From b89b0def931ae5558368c24079fbcded9facfb23 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Fri, 8 May 2026 11:00:12 +0000
Subject: [PATCH] =?UTF-8?q?mk:=202x2=20Latin=20square=20=E2=80=94=20small?=
 =?UTF-8?q?=20classic=20FD=20constraint=20demo?=
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Defines latin-2x2 over 4 cells and 4 all-distincto constraints. Enumerates
exactly 2 squares ((1 2)(2 1)) and ((2 1)(1 2)); a corner clue narrows to
one. 3 new tests, 269/269 cumulative.

3x3 (12 squares, the natural showcase) is too slow under naive enumerate-
then-filter — that is the motivating test for Phase 6 arc-consistency.
---
 lib/minikanren/tests/latin.sx | 61 +++++++++++++++++++++++++++++++++++
 plans/minikanren-on-sx.md     |  6 ++++
 2 files changed, 67 insertions(+)
 create mode 100644 lib/minikanren/tests/latin.sx

diff --git a/lib/minikanren/tests/latin.sx b/lib/minikanren/tests/latin.sx
new file mode 100644
index 00000000..8a0afabd
--- /dev/null
+++ b/lib/minikanren/tests/latin.sx
@@ -0,0 +1,61 @@
+;; lib/minikanren/tests/latin.sx — 2x2 Latin square via ino + all-distincto.
+;;
+;; A 2x2 Latin square has 2 distinct fillings:
+;;   ((1 2) (2 1))  and  ((2 1) (1 2)).
+;; The 3x3 version has 12 fillings but takes minutes under naive search;
+;; full CLP(FD) (Phase 6 proper) would handle it in milliseconds.
+
+(define
+  latin-2x2
+  (fn
+    (cells)
+    (let
+      ((c11 (nth cells 0))
+        (c12 (nth cells 1))
+        (c21 (nth cells 2))
+        (c22 (nth cells 3))
+        (dom (list 1 2)))
+      (mk-conj
+        (ino c11 dom)
+        (ino c12 dom)
+        (ino c21 dom)
+        (ino c22 dom)
+        (all-distincto (list c11 c12))
+        (all-distincto (list c21 c22))
+        (all-distincto (list c11 c21))
+        (all-distincto (list c12 c22))))))   ;; col 2
+
+(mk-test
+  "latin-2x2-count"
+  (let
+    ((squares (run* q (fresh (a b c d) (== q (list a b c d)) (latin-2x2 (list a b c d))))))
+    (len squares))
+  2)
+
+(mk-test
+  "latin-2x2-as-set"
+  (let
+    ((squares (run* q (fresh (a b c d) (== q (list a b c d)) (latin-2x2 (list a b c d))))))
+    (and
+      (= (len squares) 2)
+      (and
+        (some
+          (fn (s) (= s (list 1 2 2 1)))
+          squares)
+        (some
+          (fn (s) (= s (list 2 1 1 2)))
+          squares))))
+  true)
+
+(mk-test
+  "latin-2x2-with-clue"
+  (run*
+    q
+    (fresh
+      (a b c d)
+      (== a 1)
+      (== q (list a b c d))
+      (latin-2x2 (list a b c d))))
+  (list (list 1 2 2 1)))
+
+(mk-tests-run!)
diff --git a/plans/minikanren-on-sx.md b/plans/minikanren-on-sx.md
index 117f88b7..82f2c568 100644
--- a/plans/minikanren-on-sx.md
+++ b/plans/minikanren-on-sx.md
@@ -173,6 +173,12 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **2x2 Latin square**: small classic constraint demo using
+  `ino` + 4 `all-distincto` constraints. Enumerates exactly 2 squares
+  (`((1 2)(2 1))` and `((2 1)(1 2))`); a clue (top-left = 1) narrows to one.
+  3 new tests, 269/269 cumulative. Note: 3x3 (12 squares) is the natural
+  showcase but too slow under naive enumerate-then-filter — needs Phase 6
+  arc-consistency.
 - **2026-05-08** — **rembero / assoco / nth-o**: more standard list relations.
   rembero removes the first occurrence (uses `nafc (== a x)` to gate the
   skip clause, so it's well-defined on ground lists). assoco is alist