playground: implement source so just dev/test/probability work (#6)

The playground/ had its toolchain (Justfile, deno.json, rescript.json) but
empty src/ test/ — every runnable recipe failed. Add a faithful TypeScript
realisation of BetLang's core:

- src/ternary.ts     — Kleene 3-valued logic (T/F/U) + lazy (bet A B C);
                        AND/OR match the table documented in the Justfile
- src/probability.ts — bet/weighted, bet_conditional, seeded RNG, expectation
- src/main.ts        — dev entry point wiring both demos
- examples/uncertainty.ts — interval + Gaussian number-tower sample
- test/*_test.ts     — 10 Deno tests (truth tables, De Morgan, laziness,
                        weighted-draw tolerance, EV convergence)

just dev/test/test-verbose/ternary-demo/probability/uncertainty now all run;
deno check + fmt + lint clean; test is no longer a no-op (10 passed).

Closes #6

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

Author: hyperpolymath

playground/examples/uncertainty.ts

@@ -0,0 +1,81 @@
+// SPDX-License-Identifier: PMPL-1.0-or-later
+// SPDX-FileCopyrightText: 2025 hyperpolymath
+//
+// BetLang playground — uncertainty-aware number tower (sample).
+//
+// The full language exposes ~14 uncertainty number systems as its type
+// system. This example demonstrates two of them — interval arithmetic and
+// Gaussian (mean ± sd) propagation — and how the lazy ternary core lets a
+// comparison return Unknown when two uncertain quantities overlap.
+
+import { type Tri } from '../src/ternary.ts';
+
+/** Closed real interval [lo, hi]. */
+export interface Interval {
+  lo: number;
+  hi: number;
+}
+
+export const iv = (lo: number, hi: number): Interval => ({
+  lo: Math.min(lo, hi),
+  hi: Math.max(lo, hi),
+});
+
+export function addI(a: Interval, b: Interval): Interval {
+  return iv(a.lo + b.lo, a.hi + b.hi);
+}
+
+export function mulI(a: Interval, b: Interval): Interval {
+  const ps = [a.lo * b.lo, a.lo * b.hi, a.hi * b.lo, a.hi * b.hi];
+  return iv(Math.min(...ps), Math.max(...ps));
+}
+
+/** Ternary comparison: definite when disjoint, Unknown when they overlap. */
+export function ltI(a: Interval, b: Interval): Tri {
+  if (a.hi < b.lo) return 'T';
+  if (a.lo > b.hi) return 'F';
+  return 'U';
+}
+
+/** Gaussian number: mean with standard deviation. */
+export interface Gaussian {
+  mu: number;
+  sd: number;
+}
+
+export const gauss = (mu: number, sd: number): Gaussian => ({ mu, sd: Math.abs(sd) });
+
+/** First-order (uncorrelated) propagation through sum and product. */
+export function addG(a: Gaussian, b: Gaussian): Gaussian {
+  return gauss(a.mu + b.mu, Math.hypot(a.sd, b.sd));
+}
+
+export function mulG(a: Gaussian, b: Gaussian): Gaussian {
+  const mu = a.mu * b.mu;
+  const rel = Math.hypot(a.sd / a.mu, b.sd / b.mu);
+  return gauss(mu, Math.abs(mu) * rel);
+}
+
+function main(): void {
+  console.log('=== BetLang Uncertainty Modeling ===\n');
+
+  const a = iv(2, 4);
+  const b = iv(3, 5);
+  console.log(`Intervals: a=[${a.lo},${a.hi}]  b=[${b.lo},${b.hi}]`);
+  console.log(`  a + b = [${addI(a, b).lo}, ${addI(a, b).hi}]`);
+  console.log(`  a * b = [${mulI(a, b).lo}, ${mulI(a, b).hi}]`);
+  console.log(`  a < b ? -> ${ltI(a, b)}  (overlap => Unknown, not a false certainty)`);
+  console.log(`  [0,1] < [5,6] ? -> ${ltI(iv(0, 1), iv(5, 6))}`);
+
+  const g1 = gauss(10, 1);
+  const g2 = gauss(20, 2);
+  const s = addG(g1, g2);
+  const p = mulG(g1, g2);
+  console.log(`\nGaussians: g1=${g1.mu}±${g1.sd}  g2=${g2.mu}±${g2.sd}`);
+  console.log(`  g1 + g2 = ${s.mu}±${s.sd.toFixed(4)}`);
+  console.log(`  g1 * g2 = ${p.mu}±${p.sd.toFixed(4)}`);
+}
+
+if (import.meta.main) {
+  main();
+}

playground/src/main.ts

@@ -0,0 +1,22 @@
+// SPDX-License-Identifier: PMPL-1.0-or-later
+// SPDX-FileCopyrightText: 2025 hyperpolymath
+//
+// BetLang playground entry point (`deno task dev` / `just dev`).
+//
+// Runs the ternary core demo and the probabilistic layer demo in sequence,
+// giving a contributor a single runnable surface for the sandbox.
+
+import { main as ternaryDemo } from './ternary.ts';
+import { main as probabilityDemo } from './probability.ts';
+
+function main(): void {
+  console.log('BetLang Playground — Symbolic Probabilistic Metalanguage\n');
+  ternaryDemo();
+  console.log('\n' + '-'.repeat(60) + '\n');
+  probabilityDemo();
+  console.log('\nDone. See `just --list` for individual demos.');
+}
+
+if (import.meta.main) {
+  main();
+}

playground/src/probability.ts

@@ -0,0 +1,106 @@
+// SPDX-License-Identifier: PMPL-1.0-or-later
+// SPDX-FileCopyrightText: 2025 hyperpolymath
+//
+// BetLang playground — probabilistic layer.
+//
+// Builds the non-uniform / predicate-driven choice forms on top of the
+// lazy ternary core:
+//   (bet/weighted ...)     — non-uniform probabilities
+//   (bet_conditional ...)  — predicate-driven selection
+//
+// Evaluation stays lazy: a Bet is a *description* of a choice; only the
+// branch that wins a draw is forced.
+
+import { bet, type Tri } from './ternary.ts';
+
+/** A lazy, weighted branch: a relative weight and a thunk producing a value. */
+export interface Branch<A> {
+  weight: number;
+  value: () => A;
+}
+
+/** Deterministic, seedable PRNG (mulberry32) so demos/tests are reproducible. */
+export function rng(seed: number): () => number {
+  let s = seed >>> 0;
+  return () => {
+    s = (s + 0x6d2b79f5) >>> 0;
+    let t = s;
+    t = Math.imul(t ^ (t >>> 15), t | 1);
+    t ^= t + Math.imul(t ^ (t >>> 7), t | 61);
+    return ((t ^ (t >>> 14)) >>> 0) / 4294967296;
+  };
+}
+
+/** Force exactly one branch, chosen with probability proportional to weight. */
+export function betWeighted<A>(branches: Branch<A>[], draw: () => number): A {
+  const total = branches.reduce((acc, b) => acc + b.weight, 0);
+  if (total <= 0) throw new Error('betWeighted: weights must sum to a positive number');
+  let r = draw() * total;
+  for (const b of branches) {
+    r -= b.weight;
+    if (r <= 0) return b.value();
+  }
+  return branches[branches.length - 1].value(); // float-rounding fallback
+}
+
+/**
+ * Predicate-driven ternary selection. The predicate yields a Tri; a definite
+ * answer takes the matching branch, Unknown defers to the `uncertain` branch.
+ */
+export function betConditional<A>(
+  predicate: () => Tri,
+  ifTrue: () => A,
+  uncertain: () => A,
+  ifFalse: () => A,
+): A {
+  return bet(predicate, ifTrue, uncertain, ifFalse);
+}
+
+/** Monte-Carlo expectation of a numeric weighted bet over `n` samples. */
+export function expectation(branches: Branch<number>[], n: number, draw: () => number): number {
+  let sum = 0;
+  for (let i = 0; i < n; i++) sum += betWeighted(branches, draw);
+  return sum / n;
+}
+
+export function main(): void {
+  console.log('=== BetLang Probabilistic Layer ===\n');
+
+  // A loaded three-sided "coin": 60% True, 30% Unknown, 10% False.
+  const loaded: Branch<Tri>[] = [
+    { weight: 0.6, value: () => 'T' as Tri },
+    { weight: 0.3, value: () => 'U' as Tri },
+    { weight: 0.1, value: () => 'F' as Tri },
+  ];
+  const draw = rng(42);
+  const counts: Record<Tri, number> = { T: 0, U: 0, F: 0 };
+  const N = 100_000;
+  for (let i = 0; i < N; i++) counts[betWeighted(loaded, draw)]++;
+  console.log(`Empirical distribution over ${N.toLocaleString()} draws (target 0.60/0.30/0.10):`);
+  console.log(
+    `  T=${(counts.T / N).toFixed(3)}  U=${(counts.U / N).toFixed(3)}  ` +
+      `F=${(counts.F / N).toFixed(3)}`,
+  );
+
+  // Expected payout of a weighted numeric bet.
+  const payout: Branch<number>[] = [
+    { weight: 1, value: () => 100 },
+    { weight: 2, value: () => 10 },
+    { weight: 7, value: () => 0 },
+  ];
+  const ev = expectation(payout, 200_000, rng(7));
+  console.log(`\nExpected payout (analytic = 12.0): ${ev.toFixed(2)}`);
+
+  // Conditional choice that stays total under Unknown.
+  const choice = betConditional(
+    () => 'U' as Tri,
+    () => 'committed',
+    () => 'hedged (predicate was Unknown)',
+    () => 'declined',
+  );
+  console.log(`\nbet_conditional under Unknown -> ${choice}`);
+}
+
+if (import.meta.main) {
+  main();
+}

playground/src/ternary.ts

@@ -0,0 +1,106 @@
+// SPDX-License-Identifier: PMPL-1.0-or-later
+// SPDX-FileCopyrightText: 2025 hyperpolymath
+//
+// BetLang playground — ternary core.
+//
+// BetLang's minimal core is a Kleene strong three-valued logic over
+// { True, False, Unknown } plus the lazy ternary choice primitive
+//   (bet A B C)
+// where only the selected branch is ever evaluated.
+//
+// The AND truth table here is exactly the one documented in the playground
+// Justfile (`just ternary-demo`): conjunction is `min`, disjunction is `max`
+// under the order  F < U < T.
+
+/** The three logical values of the BetLang core. */
+export type Tri = 'T' | 'F' | 'U';
+
+const ORDER: Record<Tri, number> = { F: 0, U: 1, T: 2 };
+const BY_RANK: Tri[] = ['F', 'U', 'T'];
+
+/** Kleene negation: swaps T/F, fixes U. */
+export function not(a: Tri): Tri {
+  if (a === 'T') return 'F';
+  if (a === 'F') return 'T';
+  return 'U';
+}
+
+/** Kleene conjunction = min under F < U < T. */
+export function and(a: Tri, b: Tri): Tri {
+  return BY_RANK[Math.min(ORDER[a], ORDER[b])];
+}
+
+/** Kleene disjunction = max under F < U < T. */
+export function or(a: Tri, b: Tri): Tri {
+  return BY_RANK[Math.max(ORDER[a], ORDER[b])];
+}
+
+/** Material implication, defined as `or(not(a), b)`. */
+export function implies(a: Tri, b: Tri): Tri {
+  return or(not(a), b);
+}
+
+/**
+ * The lazy ternary choice primitive `(bet A B C)`.
+ *
+ * Branches are passed as thunks; exactly one is forced. `selector` decides
+ * which branch wins — when it returns 'U' the middle branch is taken, which
+ * is what makes the choice *total* even under uncertainty.
+ */
+export function bet<A>(
+  selector: () => Tri,
+  onTrue: () => A,
+  onUnknown: () => A,
+  onFalse: () => A,
+): A {
+  switch (selector()) {
+    case 'T':
+      return onTrue();
+    case 'F':
+      return onFalse();
+    default:
+      return onUnknown();
+  }
+}
+
+/** Render a full binary truth table for a Tri operator. */
+function table(name: string, op: (a: Tri, b: Tri) => Tri): string {
+  const vals: Tri[] = ['T', 'U', 'F'];
+  const rows = vals.flatMap((a) => vals.map((b) => `  ${a} ${name} ${b} = ${op(a, b)}`));
+  return [`${name} truth table:`, ...rows].join('\n');
+}
+
+export function main(): void {
+  console.log('=== BetLang Ternary Core ===');
+  console.log('Values: True (T), False (F), Unknown (U)\n');
+  console.log(table('AND', and));
+  console.log();
+  console.log(table('OR', or));
+  console.log();
+  console.log('NOT: NOT T = ' + not('T') + ', NOT U = ' + not('U') + ', NOT F = ' + not('F'));
+  console.log();
+
+  // Laziness demonstration: only the selected thunk runs.
+  let evaluated = '';
+  const result = bet(
+    () => 'U',
+    () => {
+      evaluated = 'true-branch';
+      return 1;
+    },
+    () => {
+      evaluated = 'unknown-branch';
+      return 0;
+    },
+    () => {
+      evaluated = 'false-branch';
+      return -1;
+    },
+  );
+  console.log(`Lazy (bet ? : :) on Unknown -> result=${result}, evaluated=${evaluated}`);
+  console.log('(only the Unknown branch ran; True/False thunks were never forced)');
+}
+
+if (import.meta.main) {
+  main();
+}

playground/test/probability_test.ts

@@ -0,0 +1,56 @@
+// SPDX-License-Identifier: PMPL-1.0-or-later
+// SPDX-FileCopyrightText: 2025 hyperpolymath
+
+import { assert, assertEquals, assertThrows } from '@std/assert';
+import { betConditional, betWeighted, type Branch, expectation, rng } from '../src/probability.ts';
+import { type Tri } from '../src/ternary.ts';
+
+Deno.test('rng is deterministic for a fixed seed and stays in [0,1)', () => {
+  const a = rng(123);
+  const b = rng(123);
+  for (let i = 0; i < 50; i++) {
+    const x = a();
+    assertEquals(x, b());
+    assert(x >= 0 && x < 1);
+  }
+});
+
+Deno.test('betWeighted respects weights within Monte-Carlo tolerance', () => {
+  const branches: Branch<Tri>[] = [
+    { weight: 0.6, value: () => 'T' },
+    { weight: 0.3, value: () => 'U' },
+    { weight: 0.1, value: () => 'F' },
+  ];
+  const draw = rng(42);
+  const counts: Record<Tri, number> = { T: 0, U: 0, F: 0 };
+  const N = 50_000;
+  for (let i = 0; i < N; i++) counts[betWeighted(branches, draw)]++;
+  assert(Math.abs(counts.T / N - 0.6) < 0.02);
+  assert(Math.abs(counts.U / N - 0.3) < 0.02);
+  assert(Math.abs(counts.F / N - 0.1) < 0.02);
+});
+
+Deno.test('betWeighted rejects non-positive total weight', () => {
+  assertThrows(() => betWeighted([{ weight: 0, value: () => 1 }], rng(1)));
+});
+
+Deno.test('expectation converges to the analytic mean', () => {
+  const payout: Branch<number>[] = [
+    { weight: 1, value: () => 100 },
+    { weight: 2, value: () => 10 },
+    { weight: 7, value: () => 0 },
+  ];
+  // analytic EV = (1*100 + 2*10 + 7*0) / 10 = 12
+  assert(Math.abs(expectation(payout, 100_000, rng(7)) - 12) < 0.5);
+});
+
+Deno.test('betConditional defers to the uncertain branch on Unknown', () => {
+  assertEquals(
+    betConditional(() => 'U', () => 'yes', () => 'maybe', () => 'no'),
+    'maybe',
+  );
+  assertEquals(
+    betConditional(() => 'T', () => 'yes', () => 'maybe', () => 'no'),
+    'yes',
+  );
+});