ocaml: phase 5.1 fraction.ml baseline (rational arithmetic, 4/3 -> num+den=7)

Defines:

  type frac = { num : int; den : int }
  let rec gcd a b = if b = 0 then a else gcd b (a mod b)
  let make n d =                        (* canonicalise: gcd-reduce and
                                           force den > 0 *)
  let add x y = make (x.num * y.den + y.num * x.den) (x.den * y.den)
  let mul x y = make (x.num * y.num) (x.den * y.den)

Test:
  let r = add (make 1 2) (make 1 3) in     (* 5/6 *)
  let s = mul (make 2 3) (make 3 4) in     (* 1/2 *)
  let t = add r s in                       (* 5/6 + 1/2 = 4/3 *)
  t.num + t.den                            (* = 7 *)

Exercises records, recursive gcd, mod, abs, integer division (the
truncate-toward-zero semantics from iter 94 are essential here —
make would diverge from real OCaml's behaviour with float division).
28 baseline programs total.

lib/ocaml/baseline/expected.json

@@ -10,6 +10,7 @@
   "exception_handle.ml": 4,
   "expr_eval.ml": 16,
   "factorial.ml": 3628800,
+  "fraction.ml": 7,
   "frequency.ml": 5,
   "fizzbuzz.ml": 57,
   "list_ops.ml": 30,

lib/ocaml/baseline/fraction.ml

@@ -0,0 +1,20 @@
+type frac = { num : int; den : int }
+
+let rec gcd a b = if b = 0 then a else gcd b (a mod b)
+
+let make n d =
+  let g = gcd (abs n) (abs d) in
+  if d < 0 then { num = -n / g; den = -d / g }
+  else { num = n / g; den = d / g }
+
+let add x y =
+  make (x.num * y.den + y.num * x.den) (x.den * y.den)
+
+let mul x y = make (x.num * y.num) (x.den * y.den)
+
+;;
+
+let r = add (make 1 2) (make 1 3) in
+let s = mul (make 2 3) (make 3 4) in
+let t = add r s in
+t.num + t.den

plans/ocaml-on-sx.md

@@ -407,6 +407,13 @@ _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 — fraction.ml baseline (rational arithmetic
+  via record + gcd canonicalization). Defines `type frac = { num;
+  den }`, `make` that reduces via gcd and forces den > 0, `add` and
+  `mul` constructors. Computes (1/2 + 1/3) + (2/3 * 3/4) = 4/3, sums
+  num + den = 7. Exercises records, recursive gcd, `mod`, `abs`,
+  integer division, and the new `Int.rem`-style truncate-zero
+  division semantics from iteration 94. 28 baseline programs total.
 - 2026-05-09 Phase 6 — Seq module (eager, list-backed) (+4 tests,
   576 total). Real OCaml's Seq is lazy (a thunk producing
   Cons / Nil); ours is just a list, which is adequate for most