From d4eb57fa07bf4a46078a7bc42dbf8be32e1ef68e Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Sat, 9 May 2026 21:06:10 +0000
Subject: [PATCH] ocaml: phase 5.1 catalan.ml baseline (Catalan number C(5) =
 42)
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DP recurrence:

  C(0) = 1
  C(n) = sum_{j=0}^{n-1} C(j) * C(n-1-j)

  let catalan n =
    let dp = Array.make (n + 1) 0 in
    dp.(0) <- 1;
    for i = 1 to n do
      for j = 0 to i - 1 do
        dp.(i) <- dp.(i) + dp.(j) * dp.(i - 1 - j)
      done
    done;
    dp.(n)

C(5) = 42 — also the count of distinct binary trees with 5 internal
nodes, balanced paren strings of length 10, monotonic lattice paths,
etc.

106 baseline programs total.
---
 lib/ocaml/baseline/catalan.ml    | 13 +++++++++++++
 lib/ocaml/baseline/expected.json |  1 +
 plans/ocaml-on-sx.md             |  6 ++++++
 3 files changed, 20 insertions(+)
 create mode 100644 lib/ocaml/baseline/catalan.ml

diff --git a/lib/ocaml/baseline/catalan.ml b/lib/ocaml/baseline/catalan.ml
new file mode 100644
index 00000000..b487ca47
--- /dev/null
+++ b/lib/ocaml/baseline/catalan.ml
@@ -0,0 +1,13 @@
+let catalan n =
+  let dp = Array.make (n + 1) 0 in
+  dp.(0) <- 1;
+  for i = 1 to n do
+    for j = 0 to i - 1 do
+      dp.(i) <- dp.(i) + dp.(j) * dp.(i - 1 - j)
+    done
+  done;
+  dp.(n)
+
+;;
+
+catalan 5
diff --git a/lib/ocaml/baseline/expected.json b/lib/ocaml/baseline/expected.json
index 48ce7dd1..7613a491 100644
--- a/lib/ocaml/baseline/expected.json
+++ b/lib/ocaml/baseline/expected.json
@@ -18,6 +18,7 @@
   "bsearch.ml": 7,
   "caesar.ml": 215,
   "calc.ml": 13,
+  "catalan.ml": 42,
   "closures.ml": 315,
   "coin_change.ml": 6,
   "count_change.ml": 406,
diff --git a/plans/ocaml-on-sx.md b/plans/ocaml-on-sx.md
index 410a534f..e9809c3a 100644
--- a/plans/ocaml-on-sx.md
+++ b/plans/ocaml-on-sx.md
@@ -407,6 +407,12 @@ _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 — catalan.ml baseline (Catalan number C(5)
+  via DP recurrence = 42). DP recurrence `C(n) = sum_{j=0}^{n-1}
+  C(j) * C(n-1-j)`. C(5) = 42 — also the count of distinct binary
+  trees with 5 internal nodes, balanced paren strings of length
+  10, etc. Tests nested for-loop over Array with arr.(i) read +
+  write. 106 baseline programs total.
 - 2026-05-09 Phase 5.1 — fizz_classifier.ml baseline (FizzBuzz with
   polymorphic variants, 1..30 weighted score = 540). Two functions:
   classify maps i → ` `FizzBuzz | `Fizz | `Buzz | `Num n``, and score