ocaml: phase 5.1 hist.ml baseline (Hashtbl int histogram, total * max = 75)

Three small functions:

  hist xs       build a Hashtbl of count-by-value
  max_value h   Hashtbl.fold to find the max bin
  total h       Hashtbl.fold to sum all bins

For the 15-element list [1;2;3;1;4;5;1;2;6;7;1;8;9;1;0]:
  total      = 15
  max_value  =  5 (the number 1 appears 5 times)
  product    = 75

Companion to bag.ml (string keys) and frequency.ml (char keys) —
same Hashtbl.fold + Hashtbl.find_opt pattern, exercised on int
keys this time.

71 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -31,6 +31,7 @@
   "group_consec.ml": 53,
   "hailstone.ml": 111,
   "hanoi.ml": 1023,
+  "hist.ml": 75,
   "fizzbuzz.ml": 57,
   "flatten_tree.ml": 28,
   "list_ops.ml": 30,

lib/ocaml/baseline/hist.ml

@@ -0,0 +1,21 @@
+let hist xs =
+  let h = Hashtbl.create 8 in
+  List.iter (fun x ->
+    let n = match Hashtbl.find_opt h x with
+            | Some n -> n + 1
+            | None -> 1
+    in
+    Hashtbl.replace h x n
+  ) xs;
+  h
+
+let max_value h =
+  Hashtbl.fold (fun _ v acc -> if v > acc then v else acc) h 0
+
+let total h =
+  Hashtbl.fold (fun _ v acc -> acc + v) h 0
+
+;;
+
+let h = hist [1;2;3;1;4;5;1;2;6;7;1;8;9;1;0] in
+total h * max_value h

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 — hist.ml baseline (Hashtbl-based int
+  histogram, total * max = 75). Three small functions: hist builds
+  the count table, max_value finds the maximum bin, total sums all
+  bins. For a 15-element list with a top frequency of 5 (the
+  number 1), product = 75. Companions to bag.ml (string keys) and
+  frequency.ml (char keys) — same Hashtbl.fold + Hashtbl.find_opt
+  pattern, exercised on int keys this time. 71 baseline programs
+  total.
 - 2026-05-09 Phase 5.1 — mortgage.ml baseline (monthly mortgage
   payment formula, 200k @ 5% / 30y → $1073). Manual `(1+r)^n`
   computed via for-loop because `Float.pow` may not be available