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/Random.fs

@@ -0,0 +1,31 @@
+/// m04 random: a tiny "state monad" for randomness. A Random<'a> wraps a function seed -> (value, nextSeed),
+/// so every draw is a pure function and the seed is passed along explicitly instead of hidden.
+/// Seeds and values are unsigned 32-bit numbers (uint32).
+module Snake.Random
+
+type Random<'a> = Random of (uint32 -> 'a * uint32)
+
+let run (seed: uint32) (Random f: Random<'a>) : 'a * uint32 = f seed
+
+let pure (a: 'a) : Random<'a> = Random(fun seed -> (a, seed))
+
+let map (f: 'a -> 'b) (r: Random<'a>) : Random<'b> =
+    Random(fun seed ->
+        let a, next = run seed r
+        (f a, next))
+
+let bind (f: 'a -> Random<'b>) (r: Random<'a>) : Random<'b> =
+    Random(fun seed ->
+        let a, next = run seed r
+        run next (f a))
+
+// mulberry32. uint32 arithmetic wraps around at 2^32 (F# operators are unchecked) and `>>>` on uint32 is an
+// unsigned shift, so the formula can be written down as it is.
+let nextUint32: Random<uint32> =
+    Random(fun seed ->
+        let s = seed + 0x6D2B79F5u
+        let t1 = (s ^^^ (s >>> 15)) * (s ||| 1u)
+        let t2 = t1 ^^^ (t1 + (t1 ^^^ (t1 >>> 7)) * (t1 ||| 61u))
+        (t2 ^^^ (t2 >>> 14), s))
+
+let intBelow (n: int) : Random<int> = map (fun v -> int (v % uint32 n)) nextUint32