From d992788a03b2a627f7dbaf0ebdf83c9de3408267 Mon Sep 17 00:00:00 2001
From: giles <giles.bradshaw@rose-ash.com>
Date: Fri, 8 May 2026 11:49:47 +0000
Subject: [PATCH] =?UTF-8?q?mk:=20even-i=20/=20odd-i=20=E2=80=94=20host-ari?=
 =?UTF-8?q?thmetic=20parity=20goals?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Two-line definitions over project + host even?/odd?. Ground-only — no
relational behaviour, but they pair cleanly with membero for filtered
enumeration:
  (fresh (x) (membero x (list 1 2 3 4 5 6)) (even-i x) (== q x))
    -> (2 4 6)

5 new tests, 416/416 cumulative.
---
 lib/minikanren/intarith.sx       |  8 ++++++++
 lib/minikanren/tests/intarith.sx | 14 ++++++++++++++
 plans/minikanren-on-sx.md        |  1 +
 3 files changed, 23 insertions(+)

diff --git a/lib/minikanren/intarith.sx b/lib/minikanren/intarith.sx
index 1ca9aee2..ed3692a9 100644
--- a/lib/minikanren/intarith.sx
+++ b/lib/minikanren/intarith.sx
@@ -60,3 +60,11 @@
 (define stringo (fn (x) (project (x) (if (string? x) succeed fail))))
 
 (define symbolo (fn (x) (project (x) (if (symbol? x) succeed fail))))
+
+(define
+  even-i
+  (fn (n) (project (n) (if (and (number? n) (even? n)) succeed fail))))
+
+(define
+  odd-i
+  (fn (n) (project (n) (if (and (number? n) (odd? n)) succeed fail))))
diff --git a/lib/minikanren/tests/intarith.sx b/lib/minikanren/tests/intarith.sx
index d81db4c1..baab8fe2 100644
--- a/lib/minikanren/tests/intarith.sx
+++ b/lib/minikanren/tests/intarith.sx
@@ -86,4 +86,18 @@
       (== q x)))
   (list 1 2))
 
+(mk-test "even-i-pos" (run* q (even-i 4)) (list (make-symbol "_.0")))
+
+(mk-test "even-i-neg" (run* q (even-i 5)) (list))
+
+(mk-test "odd-i-pos" (run* q (odd-i 7)) (list (make-symbol "_.0")))
+
+(mk-test "odd-i-neg" (run* q (odd-i 4)) (list))
+
+(mk-test
+  "even-i-filter"
+  (run* q (fresh (x) (membero x (list 1 2 3 4 5 6)) (even-i x) (== q x)))
+  (list 2 4 6))
+
 (mk-tests-run!)
+
diff --git a/plans/minikanren-on-sx.md b/plans/minikanren-on-sx.md
index b040fb45..07f05f2c 100644
--- a/plans/minikanren-on-sx.md
+++ b/plans/minikanren-on-sx.md
@@ -173,6 +173,7 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **even-i / odd-i (intarith)**: ground-only parity goals via project. Composes with membero for filtered enumeration:  -> . 5 new tests, 416/416 cumulative.
 - **2026-05-08** — **selecto**: classic miniKanren "choose an element + rest". Direct base (l = (x . rest)) plus skip-head recurse. Enumerates all (element, rest) splits in run*; runs forward, backward, mid-pipeline. 6 new tests, 411/411 cumulative.
 - **2026-05-08** — **subo (contiguous sublist)**: Two appendos chained — l = front ++ s ++ back. Goal order matters: appendo on the ground l first, so the search is finitary; then constrain front. 7 new tests, 405/405 cumulative.
 - **2026-05-08** — **prefixo + suffixo**: classic appendo-derived sublist relations. (prefixo p l) ≡ p ⊕ ? = l; (suffixo s l) ≡ ? ⊕ s = l. Both enumerate all prefixes/suffixes when given a fresh first arg. 9 new tests, 398/398 cumulative.