feat(course): audit fixes and twelve extensions (Modules 7b, 12, 13)

Audit pass:
- Frame rule counts frames since the last move, so every step lasts
  exactly movesEvery(score) frames, also right after a speed-up
- clampTime + MAX_GAP_MS: a hidden tab no longer replays the whole gap
- Pong Restart keeps held keys
- Fact corrections (mulberry32 output coverage, Haskell IO, uniform)
- New fixture cases from a mutation analysis

Extensions (all three tracks, shared fixtures, course text):
- Turn queue (Exercise 10.6), persisted high score (10.7),
  replay viewer (10.8), play() end-to-end helper (9.5)
- Optional State (4.7) and optional Module 7b, stack-safe IO
- Module 12, property-based testing with generators, shrinking,
  invariants and a model-based oracle
- Module 13, Conway's Life with a Click event
- JS type checking via jsconfig, JSDoc and types.d.ts
- Maintainer tools: scripts/mutate.mjs, scripts/typecheck-js.sh,
  Playwright end-to-end suite (e2e/, scripts/e2e.sh)

Docs: docs/contract.md is the canonical contract; specs and build log
under docs/superpowers.

Verified: JS 728, Scala 689, F# 691 unit tests; stubs and progression
M01-M13 and M07b; 176 end-to-end tests on Chromium and WebKit.

Co-Authored-By: Claude Fable 5.2 <noreply@anthropic.com>

scala/solutions/life/App.scala

@@ -0,0 +1,36 @@
+package snake
+package life
+
+import LifeModel.*
+
+/** m13 life app: the same wiring as Snake and Pong, with a third kind of input, the mouse. */
+object LifeApp:
+
+  val GEN_MS: Long = 150
+
+  def lifeKey(key: String): Option[LifeAction] = key match
+    case " "       => Some(LifeAction.TogglePause)
+    case "n" | "N" => Some(LifeAction.Step)
+    case "c" | "C" => Some(LifeAction.Clear)
+    case "r" | "R" => Some(LifeAction.Randomize)
+    case _         => None
+
+  // The pixel is checked before dividing: integer division rounds towards zero, so -1 / 16 would be cell 0.
+  def lifeClick(x: Int, y: Int): Option[LifeAction] =
+    if x >= 0 && y >= 0 && x / LCELL < LW && y / LCELL < LH then Some(LifeAction.Toggle(Point(x / LCELL, y / LCELL)))
+    else None
+
+  lazy val lifeActions: Stream[LifeAction] =
+    Stream
+      .interval(GEN_MS)
+      .map(_ => LifeAction.Frame)
+      .merge(Stream.keyDowns.filterMap(lifeKey))
+      .merge(Stream.clicks.filterMap(lifeClick(_, _)))
+
+  def lifeStates(seed: Long, actions: Stream[LifeAction]): Stream[LifeState] =
+    actions.scan(initialLife(seed))(LifeRules.lifeUpdate).startWith(initialLife(seed))
+
+  lazy val lifeMain: IO[Stream[IO[Unit]]] =
+    IO.randomSeed.map(seed =>
+      lifeStates(seed, lifeActions).map(state => IO.drawScene(LifeView.lifeView(state))).clampTime(App.MAX_GAP_MS)
+    )

scala/solutions/life/Model.scala

@@ -0,0 +1,32 @@
+package snake
+package life
+
+// m13 life model: the whole world is one value, like the snake and the match.
+
+/**
+ * The whole world. `cells` are the live cells, always kept canonical: sorted row-major (by `y`, then by `x`), each cell
+ * at most once, all on the board. `seed` is the unsigned 32-bit seed that `Randomize` draws from; `generation` counts
+ * the generations since the board was last cleared or randomized.
+ */
+final case class LifeState(cells: List[Point], running: Boolean, seed: Long, generation: Int)
+
+/** Everything that can happen to the world, as data. `Toggle` carries the cell that was clicked. */
+enum LifeAction:
+  case Frame
+  case Toggle(cell: Point)
+  case TogglePause, Step, Clear, Randomize
+
+object LifeModel:
+
+  // The board, in cells: LW columns, LH rows, LCELL pixels per cell. Below it the page shows a status strip.
+  val LW = 40
+  val LH = 30
+
+  /** Pixels per cell. */
+  val LCELL = 16
+
+  /** Height of the status strip under the board, in pixels. */
+  val STRIP = 24
+
+  /** A fresh world: no live cells, paused, the given seed, generation 0. */
+  def initialLife(seed: Long): LifeState = LifeState(Nil, running = false, seed, generation = 0)

scala/solutions/life/Rules.scala

@@ -0,0 +1,59 @@
+package snake
+package life
+
+import LifeModel.*
+
+/** m13 life rules: the next generation is a function of the whole old board, and nothing else. */
+object LifeRules:
+
+  // Every cell of the board, row-major (y, then x). Filtering this list keeps any result in canonical order for free.
+  private val board: List[Point] = (for y <- 0 until LH; x <- 0 until LW yield Point(x, y)).toList
+
+  private def onBoard(p: Point): Boolean = p.x >= 0 && p.x < LW && p.y >= 0 && p.y < LH
+
+  // A cell's position in row-major order: the order the canonical list is sorted by.
+  private def index(p: Point): Int = p.y * LW + p.x
+
+  private val offsets = List((-1, -1), (0, -1), (1, -1), (-1, 0), (1, 0), (-1, 1), (0, 1), (1, 1))
+
+  // The up to eight neighbours of `p` that are on the board (the edges are dead: nothing wraps around).
+  private def neighbours(p: Point): List[Point] =
+    offsets.map((dx, dy) => Point(p.x + dx, p.y + dy)).filter(onBoard)
+
+  // B3/S23, every cell judged on the *old* list only. A Set of the old cells makes "is this neighbour alive?" one
+  // lookup, so a generation is 1200 x 8 lookups however many cells live.
+  def lifeStep(cells: List[Point]): List[Point] =
+    val alive = cells.toSet
+    board.filter { p =>
+      val n = neighbours(p).count(alive)
+      n == 3 || (n == 2 && alive(p))
+    }
+
+  // Add a dead cell or remove a live one, keeping the list sorted row-major without duplicates. Off the board: unchanged.
+  private def toggle(cells: List[Point], p: Point): List[Point] =
+    if !onBoard(p) then cells
+    else if cells.contains(p) then cells.filterNot(_ == p)
+    else cells.filter(index(_) < index(p)) ++ (p :: cells.filter(index(_) > index(p)))
+
+  // One intBelow(4) per board cell in row-major order, the cell alive when the draw is 0 (about one cell in four).
+  // A fold carries the seed; the live cells are collected in reverse and turned round once at the end.
+  private def randomCells(seed: Long): (List[Point], Long) =
+    val (aliveReversed, next) = board.foldLeft((List.empty[Point], seed)) { case ((acc, s), p) =>
+      val (d, s2) = Random.intBelow(4).run(s)
+      (if d == 0 then p :: acc else acc, s2)
+    }
+    (aliveReversed.reverse, next)
+
+  private def nextGeneration(state: LifeState): LifeState =
+    state.copy(cells = lifeStep(state.cells), generation = state.generation + 1)
+
+  def lifeUpdate(state: LifeState, action: LifeAction): LifeState = action match
+    case LifeAction.Frame       => if state.running then nextGeneration(state) else state
+    case LifeAction.Step        => if state.running then state else nextGeneration(state)
+    case LifeAction.TogglePause => state.copy(running = !state.running)
+    // Clicking edits the world whether it runs or not: the click is one action between two generations.
+    case LifeAction.Toggle(cell) => state.copy(cells = toggle(state.cells, cell))
+    case LifeAction.Clear        => state.copy(cells = Nil, generation = 0)
+    case LifeAction.Randomize =>
+      val (cells, seed) = randomCells(state.seed)
+      state.copy(cells = cells, seed = seed, generation = 0)

scala/solutions/life/View.scala

@@ -0,0 +1,21 @@
+package snake
+package life
+
+import LifeModel.*
+
+/** m13 life view: live cells as squares, and a status strip under the board. */
+object LifeView:
+
+  private val W = LW * LCELL
+  private val H = LH * LCELL
+
+  private def text(x: Int, y: Int, str: String, align: String): Shape = Shape.Text(x, y, str, "#ffffff", 14, align)
+
+  def lifeView(state: LifeState): Scene =
+    Shape.Rect(0, 0, W, H, "#111111") ::
+      state.cells.map(p => Shape.Rect(p.x * LCELL + 1, p.y * LCELL + 1, LCELL - 2, LCELL - 2, "#7cb342")) ++
+      List(
+        Shape.Rect(0, H, W, STRIP, "#222222"),
+        text(6, H + 17, s"Generation ${state.generation}", "left"),
+        text(W - 6, H + 17, if state.running then "Running: Space pauses" else "Paused: Space runs, N steps", "right")
+      )