From 186171fec3d87424b0709ce00fadbbf4f6137161 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Fri, 8 May 2026 11:07:33 +0000
Subject: [PATCH] =?UTF-8?q?mk:=20pythagorean=20triples=20search=20?=
 =?UTF-8?q?=E2=80=94=20intarith=20showcase?=
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Finds all (a, b, c) with a, b, c in [1..10], a <= b, a^2 + b^2 = c^2.
Result: ((3 4 5) (6 8 10)) — the two smallest Pythagorean triples
within the domain.

Demonstrates the enumerate-then-filter pattern:
  (ino a dom) (ino b dom) (ino c dom) — generate
  (lteo-i a b) — symmetry break
  (*o-i a a a-sq) (*o-i b b b-sq) (*o-i c c c-sq) — squares
  (pluso-i a-sq b-sq sum) (== sum c-sq) — Pythagorean equation

288/288 cumulative.
---
 lib/minikanren/tests/pythag.sx | 36 ++++++++++++++++++++++++++++++++++
 plans/minikanren-on-sx.md      |  5 +++++
 2 files changed, 41 insertions(+)
 create mode 100644 lib/minikanren/tests/pythag.sx

diff --git a/lib/minikanren/tests/pythag.sx b/lib/minikanren/tests/pythag.sx
new file mode 100644
index 00000000..c8015ea6
--- /dev/null
+++ b/lib/minikanren/tests/pythag.sx
@@ -0,0 +1,36 @@
+;; lib/minikanren/tests/pythag.sx — Pythagorean triple search.
+;;
+;; Uses ino + intarith goals to find triples (a, b, c) with
+;; a, b, c ∈ [1..N], a ≤ b, a² + b² = c². With intarith escapes
+;; the search runs at host-arithmetic speed.
+
+(define
+  digits-1-10
+  (list
+    1
+    2
+    3
+    4
+    5
+    6
+    7
+    8
+    9
+    10))
+
+(mk-test
+  "pythag-triples-1-to-10"
+  (let
+    ((triples (run* q (fresh (a b c a-sq b-sq sum c-sq) (ino a digits-1-10) (ino b digits-1-10) (ino c digits-1-10) (lteo-i a b) (*o-i a a a-sq) (*o-i b b b-sq) (*o-i c c c-sq) (pluso-i a-sq b-sq sum) (== sum c-sq) (== q (list a b c))))))
+    (and
+      (= (len triples) 2)
+      (and
+        (some
+          (fn (t) (= t (list 3 4 5)))
+          triples)
+        (some
+          (fn (t) (= t (list 6 8 10)))
+          triples))))
+  true)
+
+(mk-tests-run!)
diff --git a/plans/minikanren-on-sx.md b/plans/minikanren-on-sx.md
index 8e58641c..50510316 100644
--- a/plans/minikanren-on-sx.md
+++ b/plans/minikanren-on-sx.md
@@ -173,6 +173,11 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **Pythagorean triples (intarith showcase)**: search for
+  (a, b, c) ∈ [1..10]³, a ≤ b, a² + b² = c² via `ino + lteo-i + *o-i +
+  pluso-i + ==`. Finds exactly `(3 4 5)` and `(6 8 10)`. Demonstrates the
+  enumerate-then-filter pattern with intarith escape into host arithmetic.
+  1 new test, 288/288 cumulative.
 - **2026-05-08** — **intarith.sx — fast ground-only integer arithmetic**:
   pluso-i / minuso-i / *o-i / lto-i / lteo-i / neqo-i wrap host arithmetic
   via `project`. They are not relational like Peano `pluso` (require args