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PolyglotFormalisms.Elixir — Project Topology

System Architecture

                        ┌─────────────────────────────────────────┐
                        │              POLYGLOT SYSTEM            │
                        │        (Cross-Language Verification)    │
                        └───────────────────┬─────────────────────┘
                                            │
                                            ▼
                        ┌─────────────────────────────────────────┐
                        │           ELIXIR IMPLEMENTATION         │
                        │                                         │
                        │  ┌───────────┐  ┌───────────────────┐  │
                        │  │ Arithmetic│  │  Comparison       │  │
                        │  │ Module    │  │  Module           │  │
                        │  └─────┬─────┘  └────────┬──────────┘  │
                        │        │                 │              │
                        │  ┌─────▼─────┐  ┌────────▼──────────┐  │
                        │  │ Logical   │  │  Behavioral       │  │
                        │  │ Module    │  │  Semantics (BEAM) │  │
                        │  └─────┬─────┘  └────────┬──────────┘  │
                        └────────│─────────────────│──────────────┘
                                 │                 │
                                 ▼                 ▼
                        ┌─────────────────────────────────────────┐
                        │           SEMANTIC EQUIVALENCE          │
                        │  ┌───────────┐  ┌───────────┐  ┌───────┐│
                        │  │ Julia     │  │ ReScript  │  │ Gleam ││
                        │  └───────────┘  └───────────┘  └───────┘│
                        └─────────────────────────────────────────┘

                        ┌─────────────────────────────────────────┐
                        │          REPO INFRASTRUCTURE            │
                        │  Justfile / mix.exs .machine_readable/  │
                        │  ExUnit / Doctest   AI.a2ml             │
                        └─────────────────────────────────────────┘

Completion Dashboard

COMPONENT                          STATUS              NOTES
─────────────────────────────────  ──────────────────  ─────────────────────────────────
FORMAL MODULES
  Arithmetic (add, sub, etc)        ██████████ 100%    IEEE 754 parity verified
  Comparison (equal, less, etc)     ██████████ 100%    Transitivity proven
  Logical (and, or, not)            ██████████ 100%    De Morgan's laws verified

SEMANTICS & VERIF
  BEAM Behavioral Semantics         ██████████ 100%    Float/Integer edge cases stable
  Cross-Language Verification       ████████░░  80%    Julia/ReScript parity verified
  Mathematical Properties           ██████████ 100%    Commutativity/Associativity stable

REPO INFRASTRUCTURE
  Justfile Automation               ██████████ 100%    Standard build/test tasks
  .machine_readable/                ██████████ 100%    STATE tracking active
  ExUnit Test Suite                 ██████████ 100%    High unit + doctest coverage

─────────────────────────────────────────────────────────────────────────────
OVERALL:                            █████████░  ~90%   Stable Elixir implementation

Key Dependencies

Common Spec ──────► Elixir Implementation ──────► Behavioral Proof
     │                      │                        │
     ▼                      ▼                        ▼
Property Tests ───► Cross-Lang Parity ──────► Semantic Equivalence

Update Protocol

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