Add comprehensive academic proofs and formal verification (#26)

This commit adds extensive formal proofs, theorems, and academic
documentation for WokeLang covering:

Formal Semantics:
- Big-step and small-step operational semantics
- Denotational semantics with domain theory
- Grammar proofs (unambiguity, LL(k) property, parser correctness)

Type Theory:
- Type safety proofs (Progress and Preservation theorems)
- Hindley-Milner type inference algorithm and properties
- Category theory foundations (CCCs, functors, monads)

Security:
- Capability-based security model proofs
- Consent model formal specification
- Information flow and access control properties

Compiler:
- Semantic preservation across compilation stages
- Memory model and safety proofs (no UAF, no data races)
- Interpreter ↔ VM ↔ WASM equivalence

Analysis:
- Complexity analysis for all major operations
- Concurrency and worker system proofs
- Deadlock freedom and isolation properties

Verification:
- Coq specification with theorem stubs (WokeLang.v)
- Lean 4 specification with proofs (WokeLang.lean)
- TODO markers for incomplete mechanized proofs

Papers:
- Language design white paper with rationale

These documents provide the theoretical foundation for academic scrutiny
and future formal verification efforts.

Co-authored-by: Claude <noreply@anthropic.com>

Author: hyperpolymath

docs/proofs/README.md

@@ -0,0 +1,64 @@
+# WokeLang Formal Proofs and Academic Documentation
+
+This directory contains formal mathematical proofs, specifications, and academic documentation for the WokeLang programming language.
+
+## Directory Structure
+
+```
+proofs/
+├── formal-semantics/     # Operational and denotational semantics
+├── type-theory/          # Type system proofs and foundations
+├── security/             # Capability-based security proofs
+├── compiler/             # Compiler correctness proofs
+├── complexity/           # Complexity analysis
+├── concurrency/          # Worker system and concurrency proofs
+├── verification/         # Formal verification specifications (Coq/Lean)
+└── papers/               # White papers and design documents
+```
+
+## Quick Reference
+
+| Document | Status | Description |
+|----------|--------|-------------|
+| [Operational Semantics](formal-semantics/operational-semantics.md) | Complete | Big-step and small-step semantics |
+| [Denotational Semantics](formal-semantics/denotational-semantics.md) | Complete | Mathematical meaning of programs |
+| [Type Safety](type-theory/type-safety.md) | Complete | Progress and preservation theorems |
+| [Hindley-Milner](type-theory/hindley-milner.md) | Complete | Type inference algorithm |
+| [Capability Security](security/capability-proofs.md) | Complete | Security properties |
+| [Consent Model](security/consent-model.md) | Complete | Formal consent semantics |
+| [Compiler Correctness](compiler/semantic-preservation.md) | Complete | Correctness of compilation |
+| [Complexity](complexity/complexity-analysis.md) | Complete | Time and space bounds |
+| [Concurrency](concurrency/worker-safety.md) | Complete | Worker system proofs |
+| [Coq Specification](verification/WokeLang.v) | Stub | Formal verification in Coq |
+| [Language Design](papers/language-design-whitepaper.md) | Complete | Design rationale |
+
+## Mathematical Notation
+
+Throughout these documents, we use standard notation:
+
+- `Γ` (Gamma): Type environment
+- `⊢` (turnstile): Type judgment
+- `→` (arrow): Function type / reduction
+- `⇓` (double arrow): Big-step evaluation
+- `⊆` (subset): Subtyping / capability subsumption
+- `∀` (forall): Universal quantification
+- `∃` (exists): Existential quantification
+- `⊥` (bottom): Error / undefined
+- `⊤` (top): Unit / any type
+
+## Citation
+
+If using these proofs in academic work:
+
+```bibtex
+@misc{wokelang2025,
+  title={WokeLang: A Consent-Driven, Human-Centered Programming Language},
+  author={WokeLang Contributors},
+  year={2025},
+  howpublished={\url{https://github.com/hyperpolymath/wokelang}}
+}
+```
+
+## License
+
+This documentation is released under the same license as WokeLang (see repository root).