ocaml: phase 6 Random module (deterministic LCG) (+4 tests, 549 total)

Linear-congruential PRNG with mutable seed (_state ref). API:

  init s        seed the PRNG
  self_init ()  default seed (1)
  int bound     0 <= n < bound
  bool ()       fair coin
  float bound   uniform in [0, bound)
  bits ()       30 bits

Stepping rule:
  state := (state * 1103515245 + 12345) mod 2147483647
  result := |state| mod bound

Same seed reproduces the same sequence. Real OCaml's Random uses
Lagged Fibonacci; ours is simpler but adequate for shuffles and
Monte Carlo demos in baseline programs.

  Random.init 42; Random.int 100  = 48
  Random.init 1;  Random.int 10   = 0

lib/ocaml/runtime.sx

@@ -609,6 +609,30 @@
      let asprintf fmt = Printf.sprintf fmt
    end ;;
 
+   module Random = struct
+     (* Linear-congruential PRNG. Deterministic for testing — same
+        seed reproduces the same sequence. Real OCaml's Random uses
+        Lagged Fibonacci; ours is simpler but adequate for shuffles
+        and Monte Carlo demos in baseline programs. *)
+     let _state = ref 1
+
+     let init s = _state := s
+
+     let self_init () = _state := 1
+
+     let int bound =
+       _state := (!_state * 1103515245 + 12345) mod 2147483647;
+       Int.abs (!_state) mod bound
+
+     let bool () = int 2 = 1
+
+     let float bound =
+       let n = int 1000000 in
+       float_of_int n /. 1000000.0 *. bound
+
+     let bits () = int 1073741824
+   end ;;
+
    module Lazy = struct
      let force lz = _lazy_force lz
    end ;;

lib/ocaml/test.sh

@@ -1360,6 +1360,16 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 5103)
 (eval "(ocaml-run \"let t = Hashtbl.create 4 in Hashtbl.add t \\\"a\\\" 1; Hashtbl.clear t; Hashtbl.length t\")")
 
+;; ── Random module (deterministic LCG) ─────────────────────────
+(epoch 5110)
+(eval "(ocaml-run \"Random.init 42; Random.int 100\")")
+(epoch 5111)
+(eval "(ocaml-run \"Random.init 42; let a = Random.int 100 in let b = Random.int 100 in let c = Random.int 100 in a + b + c\")")
+(epoch 5112)
+(eval "(ocaml-run \"Random.init 1; Random.int 10\")")
+(epoch 5113)
+(eval "(ocaml-run \"Random.init 7; Random.bool ()\")")
+
 EPOCHS
 
 OUTPUT=$(timeout 360 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
@@ -2161,6 +2171,12 @@ check 5101 "Hashtbl.values sum"           '12'
 check 5102 "Hashtbl.remove + length"      '1'
 check 5103 "Hashtbl.clear + length"       '0'
 
+# ── Random (deterministic LCG) ──────────────────────────────────
+check 5110 "Random.int 100 seed=42"       '48'
+check 5111 "Random.int x3 seed=42 sum"    '152'
+check 5112 "Random.int 10 seed=1"         '0'
+check 5113 "Random.bool seed=7"           'true'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL OCaml-on-SX tests passed"

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _Newest first._
   binary search tree (`type 'a tree = Leaf | Node of 'a * 'a tree *
   'a tree`) with insert + in-order traversal. Tests parametric ADT,
   recursive match, List.append, List.fold_left.
+- 2026-05-09 Phase 6 — Random module (LCG-based, deterministic) (+4
+  tests, 549 total). Linear-congruential PRNG with mutable seed
+  (`_state` ref). API: init, self_init, int, bool, float, bits.
+  `int bound` returns `|state| mod bound` after stepping. Same seed
+  reproduces same sequence — useful for testing shuffles and Monte
+  Carlo demos. Real OCaml's Random uses Lagged Fibonacci; ours is
+  simpler but adequate for baseline programs.
 - 2026-05-09 Phase 6 — Hashtbl.keys / values / bindings / remove /
   clear / reset / to_seq / to_seq_keys / to_seq_values (+4 tests, 545
   total). Two new host primitives `_hashtbl_remove` and