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| --- | |
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| ``` | |
| ____ ____ ____ ____ ____ _ _ ___ ____ ____ _ _ ____ ____ | |
| / ___)( _ \\( _ \\( __)( \\( \\/ )/ __)( __)( _ \\( \\/ )( __)( _ \\ | |
| \\___ \\ ) / ) __/ ) _) ) D ( \\ / \\__ \\ ) _) ) __/ \\ / ) _) ) / | |
| (____/(__\\_)(__) (____)(____/ \\/ (___/(____)(__) (__) (____)(__\\_) | |
| A R R A Y L A N G U A G E · A R R A Y I α = I → α | |
| ``` | |
| **Array I α = I → α · broadcast = pullback π : J → I · pmap₂ = Π-map · no sorry remains** | |
| </div> | |
| --- | |
| # Sovereign Array Language — Front-End | |
| The **front-end** for the [Sovereign Array Language](../sovereign-array): an | |
| interactive browser playground that runs the *same denotational semantics* | |
| as the Lean 4 spec and the C++20 kernel — no Abjad, no digital root, no NP-magic. | |
| > The denotational semantics of array computing *are* exactly a slice of | |
| > dependent type theory. This front-end is the view layer over that substrate. | |
| ## What this repo is | |
| | Layer | Repo | Role | | |
| |-------|------|------| | |
| | **Spec** | [`sovereign-array`](../sovereign-array) | Lean 4 — `Array I α = I → α`, zero-sorry proofs | | |
| | **Kernel** | [`sovereign-array`](../sovereign-array) | C++20 — `Array<T>`, `pmap2`, `broadcast`, `softmax`, `nand_attention` | | |
| | **Front-End** | **`sovereign-array-frontend`** (this repo) | Browser playground + usage guide | | |
| ## Quick Start | |
| ```bash | |
| # Serve the playground (any static server) | |
| cd sovereign-array-frontend | |
| python -m http.server 8080 | |
| # open http://localhost:8080 | |
| ``` | |
| No build step. Pure HTML/CSS/JS (ES modules). | |
| ## How to use the language | |
| 1. **Spec (Lean 4)** — define arrays as dependent functions `Fin n → α`; | |
| prove `broadcast_is_pullback` and `softmax_is_pmap` with `lake build` (zero sorry). | |
| 2. **Kernel (C++20)** — `#include "sovereign_array.h"`; build with CMake; | |
| run `sovarr_test` (11/11 checks). | |
| 3. **Front-end (this page)** — open `index.html`; the playground runs the | |
| same denotational semantics in the browser. | |
| 4. **Compose** — chain `pmap₂` / `broadcast` / `softmax` / `nand_attention`; | |
| fusion is Π-map fusion — no loop in the denotation. | |
| ## Usage Guide (SVG) | |
|  | |
| ## Kernels demonstrated | |
| | Kernel | Semantics | Status | | |
| |--------|-----------|--------| | |
| | `pmap₂` | Pointwise `Π`-map over index space `I` | ✅ | | |
| | `broadcast` | Pullback along projection `π : J → I` | ✅ | | |
| | `softmax` | `Π`-map normalization (shift-invariant) | ✅ | | |
| | `nand` | Universal boolean gate | ✅ | | |
| | `nand_attention` | NAND-extracted attention spec | ✅ | | |
| ## Layout | |
| ``` | |
| sovereign-array-frontend/ | |
| ├── index.html # Playground page | |
| ├── css/style.css # Sovereign dark theme | |
| ├── js/ | |
| │ ├── array-lang.js # Browser reference impl (SOVArray, broadcast, softmax, nand) | |
| │ └── app.js # Playground wiring | |
| ├── assets/ | |
| │ ├── logo.svg # Σ · I → α mark | |
| │ └── usage.svg # SVG usage guide | |
| └── README.md | |
| ``` | |
| ## The forbidden list (fatal conflations we do NOT make) | |
| - ❌ Proof `O(1)` substitution ⇒ `O(1)` decision procedure (NP stays hard) | |
| - ❌ Abjad / digital root as universal arithmetic (quotients lose information) | |
| - ❌ "Univalence replaces SIMD" (needs a compiler: Lean → C → LLVM → SIMD) | |
| --- | |
| <div align="center"> | |
| **The substrate is always free. The array is a function.** | |
| ``` | |
| Array I α = I → α | |
| broadcast = pullback π | |
| pmap₂ = Π-map | |
| no sorry remains. | |
| ``` | |
| *Sovereign Array Language · Front-End · 2026 · Ahmad Ali Parr* | |
| </div> | |