c2e3ecb3e3
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Implements the cells-spec vision: a computation space that preserves auditability, correctness, interactivity. Phase 1 (Lean kernel + naga-IR Rust backend) is closed; foundation hypothesis stack (Selection H1+H2, Subobject H3, Trace H5, Obs.Ctx C2, Cubical.Trace) landed. Highlights: - Cubical-HoTT syntax + value/eval/readback in Lean - naga-IR pipeline (no GLSL string crosses FFI; 17/17 probes pass) - Honesty audit: every non-transport (sealed cells, vertex shader, Y-flip, presentation conventions) is documented as such - Polymorphic Trace α as free monoid; Cubical.Trace gives CTerm → Trace CTerm by structural fold (homomorphism = definition) - Selection as Huet zipper; Subobject as Boolean algebra over WCell - All theorems proven; the proof IS the implementation See STATUS.md for the resume guide. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
152 lines
5.2 KiB
Markdown
152 lines
5.2 KiB
Markdown
# Topolei — References
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Papers and code referenced for implementation. Organized by subsystem.
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---
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## Cubical Type Theory — Foundational Papers
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**CCHM — the primary reference for our cubical core.**
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Cohen, Coquand, Huber, Mörtberg (2016)
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"Cubical Type Theory: a constructive interpretation of the univalence axiom"
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arXiv:1611.02108
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https://arxiv.org/abs/1611.02108
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> De Morgan interval algebra, face formulas, hcomp, transport, Glue types, univalence.
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> This is the spec for Cells/Cubical/*.lean.
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**De Morgan Implementation Tutorial — how to actually build it.**
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Mörtberg (2022)
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"A tutorial on implementing De Morgan cubical type theory"
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arXiv:2210.08232
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https://arxiv.org/abs/2210.08232
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> Type-checking algorithms, cofibration handling, evaluator structure.
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> Closest thing to a recipe for our Eval.lean and Transport.lean.
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**ABCFHL — Cartesian cubical variant (alternative to de Morgan).**
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Angiuli, Brunerie, Coquand, Favonia, Harper, Licata
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"Syntax and Models of Cartesian Cubical Type Theory"
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https://www.cs.cmu.edu/~rwh/papers/uniform/uniform.pdf
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> Read if de Morgan interval causes problems with Lean's kernel; Cartesian
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> variant has different composition rules that may embed more cleanly.
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**Univalence in cubical sets.**
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Bezem, Coquand, Huber (2017)
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arXiv:1710.10941
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https://arxiv.org/abs/1710.10941
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**Axioms for cubical type theory in a topos.**
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Orton, Pitts (2017)
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arXiv:1712.04864
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https://arxiv.org/abs/1712.04864
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**Unifying cubical and multimodal type theory.**
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Aagaard, Kristensen, Gratzer, Birkedal (2022)
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arXiv:2203.13000
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https://arxiv.org/abs/2203.13000
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---
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## Cubical Type Theory — Reference Code
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**cubicaltt — original Haskell implementation by Mörtberg et al.**
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https://github.com/mortberg/cubicaltt
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> Reference for hcomp algorithm, face formula solver, evaluator structure.
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> Read the source, do not depend on it.
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**Agda Cubical Library — target architecture for our Lean embedding.**
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https://github.com/agda/cubical
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> Key files to read:
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> Cubical/Core/Primitives.agda — interval, face, transport primitives
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> Cubical/Foundations/Transport.agda — transport lemmas
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> Cubical/Core/Glue.agda — Glue type and univalence
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> We are reimplementing this structure in Lean 4 as a deep embedding.
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> Do not import; use as architectural reference only.
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**Ground Zero — Lean 4 synthetic HoTT library.**
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https://github.com/rzrn/ground_zero
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> Shows how to avoid Lean's native equality and build HoTT synthetically in Lean 4.
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> Read for: eliminator construction patterns, HIT techniques via quotients.
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> cells-spec constraint: do not take it as a dependency.
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---
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## EML — Exp-Minus-Log Binary Primitive
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**The EML paper. Primary computational reference for this project.**
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Odrzywolek, Andrzej (2026)
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"All elementary functions from a single operator"
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arXiv:2603.21852
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https://arxiv.org/abs/2603.21852
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Local copy: exp-log.pdf
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> eml(x,y) = exp(x) − ln(y) with constant 1 generates all elementary functions.
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> Grammar: S → 1 | eml(S,S). Constructive proof for sin, cos, +, ×, π, etc.
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> Foundation for H1. See HYPOTHESES.md.
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---
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## Factorization Homology — FM^fr Notation Layer
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**The primer — best entry point.**
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Ayala, Francis (2019)
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"A factorization homology primer"
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arXiv:1903.10961
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https://arxiv.org/abs/1903.10961
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> E_n-algebras, framed manifolds, ⊗-excision. Read this first for H4.
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**Original paper.**
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Ayala, Francis (2012)
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"Factorization homology of topological manifolds"
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arXiv:1206.5522
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https://arxiv.org/abs/1206.5522
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**Higher categories.**
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Ayala, Francis (2015)
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"Factorization homology I: higher categories"
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arXiv:1504.04007
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https://arxiv.org/abs/1504.04007
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**Stratified spaces (for mixed text/graph layouts).**
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Ayala, Francis, Tanaka (2014)
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"Factorization homology of stratified spaces"
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arXiv:1409.0848
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https://arxiv.org/abs/1409.0848
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> Relevant when notation mixes 1D (text) and 2D (diagram) regions.
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**Traces in dimension 1 (for linear/sequential syntax).**
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arXiv:2105.01143
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https://arxiv.org/abs/2105.01143
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> Circle-invariant traces; relevant for cyclic/recursive notation structures.
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---
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## Verified Compiler / Shader IR
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**Lean4Lean — verified Lean typechecker in Lean. Pattern reference.**
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Carneiro (2024)
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"Lean4Lean: Verifying a Typechecker for Lean, in Lean"
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arXiv:2403.14064
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https://arxiv.org/abs/2403.14064
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> Reference for: how to structure a verified evaluator/compiler in Lean 4.
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> Our EML → ShaderIR compiler should follow similar patterns.
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**SPIR-V specification.**
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Khronos Group
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https://www.khronos.org/spirv/
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> Binary format target for native GPU path. Formal grammar maps onto our ShaderIR.
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**MLIR SPIR-V dialect — IR structure reference.**
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https://mlir.llvm.org/docs/Dialects/SPIR-V/
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> Reference for what a typed shader IR looks like before binary encoding.
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> Informs the design of Topolei/Shader/IR.lean.
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---
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## Recommended Reading Order
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1. CCHM (1611.02108) — understand the cubical core we are embedding
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2. De Morgan tutorial (2210.08232) — implementation recipe
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3. cubicaltt source — see the evaluator and hcomp in action
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4. Agda Cubical library — see the Lean-side target architecture
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5. EML paper (2603.21852) — already read; revisit Sect. 3 for derivation tables
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6. Ayala-Francis primer (1903.10961) — FM^fr foundation for H4
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7. Lean4Lean (2403.14064) — verified compiler patterns before writing ShaderIR
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