ocaml: phase 5.1 peano.ml baseline (Peano arithmetic, 5*6 = 30)

Defines unary Peano numerals with two recursive functions for
arithmetic:

  type peano = Zero | Succ of peano

  let rec plus a b = match a with
    | Zero -> b
    | Succ a' -> Succ (plus a' b)

  let rec mul a b = match a with
    | Zero -> Zero
    | Succ a' -> plus b (mul a' b)

mul is defined inductively: mul Zero _ = Zero; mul (Succ a) b =
b + (a * b).

  to_int (mul (from_int 5) (from_int 6)) = 30

The result is a Peano value with 30 nested Succ wrappers; to_int
unrolls them to a host int. Tests recursive ADT with a single-arg
constructor + four mutually-defined recursive functions (no rec/and
needed since each is defined separately).

80 baseline programs total — milestone.

lib/ocaml/baseline/expected.json

@@ -56,6 +56,7 @@
   "paren_depth.ml": 7,
   "pancake_sort.ml": 910,
   "pascal.ml": 252,
+  "peano.ml": 30,
   "pi_leibniz.ml": 314,
   "prefix_sum.ml": 66,
   "pretty_table.ml": 64,

lib/ocaml/baseline/peano.ml

@@ -0,0 +1,21 @@
+type peano = Zero | Succ of peano
+
+let rec to_int p = match p with
+  | Zero -> 0
+  | Succ p' -> 1 + to_int p'
+
+let rec from_int n =
+  if n = 0 then Zero
+  else Succ (from_int (n - 1))
+
+let rec plus a b = match a with
+  | Zero -> b
+  | Succ a' -> Succ (plus a' b)
+
+let rec mul a b = match a with
+  | Zero -> Zero
+  | Succ a' -> plus b (mul a' b)
+
+;;
+
+to_int (mul (from_int 5) (from_int 6))

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 — peano.ml baseline (Peano arithmetic, 5*6 =
+  30). Defines `type peano = Zero | Succ of peano` and four
+  recursive functions: to_int, from_int, plus, mul. Multiplication
+  is defined inductively: `mul Zero _ = Zero; mul (Succ a) b = plus
+  b (mul a b)`. The result of `mul (from_int 5) (from_int 6)` is a
+  Peano number with 30 nested Succ wrappers. Tests recursive ADT
+  with single-arg constructor + recursive function bodies. 80
+  baseline programs total — milestone.
 - 2026-05-09 Phase 5.1 — count_change.ml baseline (number of ways to
   make 50c from [1;2;5;10;25] = 406). Companion to coin_change.ml
   (min coins): instead of minimising, this counts distinct