Sovereign Array Language

Array I α = I → α  ·  broadcast = pullback  ·  pmap₂ = Π-map  ·  no sorry remains

Playground

pmap₂ — pointwise Π-map

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broadcast — pullback π : J → I

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softmax — Π-map normalization

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NAND — universal gate

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attention — NAND-extracted spec

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Usage Guide

Sovereign Array usage guide

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.