README.md

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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

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Sovereign Array Language — Front-End

The front-end for the Sovereign Array Language: 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	Lean 4 — Array I α = I → α, zero-sorry proofs
Kernel	sovereign-array	C++20 — Array<T>, pmap2, broadcast, softmax, nand_attention
Front-End	sovereign-array-frontend (this repo)	Browser playground + usage guide

Quick Start

# 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)

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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