feat(fsharp): m01-m06 util, model, rules, random, spawn, game, view with Expecto tests

Co-Authored-By: Claude Opus 5.5 <[email protected]>

fsharp/solutions/Game.fs

@@ -0,0 +1,38 @@
+/// m05 game: one `update` turns every action into a new state; replaying a game is a fold over its actions.
+/// m10 adds pause, restart and a frame clock that speeds up as the score grows.
+module Snake.Game
+
+open Snake.Model
+
+/// How many frames pass between game steps: 8 at first, one fewer every 3 points, never fewer than 2.
+let movesEvery (score: int) : int = max 2 (8 - score / 3)
+
+// One animation frame: count it, and every `movesEvery score`-th frame run a game step.
+let private frame (state: GameState) : GameState =
+    if state.Status <> Playing then
+        state
+    else
+        let counted = { state with Frame = state.Frame + 1 }
+        if counted.Frame % movesEvery counted.Score = 0 then Spawn.tick counted else counted
+
+// Pause and resume only make sense in those two statuses; a finished game stays finished.
+let private togglePause (state: GameState) : GameState =
+    match state.Status with
+    | Playing -> { state with Status = Paused }
+    | Paused -> { state with Status = Playing }
+    | GameOver
+    | Won -> state
+
+// Every case is listed (no `| _ ->`): adding an Action later makes the compiler point here.
+let update (state: GameState) (action: Action) : GameState =
+    match action with
+    | Tick -> Spawn.tick state
+    | Turn dir -> Rules.turn state dir
+    | TogglePause -> togglePause state
+    | Restart -> Spawn.newGame state.Seed
+    | Frame -> frame state
+
+let replay (state: GameState) (actions: Action list) : GameState = List.fold update state actions
+
+// List.scan is List.fold that keeps every intermediate result (the start state included).
+let history (state: GameState) (actions: Action list) : GameState list = List.scan update state actions