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Extend tree arity to all perfect squares #5

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Feb 9, 2025
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Extend tree arity to all perfect squares #5

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97 changes: 45 additions & 52 deletions main.js
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Original file line number Diff line number Diff line change
Expand Up @@ -43,30 +43,6 @@ const drawScreen = (worker, ctxs, colors) => {
worker.postMessage({ drawScreen: [colors, ctxs] });
};

const ctxTopLeft = (ctx) => {
const x = [ctx.x[0], ctx.x[0] + (ctx.x[1] - ctx.x[0]) / 2];
const y = [ctx.y[0], ctx.y[0] + (ctx.y[1] - ctx.y[0]) / 2];
return { x, y };
};

const ctxTopRight = (ctx) => {
const x = [ctx.x[0] + (ctx.x[1] - ctx.x[0]) / 2, ctx.x[1]];
const y = [ctx.y[0], ctx.y[0] + (ctx.y[1] - ctx.y[0]) / 2];
return { x, y };
};

const ctxBottomLeft = (ctx) => {
const x = [ctx.x[0], ctx.x[0] + (ctx.x[1] - ctx.x[0]) / 2];
const y = [ctx.y[0] + (ctx.y[1] - ctx.y[0]) / 2, ctx.y[1]];
return { x, y };
};

const ctxBottomRight = (ctx) => {
const x = [ctx.x[0] + (ctx.x[1] - ctx.x[0]) / 2, ctx.x[1]];
const y = [ctx.y[0] + (ctx.y[1] - ctx.y[0]) / 2, ctx.y[1]];
return { x, y };
};

/* lambda calculus */

// ---
Expand Down Expand Up @@ -349,15 +325,25 @@ const toColor = (t) => {
return UNKNOWN;
};

// [((((0 tl) tr) bl) br)]
const seemsScreeny = (t) =>
t.type === "abs" &&
t.body.type === "app" &&
t.body.left.type === "app" &&
t.body.left.left.type === "app" &&
t.body.left.left.left.type === "app" &&
t.body.left.left.left.left.type === "idx" &&
t.body.left.left.left.left.idx === 0;
// [((((0 tl) tr) bl) br) ...]
// (or more, as long as n is perfect square)
const seemsScreeny = (t) => {
if (t.type !== "abs") return false;
t = t.body;
let d = 0;
while ((d++, t.type === "app")) t = t.left;
return d > 4 && Math.sqrt(d - 1) % 1 === 0 && t.type === "idx" && t.idx === 0
? d - 1
: false;
};

const getSubScreens = (t) => {
if (t.type !== "abs") return false;
t = t.body;
let ts = [];
while (t.type === "app" && ts.unshift(t)) t = t.left;
return ts;
};

const clearScreen = (worker) => {
worker.postMessage({ clear: true });
Expand Down Expand Up @@ -501,7 +487,7 @@ const whnf = (t) => {
};

// screen normal form
// one of [((((0 tl) tr) bl) br)], [[0]], [[1]]
// one of [((((0 tl) tr) bl) br) ...], [[0]], [[1]]
// TODO: Is this form of caching fundamentally wrong? (incongruences after subst or idx shifts!?)
// Does this only work accidentally because of WHNF, deliberate symmetry and closed terms or sth?
const snfCache = {};
Expand Down Expand Up @@ -575,28 +561,35 @@ const reduceLoop = (conf, _t) => {
// smaller resolutions apparently crash the browser tab lol
if (ctx.x[1] - ctx.x[0] < MAXRES) continue;

if (seemsScreeny(t)) {
const tl = t.body.left.left.left.right;
const tlCtx = ctxTopLeft(ctx);
stack.push({ ctx: tlCtx, t: tl });
let n;
if ((n = seemsScreeny(t))) {
const subScreens = getSubScreens(t);
console.assert(n == subScreens.length);

const tr = t.body.left.left.right;
const trCtx = ctxTopRight(ctx);
stack.push({ ctx: trCtx, t: tr });
const splitSize = Math.sqrt(n);
const ctxWidth = (ctx.x[1] - ctx.x[0]) / splitSize;
const ctxHeight = (ctx.y[1] - ctx.y[0]) / splitSize;

const bl = t.body.left.right;
const blCtx = ctxBottomLeft(ctx);
stack.push({ ctx: blCtx, t: bl });
const ctxs = [];
const colors = [];

const br = t.body.right;
const brCtx = ctxBottomRight(ctx);
stack.push({ ctx: brCtx, t: br });
let x0 = ctx.x[0];
let y0 = ctx.y[0];

for (let i = 0; i < n; i++) {
const current = subScreens[i];
const subCtx = { x: [x0, x0 + ctxWidth], y: [y0, y0 + ctxHeight] };
ctxs.push(subCtx);
stack.push({ ctx: subCtx, t: current.right });
colors.push(toColor(current.right));

if ((i + 1) % splitSize == 0) {
x0 = ctx.x[0];
y0 += ctxHeight;
} else x0 += ctxWidth;
}

drawScreen(
worker,
[tlCtx, trCtx, blCtx, brCtx],
[toColor(tl), toColor(tr), toColor(bl), toColor(br)],
);
drawScreen(worker, ctxs, colors);
} else {
// TODO: could we risk gnfing here?
drawAt(worker, ctx.x, ctx.y, toColor(t));
Expand Down