ocaml: phase 5.1 trie.ml baseline (prefix tree, 6/9 word lookups match)

Mutable-record trie with linked-list children:

  type trie = {
    mutable terminal : bool;
    mutable children : (char * trie) list
  }

Insert {cat, car, card, cart, dog, doge}; lookup 9 words. Hits are
exactly the inserted set: cat, car, card, cart, dog, doge = 6.
Misses: ca (prefix not terminal), dogs (extends 'dog' but no 'dogs'
node), x (no path).

Tests:
  - recursive type definition with self-referential field
  - mutable record fields with .field <- v
  - Option pattern matching (Some / None)
  - tuple-cons pattern (k, v) :: rest

146 baseline programs total.

plans/ocaml-on-sx.md

@@ -407,6 +407,16 @@ _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.
+- 2026-05-10 Phase 5.1 — trie.ml baseline (prefix tree, 6 of 9
+  word lookups match). Mutable record `{ terminal; children }` with
+  `children : (char * trie) list`; insert recurses down character
+  by character, mutating children list when a path is missing.
+  Insert {cat, car, card, cart, dog, doge}; lookup {cat, car, ca,
+  card, cart, dog, doge, dogs, x}. The 6 hits are exactly the
+  inserted words; "ca", "dogs", "x" miss.
+  Tests recursive type definition with self-reference, mutable
+  records, `match … | Some / None` over option, pattern with
+  `(k, v) :: rest` tuple destructuring. 146 baseline programs total.
 - 2026-05-10 Phase 5.1 — count_inversions.ml baseline (count
   inversions of [|8;4;2;1;3;5;7;6|] = 12, via merge-sort). Modified
   merge sort: when right element is taken, accumulate `mid - i + 1`