mk: eveno + oddo — Peano parity predicates

eveno: zero, or (s (s m)) when m is even.
oddo:  one, or (s (s m)) when m is odd.

Both run forward (predicate test on a Peano number) and backward
(enumerate even / odd numbers). The two are mutually exclusive — no
number satisfies both.

12 new tests, 359/359 cumulative.

lib/minikanren/peano.sx

@@ -26,6 +26,22 @@
 
 (define lto (fn (a b) (fresh (sa) (succ-of a sa) (lteo sa b))))
 
+(define
+  eveno
+  (fn
+    (n)
+    (conde
+      ((== n :z))
+      ((fresh (m) (== n (list :s (list :s m))) (eveno m))))))
+
+(define
+  oddo
+  (fn
+    (n)
+    (conde
+      ((== n (list :s :z)))
+      ((fresh (m) (== n (list :s (list :s m))) (oddo m))))))
+
 (define
   *o
   (fn

lib/minikanren/tests/parity.sx

@@ -0,0 +1,58 @@
+;; lib/minikanren/tests/parity.sx — eveno + oddo Peano predicates.
+
+(define
+  mk-nat
+  (fn (n) (if (= n 0) :z (list :s (mk-nat (- n 1))))))
+
+(mk-test "eveno-zero" (run* q (eveno :z)) (list (make-symbol "_.0")))
+(mk-test
+  "eveno-2"
+  (run* q (eveno (mk-nat 2)))
+  (list (make-symbol "_.0")))
+(mk-test
+  "eveno-4"
+  (run* q (eveno (mk-nat 4)))
+  (list (make-symbol "_.0")))
+(mk-test "eveno-1-fails" (run* q (eveno (mk-nat 1))) (list))
+(mk-test "eveno-3-fails" (run* q (eveno (mk-nat 3))) (list))
+
+(mk-test
+  "oddo-1"
+  (run* q (oddo (mk-nat 1)))
+  (list (make-symbol "_.0")))
+(mk-test
+  "oddo-3"
+  (run* q (oddo (mk-nat 3)))
+  (list (make-symbol "_.0")))
+(mk-test "oddo-zero-fails" (run* q (oddo :z)) (list))
+(mk-test "oddo-2-fails" (run* q (oddo (mk-nat 2))) (list))
+
+;; Enumerate small evens.
+(mk-test
+  "eveno-enumerates"
+  (run 4 q (eveno q))
+  (list
+    (mk-nat 0)
+    (mk-nat 2)
+    (mk-nat 4)
+    (mk-nat 6)))
+
+;; Enumerate small odds.
+(mk-test
+  "oddo-enumerates"
+  (run 4 q (oddo q))
+  (list
+    (mk-nat 1)
+    (mk-nat 3)
+    (mk-nat 5)
+    (mk-nat 7)))
+
+;; A number is even XOR odd (no overlap).
+(mk-test
+  "even-odd-no-overlap"
+  (run*
+    q
+    (mk-conj (eveno (mk-nat 4)) (oddo (mk-nat 4))))
+  (list))
+
+(mk-tests-run!)

plans/minikanren-on-sx.md

@@ -173,6 +173,10 @@ _(none yet)_
 
 _Newest first._
 
+- **2026-05-08** — **eveno / oddo Peano predicates**: classic miniKanren parity
+  relations. eveno: 0 or successor-of-successor of even; oddo: 1 or
+  successor-of-successor of odd. Both run forward (test) and backward
+  (enumerate). 12 new tests, 359/359 cumulative.
 - **2026-05-08** — **defrel — Prolog-style relation definition macro**:
   `(defrel (NAME ARGS...) (CLAUSE1 ...) (CLAUSE2 ...) ...)` expands to
   `(define NAME (fn (ARGS...) (conde (CLAUSE1 ...) (CLAUSE2 ...) ...)))`.