalTransport.System
import CubicalTransport.CompLaws
import CubicalTransport.Soundness
import CubicalTransport.Inductive
import CubicalTransport.Bridge
import CubicalTransport.Question
import CubicalTransport.PropertyTest