ocaml: phase 5.1 bag.ml baseline + String.equal/compare/cat/empty (+3 tests, 579 total)

bag.ml: split a sentence on spaces, count each word in a Hashtbl,
return the maximum count via Hashtbl.fold.

  count_words 'the quick brown fox jumps over the lazy dog the fox'
  -> Hashtbl with 'the' = 3 as the max
  -> 3

Exercises String.split_on_char + Hashtbl.find_opt/replace +
Hashtbl.fold (k v acc -> ...). Together with frequency.ml from
iter 84 we now have two Hashtbl-counting baselines exercising
slightly different idioms. 29 baseline programs total.

String additions:
  equal a b      = a = b
  compare a b    = -1 / 0 / 1 via host < / >
  cat a b        = a ^ b
  empty          = '' (constant)

lib/ocaml/baseline/bag.ml

@@ -0,0 +1,18 @@
+let count_words text =
+  let words = String.split_on_char ' ' text in
+  let counts = Hashtbl.create 8 in
+  List.iter (fun w ->
+    let n = match Hashtbl.find_opt counts w with
+            | Some n -> n + 1
+            | None -> 1
+    in
+    Hashtbl.replace counts w n
+  ) words;
+  counts
+
+let max_count counts =
+  Hashtbl.fold (fun _ v acc -> if v > acc then v else acc) counts 0
+
+;;
+
+max_count (count_words "the quick brown fox jumps over the lazy dog the fox")

lib/ocaml/baseline/expected.json

@@ -1,5 +1,6 @@
 {
   "anagrams.ml": 3,
+  "bag.ml": 3,
   "bfs.ml": 6,
   "btree.ml": 39,
   "brainfuck.ml": 75,

lib/ocaml/runtime.sx

@@ -447,6 +447,11 @@
          | h :: t -> aux t (acc ^ h)
        in
        aux xs \"\"
+     let equal a b = a = b
+     let compare a b =
+       if a < b then -1 else if a > b then 1 else 0
+     let cat a b = a ^ b
+     let empty = \"\"
    end ;;
 
    module Bytes = struct

lib/ocaml/test.sh

@@ -1440,6 +1440,14 @@ cat > "$TMPFILE" << 'EPOCHS'
 (epoch 5193)
 (eval "(ocaml-run \"Seq.fold_left (+) 0 (Seq.unfold (fun n -> if n > 4 then None else Some (n, n + 1)) 1)\")")
 
+;; ── String.equal / compare / cat ─────────────────────────────
+(epoch 5200)
+(eval "(ocaml-run \"String.equal \\\"abc\\\" \\\"abc\\\"\")")
+(epoch 5201)
+(eval "(ocaml-run \"String.compare \\\"banana\\\" \\\"apple\\\"\")")
+(epoch 5202)
+(eval "(ocaml-run \"String.cat \\\"hello \\\" \\\"world\\\"\")")
+
 EPOCHS
 
 OUTPUT=$(timeout 360 "$SX_SERVER" < "$TMPFILE" 2>/dev/null)
@@ -2290,6 +2298,11 @@ check 5191 "Seq filter evens"             '5'
 check 5192 "Seq init 5 i*2"               '20'
 check 5193 "Seq unfold 1..4 sum"          '10'
 
+# ── String.equal / compare / cat ────────────────────────────────
+check 5200 "String.equal abc abc"         'true'
+check 5201 "String.compare banana apple"  '1'
+check 5202 "String.cat hello world"       '"hello world"'
+
 TOTAL=$((PASS + FAIL))
 if [ $FAIL -eq 0 ]; then
   echo "ok $PASS/$TOTAL OCaml-on-SX tests passed"

plans/ocaml-on-sx.md

@@ -407,6 +407,14 @@ _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 5.1 — bag.ml baseline + String.equal/compare/cat/
+  empty (+3 tests, 579 total). bag.ml: split a sentence on spaces,
+  count word frequency in a Hashtbl, return the maximum count.
+  Sentence "the quick brown fox jumps over the lazy dog the fox" has
+  "the"×3 as the most frequent → 3. Exercises String.split_on_char +
+  Hashtbl.find_opt/replace + Hashtbl.fold over (k, v) tuples. 29
+  baseline programs total. String additions: equal, compare (via host
+  `<`/`>`), cat (alias of `^`), empty.
 - 2026-05-09 Phase 5.1 — fraction.ml baseline (rational arithmetic
   via record + gcd canonicalization). Defines `type frac = { num;
   den }`, `make` that reduces via gcd and forces den > 0, `add` and