File size: 3,001 Bytes
0166e35 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 | // Sovereign Array Language — browser reference implementation
// Denotational model (valid isomorphisms only):
// Array I α ≃ I → α (dependent function, row-major storage)
// Shape ≃ finite type I (number[] index space)
// Broadcast ≃ pullback π : J → I
// VecOp ≃ Π-map over I
// No Abjad, no digital root, no NP-magic.
export class SOVArray {
constructor(shape, data) {
this.shape = shape;
this.data = data;
if (this.prod(shape) !== data.length)
throw new Error("SOVArray: shape/data size mismatch");
}
prod(s) { return s.reduce((a, b) => a * b, 1); }
rank() { return this.shape.length; }
size() { return this.data.length; }
raw() { return this.data.slice(); }
at(idx) { return this.data[this.stride(idx)]; }
stride(idx) {
if (idx.length !== this.shape.length) throw new Error("rank mismatch");
let off = 0, st = 1;
for (let d = this.shape.length; d-- > 0;) {
off += idx[d] * st;
st *= this.shape[d];
}
return off;
}
// pmap₂: pointwise binary op (the Π-map over the index space I)
pmap2(op, other) {
if (JSON.stringify(this.shape) !== JSON.stringify(other.shape))
throw new Error("pmap2: shape mismatch");
return new SOVArray(
this.shape,
this.data.map((x, i) => op(x, other.data[i]))
);
}
}
// Broadcasting = pullback along projection π : J → I (NumPy-style right-align)
export function broadcast(targetShape, v, w) {
const out = new Array(v.prod(targetShape)).fill(0);
const vRank = v.rank(), wRank = w.rank();
for (let flat = 0; flat < out.length; ++flat) {
const idx = unravel(flat, targetShape);
const vi = idx.slice(targetShape.length - vRank);
const wi = idx.slice(targetShape.length - wRank);
out[flat] = v.at(vi) + w.at(wi);
}
return new SOVArray(targetShape, out);
}
// Softmax as Π-map: out_i = exp(v_i) / Σ_j exp(v_j)
export function softmax(v) {
const s = v.data.reduce((a, x) => a + Math.exp(x), 0);
return new SOVArray(v.shape, v.data.map(x => Math.exp(x) / s));
}
// NAND gate — universal boolean connective
export function nandGate(a, b) { return !(a && b); }
// Attention spec over floats: scores = q·k, weights = softmax(scores), out = w·v
export function nandAttention(q, k, v) {
const n = q.shape[0];
const scores = new Array(n).fill(0).map((_, i) =>
new Array(n).fill(0).reduce((acc, _, j) => acc + q.at([i]) * k.at([j]), 0)
);
const w = softmax(new SOVArray([n], scores));
const out = new Array(n).fill(0).map((_, i) =>
new Array(n).fill(0).reduce((acc, _, j) => acc + w.at([i]) * v.at([j]), 0)
);
return new SOVArray([n], out);
}
function unravel(flat, shape) {
const idx = new Array(shape.length).fill(0);
let st = 1;
for (let d = shape.length; d-- > 0;) {
idx[d] = Math.floor(flat / st) % shape[d];
st *= shape[d];
}
return idx;
}
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