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.

lib/ocaml/baseline/expected.json

@@ -140,6 +140,7 @@
   "sum_squares.ml": 385,
   "tree_depth.ml": 4,
   "triangle.ml": 11,
+  "trie.ml": 6,
   "triangle_div.ml": 120,
   "twosum.ml": 5,
   "union_find.ml": 4,

lib/ocaml/baseline/trie.ml

@@ -0,0 +1,36 @@
+type trie = { mutable terminal : bool; mutable children : (char * trie) list }
+
+let make_trie () = { terminal = false; children = [] }
+
+let rec lookup_child cs c =
+  match cs with
+  | [] -> None
+  | (k, v) :: rest -> if k = c then Some v else lookup_child rest c
+
+let rec insert t s i =
+  if i = String.length s then t.terminal <- true
+  else
+    let c = s.[i] in
+    match lookup_child t.children c with
+    | Some child -> insert child s (i + 1)
+    | None ->
+      let nc = make_trie () in
+      t.children <- (c, nc) :: t.children;
+      insert nc s (i + 1)
+
+let rec contains t s i =
+  if i = String.length s then t.terminal
+  else
+    let c = s.[i] in
+    match lookup_child t.children c with
+    | Some child -> contains child s (i + 1)
+    | None -> false
+
+;;
+
+let t = make_trie () in
+List.iter (fun w -> insert t w 0) ["cat"; "car"; "card"; "cart"; "dog"; "doge"];
+let count = ref 0 in
+List.iter (fun w -> if contains t w 0 then count := !count + 1)
+  ["cat"; "car"; "ca"; "card"; "cart"; "dog"; "doge"; "dogs"; "x"];
+!count

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`